Full and partial controllability of the Kermack–McKendrick system with time-varying incidence rates

Abstract

This study contributes to epidemic control literature by introducing a time-varying incidence rate and establishing global controllability of the nonlinear SIR system, offering a practical framework for adaptive control strategies. We derive explicit solutions for partial controllability, demonstrating the feasibility of controlling the infected population, providing guidance for outbreak management. Numerical methods exploiting an algorithmic approach achieve full control, targeting a desired state (Sd, Id). A novel hybrid method integrates analytical solutions with algorithmic optimization, leveraging explicit expressions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies, advancing adaptive management approaches