Stability analysis of a multigroup SEIR epidemic model with general latency distributions. (English) Zbl 1406.92630

Summary: 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 \(\operatorname{Re}_0\) is defined and proved as the role of a threshold; that is, the disease-free equilibrium \(P_0\) is globally asymptotically stable if \(\operatorname{Re}_0 \leq 1\), while an endemic equilibrium \(P^*\) exists uniquely and is globally asymptotically stable if \(\operatorname{Re}_0 > 1\). For the proofs, we apply the classical method of Lyapunov functionals and a recently developed graph-theoretic approach.


92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI


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