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import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# Parameters
beta = 0.3  # Infection rate
gamma = 0.1  # Recovery rate
v = 0.05  # Vaccination rate

# Initial conditions: S(0), I(0), R(0)
S0 = 990
I0 = 10
R0 = 0
N = S0 + I0 + R0  # Total population

# Time points (days)
t = np.linspace(0, 160, 160)

# The SIR model differential equations
def sir_vaccination(y, t, N, beta, gamma, v):
    S, I, R = y
    dSdt = -beta * S * I / N - v * S
    dIdt = beta * S * I / N - gamma * I
    dRdt = gamma * I + v * S
    return dSdt, dIdt, dRdt

# Initial conditions vector
y0 = S0, I0, R0

# Integrate the SIR equations over the time grid
solution = odeint(sir_vaccination, y0, t, args=(N, beta, gamma, v))
S, I, R = solution.T

# Plot the data
plt.figure(figsize=(10,6))
plt.plot(t, S, 'b', label='Susceptible')
plt.plot(t, I, 'r', label='Infected')
plt.plot(t, R, 'g', label='Recovered')
plt.xlabel('Time (days)')
plt.ylabel('Population')
plt.title('SIR Model with Vaccination')
plt.legend()
plt.grid(True)
plt.show()