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

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

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

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References

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Journal of Mathematical Modeling
Volume 14, Issue 2
May 2026
Pages 673-697

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