Global analysis of an epidemic model with nonmonotone incidence rate

Dongmei Xiao; Shigui Ruan

doi:10.1016/j.mbs.2006.09.025

Global analysis of an epidemic model with nonmonotone incidence rate

Dongmei Xiao, Shigui Ruan

Mathematics

Research output: Contribution to journal › Article › peer-review

306 Scopus citations

Abstract

In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero as time evolves or the disease persists.

Original language	English (US)
Pages (from-to)	419-429
Number of pages	11
Journal	Mathematical Biosciences
Volume	208
Issue number	2
DOIs	https://doi.org/10.1016/j.mbs.2006.09.025
State	Published - Aug 2007

Keywords

Epidemic
Global stability
Nonlinear incidence
Psychological effect

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1016/j.mbs.2006.09.025

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abstract = "In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero as time evolves or the disease persists.",

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AB - In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero as time evolves or the disease persists.

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KW - Global stability

KW - Nonlinear incidence

KW - Psychological effect

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Global analysis of an epidemic model with nonmonotone incidence rate

Abstract

Keywords

ASJC Scopus subject areas

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