Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.35 et guerison gamma=0.25 via SciPy solve_ivp.

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

beta = 0.35
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: 1.4")
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=0.12 via SciPy solve_ivp.

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

beta = 0.55
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: 4.58")
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=0.09 via SciPy solve_ivp.

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

beta = 0.46
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: 5.11")
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=0.09 via SciPy solve_ivp.

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

beta = 0.28
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: 3.11")
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=0.05 via SciPy solve_ivp.

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

beta = 0.37
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: 7.4")
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=0.12 via SciPy solve_ivp.

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

beta = 0.33
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: 2.75")
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=0.78 et guerison gamma=0.19 via SciPy solve_ivp.

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

beta = 0.78
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: 4.11")
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=0.06 via SciPy solve_ivp.

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

beta = 0.55
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: 9.17")
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=0.21 via SciPy solve_ivp.

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

beta = 0.74
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: 3.52")
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=0.25 via SciPy solve_ivp.

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

beta = 0.35
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: 1.4")
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=0.14 via SciPy solve_ivp.

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

beta = 0.75
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: 5.36")
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=0.22 via SciPy solve_ivp.

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

beta = 0.3
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: 1.36")
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=0.25 via SciPy solve_ivp.

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

beta = 0.22
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: 0.88")
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=0.17 via SciPy solve_ivp.

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

beta = 0.55
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: 3.24")
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=0.25 via SciPy solve_ivp.

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

beta = 0.65
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: 2.6")
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=0.1 via SciPy solve_ivp.

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

beta = 0.59
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: 5.9")
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=0.23 via SciPy solve_ivp.

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

beta = 0.49
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: 2.13")
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=0.19 via SciPy solve_ivp.

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

beta = 0.27
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: 1.42")
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=0.24 via SciPy solve_ivp.

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

beta = 0.4
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: 1.67")
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=0.25 via SciPy solve_ivp.

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

beta = 0.33
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: 1.32")
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=0.2 via SciPy solve_ivp.

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

beta = 0.3
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: 1.5")
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=0.2 via SciPy solve_ivp.

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

beta = 0.79
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: 3.95")
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=0.14 via SciPy solve_ivp.

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

beta = 0.3
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: 2.14")
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=0.2 via SciPy solve_ivp.

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

beta = 0.44
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: 2.2")
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=0.25 via SciPy solve_ivp.

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

beta = 0.44
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: 1.76")
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=0.26 via SciPy solve_ivp.

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

beta = 0.6
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: 2.31")
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=0.18 via SciPy solve_ivp.

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

beta = 0.33
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: 1.83")
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=0.26 via SciPy solve_ivp.

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

beta = 0.57
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: 2.19")
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=0.23 via SciPy solve_ivp.

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

beta = 0.72
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: 3.13")
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=0.12 via SciPy solve_ivp.

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

beta = 0.5
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: 4.17")
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=0.2 via SciPy solve_ivp.

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

beta = 0.34
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: 1.7")
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=0.26 via SciPy solve_ivp.

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

beta = 0.22
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: 0.85")
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=0.27 via SciPy solve_ivp.

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

beta = 0.54
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: 2.0")
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=0.19 via SciPy solve_ivp.

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

beta = 0.76
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: 4.0")
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=0.15 via SciPy solve_ivp.

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

beta = 0.57
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: 3.8")
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=0.23 via SciPy solve_ivp.

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

beta = 0.63
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: 2.74")
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=0.2 via SciPy solve_ivp.

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

beta = 0.7
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: 3.5")
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=0.19 via SciPy solve_ivp.

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

beta = 0.35
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: 1.84")
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=0.54 et guerison gamma=0.23 via SciPy solve_ivp.

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

beta = 0.54
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: 2.35")
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=0.13 via SciPy solve_ivp.

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

beta = 0.45
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: 3.46")
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=0.16 via SciPy solve_ivp.

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

beta = 0.68
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: 4.25")
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=0.22 via SciPy solve_ivp.

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

beta = 0.32
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: 1.45")
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=0.77 et guerison gamma=0.22 via SciPy solve_ivp.

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

beta = 0.77
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: 3.5")
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=0.09 via SciPy solve_ivp.

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

beta = 0.52
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: 5.78")
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=0.13 via SciPy solve_ivp.

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

beta = 0.71
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: 5.46")
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=0.23 via SciPy solve_ivp.

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

beta = 0.77
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: 3.35")
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=0.21 via SciPy solve_ivp.

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

beta = 0.66
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: 3.14")
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=0.17 via SciPy solve_ivp.

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

beta = 0.55
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: 3.24")
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=0.21 via SciPy solve_ivp.

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

beta = 0.47
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: 2.24")
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=0.4 et guerison gamma=0.27 via SciPy solve_ivp.

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

beta = 0.4
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: 1.48")
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=0.19 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=0.76 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=0.75 et guerison gamma=0.3 via SciPy solve_ivp.

