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Zbl 1090.92044
Zhen, Jin; Ma, Zhien; Han, Maoan
Global stability of an SIRS epidemic model with delays. (English)
[J] Acta Math. Sci., Ser. B, Engl. Ed. 26, No. 2, 291-306 (2006). ISSN 0252-9602

Summary: An SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to ``weak delays''. Some known results are generalized.

MSC 2000:: *92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Keywords: SIRS epidemic model; time delay; global asymptotic stability; Lyapunov functional

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