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

El Mahjour, Hamza; Lahrouz, Aadil; Zakary, Omar; Redouane, Mariam

doi:10.22124/jmm.2025.31390.2818

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

Articles in Press

Document Type : Research Article

Authors

¹ MASI research Team Department of Information Systems and Communication ENSAT, Abdelmalek Esaadi University, Morocco

² LAM research laboratory Department of Mathematics FSTT, Abdelmalek Essaadi University

³ Statistics and Modelling research team Department of Mathematics FSBM, University of Hassan II

10.22124/jmm.2025.31390.2818

Abstract

This study contributes to epidemic control literature by introducing a time-varying inci-
dence 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, pro-
viding 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 expres-
sions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies,
advancing adaptive management approaches

Keywords