University of Tabriz Computational Methods for Differential Equations 2345-3982 13 2 2025 03 01 $SEI_aI_sQRS$ epidemic model for COVID-19 by using compartmental analysis and numerical simulation 592 607 18301 10.22034/cmde.2024.58656.2482 EN Hossein Gholami Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Morteza Gachpazan Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Majid Erfanian Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran. Journal Article 2023 09 29 In this paper, we developed a $SEI_aI_sQRS$ epidemic model for COVID-19 by using compartmental analysis. In this article, the dynamics of COVID-19 are divided into six compartments: susceptible, exposed, asymptomatically infected, symptomatically infected, quarantined, and recovered. The positivity and boundedness of the solutions have been proven. We calculated the basic reproduction number for our model and found both disease-free and endemic equilibria. It is shown that the disease-free equilibrium is globally asymptotically stable. We explained under what conditions, the endemic equilibrium point is locally asymptotically stable. Additionally, the center manifold theorem is applied to examine whether our model undergoes a backward bifurcation at $R_0 = 1$ or not. To finish, we have confirmed our theoretical results by numerical simulation https://cmde.tabrizu.ac.ir/article_18301_f8b05b2620ad528c45780f42406ee2ce.pdf