Nonlinear Optimal Regulation of SIR Epidemic Model via Finite-Horizon SDRE

A Susceptible-Infectious-Recovered (SIR) model is a popular and fundamental epidemiological model often used to assess the efficacy of disease prevention and control measures. SIR disease model, with the implementation of various optimal control methods, is investigated to determine the optimal ways to lessen the effects of an infectious disease. In this research work, a non-linear, closed-loop, finite-horizon, optimal regulation with state-dependent Riccati equation (FH-SDRE) is implemented in an epidemic model called SIR model with vaccination to minimize the infected and susceptible population. Given the nonlinear dynamics of the SIR epidemic model, initially, this method converts the nonlinear equations into a state-dependent coefficient (SDC) matrix, which holds the nonlinearities of the dynamical system. After that, SDRE is solved at every small time instant over a specified finite time period. The core idea here is to utilize an approximate analytical approach that transforms the differential Riccati equation (DRE) into a differential Lyapunov equation (DLE) during every time period. Then, the real-time solution of the DLE at each of these time steps will result in the control law required to achieve the desired system performance. The effectiveness of the FH-SDRE regulation for the SIR model is demonstrated by minimizing the infected and susceptible population within a desired 30-day time period.