Stability Analysis of a Multigroup SEIR Epidemic Model with General Latency Distributions

Abstract

The global stability of a multigroup SEIR epidemic model with general latency distribution and general incidence rate is investigated. Under the given assumptions, the basic reproduction number ${\Re }_0$ is defined and proved as the role of a threshold; that is, the disease-free equilibrium $P_0$ is globally asymptotically stable if ${\Re }_0\le 1$, while an endemic equilibrium $P^{*}$ exists uniquely and is globally asymptotically stable if ${\Re }_0>1$. For the proofs, we apply the classical method of Lyapunov functionals and a recently developed graph-theoretic approach.