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Global stability of an epidemic model with phased characteristics of vaccine efficacy. (Chinese. English summary) Zbl 1374.34179
Summary: An epidemic model with phased characteristics of vaccine efficacy is considered in this paper. The basic reproduction number, which characterizes the extinction or persistence of an infection, is obtained. By constructing a Lyapunov function, it is proved that the disease-free equilibrium of the system is globally stable when the basic reproduction number is less than one, and the unique endemic equilibrium of the system is globally stable when the basic reproduction number is greater than one.
MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
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