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=0.38 et guerison gamma=0.14 via SciPy solve_ivp.

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

beta = 0.38
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: 2.71")
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=0.2 via SciPy solve_ivp.

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

beta = 0.43
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: 2.15")
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=0.2 via SciPy solve_ivp.

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

beta = 0.55
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: 2.75")
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=0.54 et guerison gamma=0.16 via SciPy solve_ivp.

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

beta = 0.54
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: 3.38")
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=0.25 via SciPy solve_ivp.

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

beta = 0.68
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: 2.72")
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=0.16 via SciPy solve_ivp.

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

beta = 0.72
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: 4.5")
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=0.14 via SciPy solve_ivp.

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

beta = 0.54
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: 3.86")
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=0.08 via SciPy solve_ivp.

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

beta = 0.23
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: 2.88")
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=0.12 via SciPy solve_ivp.

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

beta = 0.62
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: 5.17")
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=0.25 via SciPy solve_ivp.

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

beta = 0.25
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: 1.0")
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=0.22 via SciPy solve_ivp.

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

beta = 0.53
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: 2.41")
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=0.3 via SciPy solve_ivp.

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

beta = 0.4
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: 1.33")
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=0.08 via SciPy solve_ivp.

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

beta = 0.7
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: 8.75")
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=0.07 via SciPy solve_ivp.

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

beta = 0.44
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: 6.29")
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=0.13 via SciPy solve_ivp.

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

beta = 0.33
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: 2.54")
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=0.19 via SciPy solve_ivp.

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

beta = 0.61
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: 3.21")
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=0.28 via SciPy solve_ivp.

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

beta = 0.69
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: 2.46")
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=0.52 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=0.79 et guerison gamma=0.22 via SciPy solve_ivp.

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

beta = 0.79
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: 3.59")
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=0.26 via SciPy solve_ivp.

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

beta = 0.44
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: 1.69")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.2 et guerison gamma=0.12 via SciPy solve_ivp.

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

beta = 0.2
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: 1.67")
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=0.17 via SciPy solve_ivp.

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

beta = 0.51
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: 3.0")
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=0.18 via SciPy solve_ivp.

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

beta = 0.29
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: 1.61")
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=0.23 via SciPy solve_ivp.

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

beta = 0.48
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: 2.09")
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=0.2 via SciPy solve_ivp.

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

beta = 0.48
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: 2.4")
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=0.24 via SciPy solve_ivp.

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

beta = 0.8
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: 3.33")
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=0.26 via SciPy solve_ivp.

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

beta = 0.42
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: 1.62")
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=0.29 via SciPy solve_ivp.

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

beta = 0.75
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: 2.59")
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=0.41 et guerison gamma=0.13 via SciPy solve_ivp.

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

beta = 0.41
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: 3.15")
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=0.11 via SciPy solve_ivp.

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

beta = 0.67
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: 6.09")
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=0.11 via SciPy solve_ivp.

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

beta = 0.31
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: 2.82")
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=0.22 via SciPy solve_ivp.

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

beta = 0.73
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: 3.32")
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=0.13 via SciPy solve_ivp.

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

beta = 0.42
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: 3.23")
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=0.48 et guerison gamma=0.27 via SciPy solve_ivp.

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

beta = 0.48
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: 1.78")
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=0.1 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=0.72 et guerison gamma=0.08 via SciPy solve_ivp.

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

beta = 0.72
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: 9.0")
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=0.19 via SciPy solve_ivp.

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

beta = 0.25
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: 1.32")
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=0.3 via SciPy solve_ivp.

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

beta = 0.35
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: 1.17")
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=0.25 via SciPy solve_ivp.

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

beta = 0.63
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: 2.52")
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=0.14 via SciPy solve_ivp.

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

beta = 0.54
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: 3.86")
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=0.08 via SciPy solve_ivp.

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

beta = 0.55
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: 6.88")
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=0.34 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=0.34 et guerison gamma=0.24 via SciPy solve_ivp.

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

beta = 0.34
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: 1.42")
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=0.13 via SciPy solve_ivp.

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

beta = 0.52
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: 4.0")
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=0.22 via SciPy solve_ivp.

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

beta = 0.29
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: 1.32")
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=0.21 via SciPy solve_ivp.

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

beta = 0.61
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: 2.9")
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=0.6 et guerison gamma=0.12 via SciPy solve_ivp.

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

beta = 0.6
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: 5.0")
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=0.1 via SciPy solve_ivp.

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

beta = 0.53
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: 5.3")
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=0.17 via SciPy solve_ivp.

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

beta = 0.66
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: 3.88")
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=0.37 et guerison gamma=0.18 via SciPy solve_ivp.

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

beta = 0.37
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: 2.06")
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=0.13 via SciPy solve_ivp.

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

beta = 0.24
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: 1.85")
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=0.17 via SciPy solve_ivp.

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

beta = 0.36
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: 2.12")
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=0.12 via SciPy solve_ivp.

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

beta = 0.58
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: 4.83")
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=0.11 via SciPy solve_ivp.

