TY - GEN A1 - Belili, Mohamed Cherif A1 - Sahari, Mohamed Lamine A1 - Kebiri, Omar A1 - Zeghdoudi, Halim T1 - Analyzing bifurcations and optimal control strategies in SIRS epidemic models: insights from theory and COVID-19 data T2 - Mathematical and Computational Applications N2 - This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread. KW - flip bifurcation KW - transcritical bifurcation KW - bifurcation curve KW - discrete epidemic model KW - stability KW - numerical simulation KW - optimal control Y1 - 2024 U6 - https://doi.org/10.3390/mca29040069 SN - 2297-8747 VL - 29 IS - 4 PB - MDPI ER -