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2009•Journal of BiomathematicsRequires access

Glogal Stability of a SEIR Epidemic Model with Nonmonotone Incidence Rate

Liujuan Chen

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Abstract

In this paper,a SEIR epidemic model with nonmonotone incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infective is getting larger,is investigated.It is shown that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R_0.If R_0≤1 holds,then the disease-free equilibrium is globally stable and the disease dies out.If R_01 holds,then the unique endemic equilibrium is globally stable and the disease persists at an endemic equilibrium state.

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What this paper is about

In this paper,a SEIR epidemic model with nonmonotone incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infective is getting larger,is investigated.It is shown that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R_0.If R_0≤1 holds,then the disease-free equilibrium is globally stable and the disease dies out.If R_01 holds,then the unique endemic equilibrium is globally stable and the disease persists at an endemic equilibrium state.

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Available abstract

In this paper,a SEIR epidemic model with nonmonotone incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infective is getting larger,is investigated.It is shown that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R_0.If R_0≤1 holds,then the disease-free equilibrium is globally stable and the disease dies out.If R_01 holds,then the unique endemic equilibrium is globally stable and the disease persists at an endemic equilibrium state.

Key concepts: Basic reproduction number, Stability (learning theory), Epidemic model, Incidence (geometry), Mathematics, Outcome (game theory), Mathematical economics, Applied mathematics

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