Global stability of an SIRS epidemic model with delays. (English) Zbl 1090.92044

Zhen, Jin; Ma, Zhien; Han, Maoan

Acta Math. Sci., Ser. B, Engl. Ed. 26, No. 2, 291-306 (2006).

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:

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