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On the general structure of epidemic systems. Global asymptotic stability. (English) Zbl 0622.92016
An n-dimensional ordinary differential equation of the form (e)ż\(=diag(z)(e+Az)+c\) is proposed to describe a general epidemic model. A motivation for such an equation is the classical SIR model.
By using the Lyapunov function of B. S. Goh [see Modeling and differential equations in biology, Conf., Carbondale 1978, Lect. Notes pure appl. Math., Vol. 58, 209-216 (1980; Zbl 0453.92015)], the authors are able to provide conditions for the global asymptotic stability of a strictly positive equilibrium \(z^*\). Finally several epidemic systems are discussed by applying the general results.
Reviewer: G.Karakostas

MSC:
92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
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