Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.22 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.22
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.46 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.46
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.75")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.4 et guerison gamma=0.2 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.4
gamma = 0.2

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.24 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.24
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.92")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.3 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.3
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.33")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.75 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.75
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.41")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.11")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.24 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.24
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.14")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.22 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.22
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.37 et guerison gamma=0.23 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.37
gamma = 0.23

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.61")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.5 et guerison gamma=0.19 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.5
gamma = 0.19

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.63")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.72 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.72
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.57")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.44 et guerison gamma=0.29 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.44
gamma = 0.29

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.52")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.21 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.21
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.75")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.54 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.54
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 7.71")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.5 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.5
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 10.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.59 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.59
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.54")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.72 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.72
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.63 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.63
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.73")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.66 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.66
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.36")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.43 et guerison gamma=0.29 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.43
gamma = 0.29

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.48")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.65 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.65
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.95")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.72 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.72
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.49 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.49
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.8")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.31 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.31
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.19")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.29 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.29
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.16")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.73 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.73
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.81")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.55 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.55
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.12")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.63 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.63
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.71")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.77 et guerison gamma=0.15 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.77
gamma = 0.15

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.13")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.33 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.33
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.3")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.79 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.79
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.17")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.65 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.65
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.1")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.39 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.39
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.48 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.48
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.71")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.56 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.56
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.56 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.56
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.31")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.32 et guerison gamma=0.15 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.32
gamma = 0.15

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.13")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.25")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.21 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.21
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.84")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.59 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.59
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.28")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.35 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.35
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.94")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.77 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.77
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.21")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.41 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.41
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.28")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.43")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.4 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.4
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.86")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.29 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.29
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.21")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.25 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.25
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.04")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.42 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.42
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.35 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.35
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.18")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.54 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.54
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.5 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.5
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.27 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.27
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.45")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.96")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.48 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.48
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.37 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.37
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.08")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.2")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.7 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.7
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 10.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.31 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.31
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.11")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.44")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.08")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 14.8")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.49 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.49
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.23")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.28 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.28
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.93")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.46 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.46
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.18")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.49 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.49
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.75")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.8 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.8
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 13.33")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.78")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.17")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.37 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.37
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.19 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.19

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.26")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.43 et guerison gamma=0.17 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.43
gamma = 0.17

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.53")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.23 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.23
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.77")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.66 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.66
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.75")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.73 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.73
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.21")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.5 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.5
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.85")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.45 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.45
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.5")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.5")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.25 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.25
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.27")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.52 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.52
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.93")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.25 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.25
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.14")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.29 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.29

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.9")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.32 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.32
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.64 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.64
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.82")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.71 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.71
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.84")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.36 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.36
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.2")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.58 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.58
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.23")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.43")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.41 et guerison gamma=0.16 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.41
gamma = 0.16

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.56")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.27 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.27
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.38")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.73 et guerison gamma=0.2 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.73
gamma = 0.2

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.65")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.32 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.32
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.57 et guerison gamma=0.2 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.57
gamma = 0.2

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.85")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.61 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.61
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.18")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.71 et guerison gamma=0.19 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.71
gamma = 0.19

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.74")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.24 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.24
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.09")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.85")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.73 et guerison gamma=0.23 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.73
gamma = 0.23

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.17")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.23 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.23

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.96")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.79 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.79
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.88")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.51 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.51
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 7.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.28 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.28
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.35 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.35
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.92")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.23 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.23
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.82")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.25 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.25
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.93")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.55 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.55
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.4 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.4
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.64")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.69 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.69
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.75")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.6 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.6
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.4")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.37 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.37
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.08")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.72 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.72
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.55")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.64 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.64
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 10.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.67 et guerison gamma=0.17 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.67
gamma = 0.17

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.94")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.29 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.29
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.8")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.07")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.57 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.57
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.11")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.59 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.59
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.54")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.3 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.3
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.78")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.54 et guerison gamma=0.06 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.54
gamma = 0.06

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.37 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.37
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.36")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.21 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.21
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.84")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.44 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.44
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.14")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.39 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.39
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.55")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.75 et guerison gamma=0.18 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.75
gamma = 0.18

