University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 Full and partial controllability of the Kermack-Mckendrick system with time- varying incidence rates 673 697 9295 10.22124/jmm.2025.31390.2818 EN Hamza El Mahjour MASI research Team Department of Information Systems and Communication ENSAT, Abdelmalek Esaadi University, Morocco Aadil Lahrouz LAM research laboratory Department of Mathematics FSTT, Abdelmalek Essaadi University Omar Zakary Statistics and Modelling research team Department of Mathematics FSBM, University of Hassan II Mariam Redouane LAM research laboratory Department of Mathematics FSTT, Abdelmalek Essaadi University Journal Article 2025 08 12 This study contributes to epidemic control literature by introducing a time-varying inci-<br />dence rate and establishing global controllability of the nonlinear SIR system, offering a<br />practical framework for adaptive control strategies. We derive explicit solutions for partial<br />controllability, demonstrating the feasibility of controlling the infected population, pro-<br />viding guidance for outbreak management. Numerical methods exploiting an algorithmic<br />approach achieve full control, targeting a desired state (Sd, Id). A novel hybrid method<br />integrates analytical solutions with algorithmic optimization, leveraging explicit expres-<br />sions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies,<br />advancing adaptive management approaches https://jmm.guilan.ac.ir/article_9295_fd6f0670afa9641d22cff7f55adf61dd.pdf