Nonlinear Sub-Optimal Control of SIR Infectious Disease Model

The Susceptible-Infectious-Recovered (SIR) disease model is a basic epidemiological framework for analyzing the spread of infectious diseases using various control theories. It plays a vital role in assessing disease control strategies and minimizing the impact of an infectious disease. This paper employs a nonlinear closed-loop infinite-horizon optimal tracking control via state-dependent Riccati equation (IH-SDRE) to the nonlinear SIR model with vaccination, aiming to reduce the number of infected individuals within a desired timeframe. This method, by transforming the nonlinear SIR model into a state-dependent coefficient form, solves the Riccati equation and the vector equation at every time step to determine the control law. The results obtained via MATLAB/Simulink demonstrate that the IH-SDRE minimizes the number of infected populations, reducing it to nearly zero within 30 days of the desired timeframe with an effective vaccination strategy. The findings show the effectiveness of the IH-SDRE as a robust method in the control and mitigation of infectious diseases.