Stability of the endemic equilibrium in epidemic models with subpopulations

Herbert W. Hethcote; Horst R. Thieme

doi:10.1016/0025-5564(85)90038-0

Stability of the endemic equilibrium in epidemic models with subpopulations

Herbert W. Hethcote
, Horst R. Thieme

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

144 Scopus citations

Abstract

For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.

Original language	English (US)
Pages (from-to)	205-227
Number of pages	23
Journal	Mathematical Biosciences
Volume	75
Issue number	2
DOIs	https://doi.org/10.1016/0025-5564(85)90038-0
State	Published - Aug 1985
Externally published	Yes

ASJC Scopus subject areas

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

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title = "Stability of the endemic equilibrium in epidemic models with subpopulations",

abstract = "For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.",

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N2 - For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.

AB - For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.

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U2 - 10.1016/0025-5564(85)90038-0

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JO - Mathematical Biosciences

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Stability of the endemic equilibrium in epidemic models with subpopulations

Abstract

ASJC Scopus subject areas

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