SIR with Sage

Very simple implementation of the SIR epidemic model using Sage
mathematical framework.

# Infected IInit = 1 # Susceptible SInit = N - IInit # Resistant RInit = 0 # Transmission rate betaInit = 0.5 # Transmission rate attenuation delta = 0.01 # Recovery rate gamma = 0.1 # Population size N = 10000 # End time tMax = 100 # Number of points points = 1000 # Standard SIR model def ODE_RHS(t, Y): (S, I, R, beta) = Y dS = - beta * S * I / N dI = beta * S * I / N - gamma * I dR = gamma * I dbeta = - beta * delta return (dS, dI, dR, dbeta) # Set up numerical solution of ODE solver = ode_solver(function = ODE_RHS, y_0 = (SInit, IInit, RInit, betaInit), t_span = (0, tMax), algorithm = 'rk8pd') # Numerically solve solver.ode_solve(num_points = points) # Plot solution show(plot(solver.interpolate_solution(i = 0), 0, tMax, legend_label = 'S(t)', color = 'green') + plot(solver.interpolate_solution(i = 1), 0, tMax, legend_label = 'I(t)', color = 'red') + plot(solver.interpolate_solution(i = 2), 0, tMax, legend_label = 'R(t)', color = 'blue'))

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Result: