SIR Epidemic Control Using a 2DoF IMC-PID with Filter Control Strategy

The COVID-19 pandemic has given rise to many significant research activities, among these a resurgence of the use of control-oriented approaches for modeling and controlling epidemics. An examination of a SIR (Susceptible-Infectious-Recovered) dynamic model under endemic conditions using Internal Model Control (IMC) shows that a two-degree-of-freedom (2DoF) PID with filter structure is a natural solution for understanding how to manage a pandemic, with model-based IMC-PID tuning being extremely effective when evaluated on a first-principles, nonlinear plant model. Dynamic modeling (nonlinear and linearized), PID controller design, and closed-loop evaluation (under conditions that include vaccination and the loss of immunity/potential for re-infection) are presented, with the results demonstrating the deep insights that can be gained from simple models and control policies. Computational models as presented in this work could be used to inform the actions of governments and individuals.