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

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117 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
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1016/0025-5564(85)90038-0

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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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Stability of the endemic equilibrium in epidemic models with subpopulations

Abstract

ASJC Scopus subject areas

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