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

Authors:
S. M. Moghadas;A. B. Gumel
Affiliations:
Department of Mathematics, University of Manitoba, Winnipeg, Man., Canada R3T 2N2;Department of Mathematics, University of Manitoba, Winnipeg, Man., Canada R3T 2N2
Venue:
Mathematics and Computers in Simulation
Year:
2002

Citing 1
Cited 2

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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.