Global stability of a two-stage epidemic model with generalized non-linear incidence

S. M. Moghadas; A. B. Gumel

doi:10.1016/S0378-4754(02)00002-2

Global stability of a two-stage epidemic model with generalized non-linear incidence

S. M. Moghadas, A. B. Gumel

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

50 Scopus citations

Abstract

A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated) provided a certain threshold R₀ (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for R₀ > 1.

Original language	English (US)
Pages (from-to)	107-118
Number of pages	12
Journal	Mathematics and Computers in Simulation
Volume	60
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4754(02)00002-2
State	Published - Jul 15 2002
Externally published	Yes

Keywords

Equilibria
Multi-stage infection
Non-linear incidence
Stability

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)
Numerical Analysis
Modeling and Simulation
Applied Mathematics

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10.1016/S0378-4754(02)00002-2

Cite this

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title = "Global stability of a two-stage epidemic model with generalized non-linear incidence",

abstract = "A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated) provided a certain threshold R0 (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for R0 > 1.",

keywords = "Equilibria, Multi-stage infection, Non-linear incidence, Stability",

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note = "Funding Information: This work was supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC). One of the authors (SMM) acknowledges the support of IIMS and the Department of Mathematics, University of Manitoba. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

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AU - Moghadas, S. M.

AU - Gumel, A. B.

N1 - Funding Information: This work was supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC). One of the authors (SMM) acknowledges the support of IIMS and the Department of Mathematics, University of Manitoba. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2002/7/15

Y1 - 2002/7/15

N2 - A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated) provided a certain threshold R0 (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for R0 > 1.

AB - A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated) provided a certain threshold R0 (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for R0 > 1.

KW - Equilibria

KW - Multi-stage infection

KW - Non-linear incidence

KW - Stability

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ER -

Global stability of a two-stage epidemic model with generalized non-linear incidence

Abstract

Keywords

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