import matplotlib.pyplot as plt

N = 2500      
beta = 0.3    
gamma = 0.1   
T = 100      
dt = 0.1  
S0, I0, R0 = 2490, 10, 0

t_values = [0]  
S = [S0]       
I = [I0]       
R = [R0]       

for t in range(1, int(T / dt)): 
    s = S[-1]
    i = I[-1]
    r = R[-1]
    
    dS = -beta * s * i / N
    dI = beta * s * i / N - gamma * i
    dR = gamma * i

    S.append(s + dS * dt)
    I.append(i + dI * dt)
    R.append(r + dR * dt)
    t_values.append(t * dt)
    
plt.plot(t_values, S, label='Susceptibles (S)', color='blue')
plt.plot(t_values, I, label='Infectés (I)', color='red')
plt.plot(t_values, R, label='Rétablis (R)', color='green')
plt.xlabel('Temps (jours)')
plt.ylabel('Population')
plt.title('Simulation du Modèle SIR')
plt.legend()
plt.xlim(0, T)
plt.ylim(0, N)
plt.grid()
plt.show()