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

beta = 0.51
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: 4.64")
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=0.24 via SciPy solve_ivp.

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

beta = 0.3
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: 1.25")
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=0.15 via SciPy solve_ivp.

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

beta = 0.44
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: 2.93")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.2 et guerison gamma=0.17 via SciPy solve_ivp.

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

beta = 0.2
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: 1.18")
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=0.27 via SciPy solve_ivp.

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

beta = 0.37
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: 1.37")
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=0.29 via SciPy solve_ivp.

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

beta = 0.39
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: 1.34")
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=0.3 via SciPy solve_ivp.

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

beta = 0.43
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: 1.43")
print("Pics d'infections:", np.max(sol.y[1]))


Instruction: Simuler un modele epidemiologique SIR avec taux de transmission beta=0.2 et guerison gamma=0.28 via SciPy solve_ivp.

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

beta = 0.2
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: 0.71")
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=0.26 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.26
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: 2.6")
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=0.15 via SciPy solve_ivp.

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

beta = 0.56
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: 3.73")
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=0.17 via SciPy solve_ivp.

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

beta = 0.8
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: 4.71")
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=0.21 via SciPy solve_ivp.

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

beta = 0.37
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: 1.76")
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=0.28 via SciPy solve_ivp.

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

beta = 0.79
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: 2.82")
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=0.29 via SciPy solve_ivp.

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

beta = 0.39
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: 1.34")
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=0.28 via SciPy solve_ivp.

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

beta = 0.75
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: 2.68")
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=0.29 via SciPy solve_ivp.

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

beta = 0.65
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: 2.24")
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=0.3 via SciPy solve_ivp.

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

beta = 0.67
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: 2.23")
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=0.27 via SciPy solve_ivp.

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

beta = 0.77
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: 2.85")
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=0.13 via SciPy solve_ivp.

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

beta = 0.69
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: 5.31")
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=0.31 et guerison gamma=0.25 via SciPy solve_ivp.

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

beta = 0.31
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: 1.24")
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=0.16 via SciPy solve_ivp.

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

beta = 0.28
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: 1.75")
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=0.17 via SciPy solve_ivp.

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

beta = 0.63
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: 3.71")
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=0.12 via SciPy solve_ivp.

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

beta = 0.58
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: 4.83")
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=0.2 via SciPy solve_ivp.

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

beta = 0.33
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: 1.65")
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=0.19 via SciPy solve_ivp.

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

beta = 0.8
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: 4.21")
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=0.14 via SciPy solve_ivp.

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

beta = 0.46
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: 3.29")
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=0.1 via SciPy solve_ivp.

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

beta = 0.65
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: 6.5")
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=0.29 via SciPy solve_ivp.

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

beta = 0.47
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: 1.62")
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=0.27 via SciPy solve_ivp.

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

beta = 0.62
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: 2.3")
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=0.15 via SciPy solve_ivp.

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

beta = 0.31
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: 2.07")
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=0.3 et guerison gamma=0.16 via SciPy solve_ivp.

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

beta = 0.3
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: 1.88")
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=0.05 via SciPy solve_ivp.

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

beta = 0.51
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: 10.2")
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=0.11 via SciPy solve_ivp.

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

beta = 0.45
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: 4.09")
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=0.24 via SciPy solve_ivp.

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

beta = 0.68
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: 2.83")
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=0.42 et guerison gamma=0.07 via SciPy solve_ivp.

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

beta = 0.42
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: 6.0")
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=0.09 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=0.41 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.41
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: 4.1")
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=0.22 et guerison gamma=0.12 via SciPy solve_ivp.

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

beta = 0.22
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: 1.83")
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=0.19 via SciPy solve_ivp.

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

beta = 0.46
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: 2.42")
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=0.57 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=0.27 et guerison gamma=0.2 via SciPy solve_ivp.

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

beta = 0.27
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: 1.35")
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=0.17 via SciPy solve_ivp.

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

beta = 0.22
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: 1.29")
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=0.22 via SciPy solve_ivp.

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

beta = 0.5
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: 2.27")
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=0.15 via SciPy solve_ivp.

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

beta = 0.26
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: 1.73")
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=0.16 via SciPy solve_ivp.

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

beta = 0.22
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: 1.38")
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=0.14 via SciPy solve_ivp.

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

beta = 0.47
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: 3.36")
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=0.22 via SciPy solve_ivp.

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

beta = 0.62
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: 2.82")
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=0.57 et guerison gamma=0.12 via SciPy solve_ivp.

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

beta = 0.57
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: 4.75")
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=0.29 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=0.51 et guerison gamma=0.09 via SciPy solve_ivp.

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

beta = 0.51
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: 5.67")
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=0.3 via SciPy solve_ivp.

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

beta = 0.37
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: 1.23")
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=0.07 via SciPy solve_ivp.

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

beta = 0.52
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: 7.43")
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=0.23 via SciPy solve_ivp.

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

beta = 0.38
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: 1.65")
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=0.3 via SciPy solve_ivp.

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

beta = 0.33
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: 1.1")
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=0.46 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=0.72 et guerison gamma=0.07 via SciPy solve_ivp.

