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

In this paper, we construct a new $SEIR$ epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number $% \mathcal{R}_{0}$ by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number $\mathcal{R}_{0}$ 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 $% \mathcal{R}_{0}.$ 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.