M. E.-B. Keddar - Department of Mathematics and Computer Science, Abdelhamid Ibn Badis Mostaganem University, Algeria.
O. Belhamiti - Department of Mathematics and Computer Science, Abdelhamid Ibn Badis Mostaganem University, Algeria.

This study presents a novel approach to understanding the global dynam-ics of COVID-۱۹ transmission with vaccination based on a discrete-time model. We establish biologically meaningful constraints on the model parameters and prove the existence of a disease-free equilibrium and an endemic equilibrium under these constraints, along with their theoretical stabilities. Furthermore, we identify the most sensitive operational param-eters that have a substantial impact on the transmission of the epidemic. Through numerical simulations, we demonstrate the local stability of the two equilibria, depending on the parameter values. Our findings reveal that the discrete-time model is not only dynamically robust but also more realistic than its continuous counterpart under biologically meaningful con-straints. These results provide a foundation for future research in this area and contribute to our understanding of the global dynamics of COVID-۱۹ transmission.

Discrete-time epidemic model, Euler Scheme, Local stability, Vaccination reproduction number