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

beta = 0.72
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: 10.29")
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=0.2 via SciPy solve_ivp.

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

beta = 0.43
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: 2.15")
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=0.12 via SciPy solve_ivp.

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

beta = 0.77
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: 6.42")
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=0.21 via SciPy solve_ivp.

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

beta = 0.54
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: 2.57")
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=0.15 via SciPy solve_ivp.

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

beta = 0.55
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: 3.67")
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=0.5 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=0.3 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=0.64 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=0.7 et guerison gamma=0.1 via SciPy solve_ivp.

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

beta = 0.7
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: 7.0")
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=0.14 via SciPy solve_ivp.

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

beta = 0.58
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: 4.14")
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=0.09 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=0.2 et guerison gamma=0.11 via SciPy solve_ivp.

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

beta = 0.2
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: 1.82")
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=0.69 et guerison gamma=0.21 via SciPy solve_ivp.

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

beta = 0.69
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: 3.29")
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=0.06 via SciPy solve_ivp.

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

beta = 0.58
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: 9.67")
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=0.12 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=0.73 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=0.8 et guerison gamma=0.24 via SciPy solve_ivp.

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

beta = 0.8
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: 3.33")
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=0.29 via SciPy solve_ivp.

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

beta = 0.55
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: 1.9")
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=0.16 via SciPy solve_ivp.

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

beta = 0.65
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: 4.06")
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=0.09 via SciPy solve_ivp.

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

beta = 0.66
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: 7.33")
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=0.1 via SciPy solve_ivp.

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

beta = 0.51
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: 5.1")
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=0.33 et guerison gamma=0.07 via SciPy solve_ivp.

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

beta = 0.33
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: 4.71")
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=0.3 via SciPy solve_ivp.

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

beta = 0.72
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: 2.4")
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=0.21 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=0.77 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=0.14 via SciPy solve_ivp.

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

beta = 0.52
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: 3.71")
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=0.19 via SciPy solve_ivp.

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

beta = 0.79
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: 4.16")
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=0.06 via SciPy solve_ivp.

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

beta = 0.77
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: 12.83")
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=0.32 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=0.71 et guerison gamma=0.16 via SciPy solve_ivp.

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

beta = 0.71
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: 4.44")
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=0.24 via SciPy solve_ivp.

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

beta = 0.43
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: 1.79")
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=0.17 via SciPy solve_ivp.

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

beta = 0.76
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: 4.47")
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=0.58 et guerison gamma=0.14 via SciPy solve_ivp.

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

beta = 0.58
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: 4.14")
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=0.21 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=0.64 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=0.61 et guerison gamma=0.18 via SciPy solve_ivp.

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

beta = 0.61
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: 3.39")
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=0.29 via SciPy solve_ivp.

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

beta = 0.45
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: 1.55")
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=0.09 via SciPy solve_ivp.

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

beta = 0.29
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: 3.22")
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=0.28 via SciPy solve_ivp.

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

beta = 0.74
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: 2.64")
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=0.15 via SciPy solve_ivp.

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

beta = 0.47
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: 3.13")
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=0.28 via SciPy solve_ivp.

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

beta = 0.59
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: 2.11")
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=0.46 et guerison gamma=0.21 via SciPy solve_ivp.

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

beta = 0.46
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: 2.19")
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=0.05 via SciPy solve_ivp.

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

beta = 0.66
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: 13.2")
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=0.26 via SciPy solve_ivp.

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

beta = 0.65
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: 2.5")
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=0.1 via SciPy solve_ivp.

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

beta = 0.73
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: 7.3")
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=0.21 via SciPy solve_ivp.

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

beta = 0.31
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: 1.48")
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=0.63 et guerison gamma=0.15 via SciPy solve_ivp.

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

beta = 0.63
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: 4.2")
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=0.28 via SciPy solve_ivp.

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

beta = 0.28
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: 1.0")
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=0.18 via SciPy solve_ivp.

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

beta = 0.69
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: 3.83")
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=0.22 via SciPy solve_ivp.

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

beta = 0.41
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: 1.86")
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=0.22 via SciPy solve_ivp.

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

beta = 0.64
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: 2.91")
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=0.06 via SciPy solve_ivp.

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

beta = 0.76
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: 12.67")
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=0.1 via SciPy solve_ivp.

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

beta = 0.27
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: 2.7")
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=0.25 via SciPy solve_ivp.

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

beta = 0.24
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: 0.96")
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=0.19 via SciPy solve_ivp.

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

beta = 0.49
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: 2.58")
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=0.23 et guerison gamma=0.21 via SciPy solve_ivp.

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

beta = 0.23
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: 1.1")
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=0.13 via SciPy solve_ivp.

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

beta = 0.75
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: 5.77")
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=0.18 via SciPy solve_ivp.

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

beta = 0.26
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: 1.44")
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=0.22 via SciPy solve_ivp.

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

beta = 0.38
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: 1.73")
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=0.16 via SciPy solve_ivp.

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

beta = 0.29
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: 1.81")
print("Pics d'infections:", np.max(sol.y[1]))