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Wang, Nan; Pang, Jingmei; Wang, Jinliang

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

Abstr. Appl. Anal. 2014, Article ID 740256, 8 p. (2014).
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.

Cited in 2 Documents

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations

Keywords:

global stability; multigroup SEIR epidemic model
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\textit{N. Wang} et al., Abstr. Appl. Anal. 2014, Article ID 740256, 8 p. (2014; Zbl 1406.92630)
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