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

beta = 0.75
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: 2.5")
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=0.23 via SciPy solve_ivp.

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

beta = 0.77
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: 3.35")
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=0.18 via SciPy solve_ivp.

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

beta = 0.5
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: 2.78")
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=0.55 et guerison gamma=0.21 via SciPy solve_ivp.

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

beta = 0.55
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: 2.62")
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=0.24 via SciPy solve_ivp.

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

beta = 0.6
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: 2.5")
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=0.27 via SciPy solve_ivp.

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

beta = 0.21
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: 0.78")
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=0.2 via SciPy solve_ivp.

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

beta = 0.61
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: 3.05")
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=0.13 via SciPy solve_ivp.

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

beta = 0.23
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: 1.77")
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=0.23 via SciPy solve_ivp.

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

beta = 0.3
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: 1.3")
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=0.13 via SciPy solve_ivp.

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

beta = 0.43
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: 3.31")
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=0.1 via SciPy solve_ivp.

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

beta = 0.5
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: 5.0")
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=0.27 via SciPy solve_ivp.

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

beta = 0.28
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: 1.04")
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=0.48 et guerison gamma=0.15 via SciPy solve_ivp.

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

beta = 0.48
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: 3.2")
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=0.22 via SciPy solve_ivp.

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

beta = 0.48
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: 2.18")
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=0.07 via SciPy solve_ivp.

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

beta = 0.74
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: 10.57")
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=0.38 et guerison gamma=0.12 via SciPy solve_ivp.

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

beta = 0.38
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: 3.17")
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=0.11 via SciPy solve_ivp.

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

beta = 0.77
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: 7.0")
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=0.75 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.75
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: 7.5")
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=0.28 via SciPy solve_ivp.

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

beta = 0.46
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: 1.64")
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=0.15 via SciPy solve_ivp.

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

beta = 0.54
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: 3.6")
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=0.29 via SciPy solve_ivp.

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

beta = 0.34
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: 1.17")
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=0.29 via SciPy solve_ivp.

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

beta = 0.69
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: 2.38")
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=0.25 via SciPy solve_ivp.

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

beta = 0.72
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: 2.88")
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=0.1 via SciPy solve_ivp.

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

beta = 0.71
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: 7.1")
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=0.25 via SciPy solve_ivp.

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

beta = 0.32
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: 1.28")
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=0.12 via SciPy solve_ivp.

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

beta = 0.45
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: 3.75")
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=0.19 via SciPy solve_ivp.

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

beta = 0.78
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: 4.11")
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=0.08 via SciPy solve_ivp.

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

beta = 0.61
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: 7.62")
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=0.13 via SciPy solve_ivp.

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

beta = 0.66
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: 5.08")
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=0.07 via SciPy solve_ivp.

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

beta = 0.22
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: 3.14")
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=0.24 via SciPy solve_ivp.

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

beta = 0.49
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: 2.04")
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=0.29 via SciPy solve_ivp.

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

beta = 0.42
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: 1.45")
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=0.06 via SciPy solve_ivp.

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

beta = 0.61
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: 10.17")
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=0.14 via SciPy solve_ivp.

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

beta = 0.33
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: 2.36")
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=0.28 via SciPy solve_ivp.

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

beta = 0.64
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: 2.29")
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=0.29 via SciPy solve_ivp.

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

beta = 0.46
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: 1.59")
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=0.24 via SciPy solve_ivp.

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

beta = 0.48
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: 2.0")
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=0.07 via SciPy solve_ivp.

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

beta = 0.73
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: 10.43")
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=0.07 via SciPy solve_ivp.

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

beta = 0.21
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: 3.0")
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=0.22 via SciPy solve_ivp.

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

beta = 0.6
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: 2.73")
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=0.1 via SciPy solve_ivp.

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

beta = 0.44
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: 4.4")
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=0.26 via SciPy solve_ivp.

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

beta = 0.45
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: 1.73")
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=0.11 via SciPy solve_ivp.

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

beta = 0.49
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: 4.45")
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=0.23 via SciPy solve_ivp.

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

beta = 0.59
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: 2.57")
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=0.14 via SciPy solve_ivp.

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

beta = 0.7
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: 5.0")
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=0.13 via SciPy solve_ivp.

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

beta = 0.35
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: 2.69")
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=0.12 via SciPy solve_ivp.

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

beta = 0.23
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: 1.92")
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=0.3 via SciPy solve_ivp.

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

beta = 0.52
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: 1.73")
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=0.76 et guerison gamma=0.18 via SciPy solve_ivp.

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

beta = 0.76
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: 4.22")
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=0.29 via SciPy solve_ivp.

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

beta = 0.21
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: 0.72")
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=0.29 via SciPy solve_ivp.

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

beta = 0.41
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: 1.41")
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=0.06 via SciPy solve_ivp.

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

beta = 0.37
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: 6.17")
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=0.38 et guerison gamma=0.09 via SciPy solve_ivp.