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.17")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.63 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.63
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.25")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.52 et guerison gamma=0.23 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.52
gamma = 0.23

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.26")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.52 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.52
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.48")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.4 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.4
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.82")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.73 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.73
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.92")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.45 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.45
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.14")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.96")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.69 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.69
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.9")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.45 et guerison gamma=0.17 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.45
gamma = 0.17

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.65")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.41 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.41
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.73")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.72 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.72
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.43")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.67 et guerison gamma=0.29 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.67
gamma = 0.29

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.31")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.96")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.5 et guerison gamma=0.16 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.5
gamma = 0.16

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.12")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.56 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.56
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 11.2")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.34 et guerison gamma=0.12 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.34
gamma = 0.12

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.83")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.47 et guerison gamma=0.17 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.47
gamma = 0.17

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.76")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.61 et guerison gamma=0.23 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.61
gamma = 0.23

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.65")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.64 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.64
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.62 et guerison gamma=0.29 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.62
gamma = 0.29

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.14")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.41 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.41
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.86")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.39 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.39
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.33")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.54 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.54
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.93")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.41 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.41
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.12")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.67 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.67
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.57")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.49 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.49
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.44")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.3 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.3
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.51 et guerison gamma=0.15 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.51
gamma = 0.15

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.4")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.57 et guerison gamma=0.17 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.57
gamma = 0.17

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.35")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.58 et guerison gamma=0.22 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.58
gamma = 0.22

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.64")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.43")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.57 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.57
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.38")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.47 et guerison gamma=0.1 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.47
gamma = 0.1

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.7")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.58 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.58
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.27")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.68 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.68
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.71")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.31 et guerison gamma=0.05 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.31
gamma = 0.05

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.2")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.27 et guerison gamma=0.27 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.27
gamma = 0.27

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.0")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.54 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.54
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.25")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.48 et guerison gamma=0.25 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.48
gamma = 0.25

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.92")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.08")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.59 et guerison gamma=0.16 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.59
gamma = 0.16

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.69")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.24")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.27 et guerison gamma=0.24 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.27
gamma = 0.24

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.13")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.51 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.51
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 6.38")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.51 et guerison gamma=0.26 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.51
gamma = 0.26

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.96")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.2 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.2

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.7")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.57 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.57
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.04")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.69 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.69
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.3")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.74 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.74
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 9.25")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.26 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.26
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.89")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.44 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.44
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.89")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.76 et guerison gamma=0.3 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.76
gamma = 0.3

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.53")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.67 et guerison gamma=0.14 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.67
gamma = 0.14

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.79")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.22 et guerison gamma=0.28 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.22
gamma = 0.28

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 0.79")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.31 et guerison gamma=0.16 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.31
gamma = 0.16

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.94")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.39 et guerison gamma=0.08 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.39
gamma = 0.08

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.88")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.21 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.21
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.33")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.65 et guerison gamma=0.19 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.65
gamma = 0.19

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.42")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.53 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.53
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 2.52")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.21 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.21
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.62")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.56 et guerison gamma=0.11 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.56
gamma = 0.11

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 5.09")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.78 et guerison gamma=0.09 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.78
gamma = 0.09

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 8.67")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.3 et guerison gamma=0.07 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.3
gamma = 0.07

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 4.29")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.64 et guerison gamma=0.19 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.64
gamma = 0.19

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.37")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.25 et guerison gamma=0.13 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.25
gamma = 0.13

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 1.92")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.65 et guerison gamma=0.21 via SciPy solve_ivp.

Output:
import numpy as np
from scipy.integrate import solve_ivp

beta = 0.65
gamma = 0.21

def sir(t, y):
    S, I, R = y
    N = S + I + R
    return [-beta*S*I/N, beta*S*I/N - gamma*I, gamma*I]

t_span = (0, 100)
y0 = [999, 1, 0]
sol = solve_ivp(sir, t_span, y0, t_eval=np.linspace(0, 100, 100))

print(f"Taux R0 calculé: 3.1")
print("Pics d'infections:", np.max(sol.y[1]))