Mathematical analysis of local and global dynamics of a new epidemic model

Abstract

In this paper, we construct a new SEIR epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number R0 by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behaviour according to whether the basic reproduction number R0 is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to R0. Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.