Version 1
: Received: 10 April 2024 / Approved: 10 April 2024 / Online: 10 April 2024 (11:45:15 CEST)
How to cite:
Belili, M.C.; Sahari, M.L.; Kebiri, O.; Zeghdoudi, H. Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data. Preprints2024, 2024040727. https://doi.org/10.20944/preprints202404.0727.v1
Belili, M.C.; Sahari, M.L.; Kebiri, O.; Zeghdoudi, H. Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data. Preprints 2024, 2024040727. https://doi.org/10.20944/preprints202404.0727.v1
Belili, M.C.; Sahari, M.L.; Kebiri, O.; Zeghdoudi, H. Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data. Preprints2024, 2024040727. https://doi.org/10.20944/preprints202404.0727.v1
APA Style
Belili, M.C., Sahari, M.L., Kebiri, O., & Zeghdoudi, H. (2024). Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data. Preprints. https://doi.org/10.20944/preprints202404.0727.v1
Chicago/Turabian Style
Belili, M.C., Omar Kebiri and Halim Zeghdoudi. 2024 "Analyzing Bifurcations and Optimal Control Strategies in SIRS Epidemic Models: Insights from Theory and COVID-19 Data" Preprints. https://doi.org/10.20944/preprints202404.0727.v1
Abstract
Our study essentially concerns the dynamic behavior of an SIRS epidemic model in discrete time. Two equilibrium points are obtained; one is disease-free while the other is endemic. We are interested in the endemic fixed point as well as its asymptotic stability. Depending on the parameters which are estimated using the data from US Department of health and SIRS modelling with optimization, two Flip and Transcritical bifurcations appear. We illustrate their diagrams, as well as their bifurcation curves using the method of Carcasses \cite{carcasses1993determination,carcasses1995singularities} for the Flip bifurcation and by an implicit function deduced from such an equation for the Transcritical bifurcation. We use the scanning of the parametric plane to have a global view of the behavior of the model and to highlight the zones of stability of the existing singularities. A superposition of the bifurcation curves with the parametric plane can show the overlap of the curves with the boundaries of the stability domains, which confirms the smooth running of the simulation and its correspondence with the theory, we finish this article with constrained optimal control applied to infection rate and recruitment rate for an SIRS discrete epidemic model. Pontryagin's maximum principle is used to determine these optimal controls. Finally using COVID-19 data in the USA, we obtain results that demonstrate the effectiveness of the proposed control strategy to mitigate the spread of the pandemic.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
