GLOBAL STABILITY OF SPATIO-TEMPORAL MODEL WITH QUARANTINE AND VACCINATION - Yaagoub, Zakaria; Sadki, Marya; Allali, Karam (Journal of the Indonesian Mathematical Society, 2024)
In this paper, we suggest a spatio-temporal epidemic model for coronavirus. Our model will be represented by a system of six partial differential non-linear equations that describe the dynamics of susceptible, exposed, infected, quarantined, removed, and vaccinated individuals. We will start the study of this model by presenting some results of the existence and uniqueness to the solution of our suggested model. By using the method of next-generation matrix, we obtain the basic reproduction number. The model has one disease-free equilibrium point and another endemic steady state. The global stability of these steady states is proved by using some Lyapunouv functions. Finally, different numerical simulations are given to confirm our results given in the theoretical part of the paper.