John Kevin Malagum Padro Syed Fahad Ahmed

Basic susceptible-infected-recovered (SIR) model with scipy.optimize module to find the optimal control strategy.

## import needed Python libraries

import numpy as np

from scipy.integrate import odeint

from scipy.optimize import minimize

# Define the SIR model

def sir_model(y, t, beta, gamma, u):

S, I, R = y

dSdt = -beta * S * I + u

dIdt = beta * S * I - gamma * I

dRdt = gamma * I

return [dSdt, dIdt, dRdt]

# Define the objective function to minimize

def objective(u, t, y0, beta, gamma):

y = odeint(sir_model, y0, t, args=(beta, gamma, u))

I = y[:, 1]

return -I[-1] # maximize the final number of infected individuals

# Define the constraints for the control variable

def constraint(u):

return 1 - u # enforce u

John Kevin Malagum Padro, This code serves as a comprehensive example of how to model and optimize the control of a disease using Python, with a focus on the COVID-19 scenario in the Philippines. It provides a practical implementation that can be used as a starting point for understanding and building more complex disease models. If you have any specific questions or need further clarification on these comments, feel free to ask !