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

beta = 0.38
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: 4.22")
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=0.09 via SciPy solve_ivp.

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

beta = 0.62
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: 6.89")
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=0.05 via SciPy solve_ivp.

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

beta = 0.72
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: 14.4")
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=0.27 via SciPy solve_ivp.

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

beta = 0.31
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: 1.15")
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=0.18 via SciPy solve_ivp.

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

beta = 0.64
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: 3.56")
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=0.05 via SciPy solve_ivp.

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

beta = 0.43
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: 8.6")
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=0.18 via SciPy solve_ivp.

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

beta = 0.67
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: 3.72")
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=0.23 et guerison gamma=0.14 via SciPy solve_ivp.

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

beta = 0.23
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: 1.64")
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=0.22 via SciPy solve_ivp.

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

beta = 0.44
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: 2.0")
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=0.09 via SciPy solve_ivp.

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

beta = 0.59
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: 6.56")
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=0.12 via SciPy solve_ivp.

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

beta = 0.46
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: 3.83")
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=0.28 via SciPy solve_ivp.

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

beta = 0.37
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: 1.32")
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=0.06 via SciPy solve_ivp.

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

beta = 0.51
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: 8.5")
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=0.25 via SciPy solve_ivp.

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

beta = 0.3
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: 1.2")
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=0.07 via SciPy solve_ivp.

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

beta = 0.45
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: 6.43")
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=0.17 via SciPy solve_ivp.

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

beta = 0.46
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: 2.71")
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=0.21 via SciPy solve_ivp.

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

beta = 0.73
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: 3.48")
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=0.09 via SciPy solve_ivp.

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

beta = 0.62
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: 6.89")
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=0.2 via SciPy solve_ivp.

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

beta = 0.21
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: 1.05")
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=0.27 et guerison gamma=0.06 via SciPy solve_ivp.

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

beta = 0.27
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: 4.5")
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=0.23 via SciPy solve_ivp.

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

beta = 0.56
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: 2.43")
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=0.12 via SciPy solve_ivp.

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

beta = 0.24
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: 2.0")
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=0.13 via SciPy solve_ivp.

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

beta = 0.55
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: 4.23")
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=0.66 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.66
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: 6.6")
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=0.3 via SciPy solve_ivp.

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

beta = 0.53
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: 1.77")
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=0.15 via SciPy solve_ivp.

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

beta = 0.33
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: 2.2")
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=0.22 via SciPy solve_ivp.

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

beta = 0.33
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: 1.5")
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=0.26 via SciPy solve_ivp.

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

beta = 0.74
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: 2.85")
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=0.1 via SciPy solve_ivp.

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

beta = 0.42
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: 4.2")
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=0.12 via SciPy solve_ivp.

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

beta = 0.64
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: 5.33")
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=0.22 via SciPy solve_ivp.

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

beta = 0.43
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: 1.95")
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=0.22 via SciPy solve_ivp.

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

beta = 0.69
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: 3.14")
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=0.15 via SciPy solve_ivp.

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

beta = 0.33
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: 2.2")
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=0.5 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.5
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: 5.0")
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=0.25 via SciPy solve_ivp.

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

beta = 0.59
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: 2.36")
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=0.61 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=0.29 via SciPy solve_ivp.

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

beta = 0.71
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: 2.45")
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=0.3 via SciPy solve_ivp.

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

beta = 0.22
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: 0.73")
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=0.17 via SciPy solve_ivp.

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

beta = 0.32
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: 1.88")
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=0.2 via SciPy solve_ivp.

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

beta = 0.34
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: 1.7")
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=0.21 via SciPy solve_ivp.

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

beta = 0.73
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: 3.48")
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=0.11 via SciPy solve_ivp.

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

beta = 0.71
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: 6.45")
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=0.21 via SciPy solve_ivp.

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

beta = 0.48
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: 2.29")
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=0.08 via SciPy solve_ivp.

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

beta = 0.45
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: 5.62")
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=0.17 via SciPy solve_ivp.

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

beta = 0.5
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: 2.94")
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=0.69 et guerison gamma=0.15 via SciPy solve_ivp.

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

beta = 0.69
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: 4.6")
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=0.26 via SciPy solve_ivp.

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

beta = 0.48
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: 1.85")
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=0.11 via SciPy solve_ivp.

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

beta = 0.26
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: 2.36")
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=0.28 via SciPy solve_ivp.

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

beta = 0.33
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: 1.18")
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=0.08 via SciPy solve_ivp.

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

beta = 0.44
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: 5.5")
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=0.09 via SciPy solve_ivp.

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

beta = 0.79
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: 8.78")
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=0.19 via SciPy solve_ivp.

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

beta = 0.52
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: 2.74")
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=0.29 via SciPy solve_ivp.

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

beta = 0.4
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: 1.38")
print("Pics d'infections:", np.max(sol.y[1]))