Journal
MATHEMATICAL BIOSCIENCES
Volume 213, Issue 1, Pages 1-12Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2008.02.005
Keywords
mathematical model; threshold condition; basic reproduction number R-0; global asymptotic stability
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One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition J(0) of the parameters of the system such that if J(0) < 1 the diseasefree equilibrium (DFE) is locally asymptotically stable (LAS), and if J(0) > 1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is 10 < 1, where R-0 is the basic reproduction number [O. Dickmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models. (C) 2008 Elsevier Inc. All rights reserved.
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