Global stability analysis of a fractional SVEIR epidemic model

Abstract

Mathematical modeling will allow us to make effective interventions by policy makers and determine a specific program for the country's health managers. In recent years, applications of differential equations of the fractional‐order in biological and epidemic models have been significantly increased. In this paper, we consider a fractional‐order SVEIR model, which represents the interaction of five distinct compartments of people in a community with an epidemic. To verify the well‐posedness of the proposed fractional‐order model, the existence and uniqueness of positive and bounded solutions have been explored. Also, through analyzing the corresponding characteristic equations, the local stability of the disease‐free equilibrium and the endemic equilibrium are discussed. Further, by constructing suitable Lyapunov functions and LaSalle's invariance principle, the asymptotic stability of the different equilibrium points of the system is also investigated. In another part of the article, we investigate the basic reproduction number index corresponding to the model, which provides a good description of the epidemic model's global dynamics. It has been shown that whenever the basic reproduction number of a system is less than unity, the disease‐free equilibrium point is globally asymptotically stable. If indicator is greater than unity, then there exists a unique endemic equilibrium point that is globally asymptotically stable. Moreover, some numerical simulations are included to verify the theoretical achievement. These results provide good evidence for the implications of the theoretical results corresponding to the model.