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Global behavior and permanence of SIRS epidemic model with time delay. (English) Zbl 1154.34390
Summary: An autonomous SIRS epidemic model with time delay is studied. The basic reproductive number R 0 is obtained which determines whether the disease is extinct or not. When the basic reproductive number is greater than 1, it is proved that the disease is permanent in the population, and explicit formula are obtained by which the eventual lower bound of the fraction of infectious individuals can be computed. Throughout the total paper, we mainly use the technique of Lyapunov functional to establish the global stability of the infection-free equilibrium and the local stability of the endemic equilibrium but need another sufficient condition.
MSC:
34K20Stability theory of functional-differential equations
34D23Global stability of ODE
92D30Epidemiology
93C23Systems governed by functional-differential equations