Global Stability of an SEIRS Model with Impulsive Vaccination and Saturating Incidence Rate
Abstract
This paper introduces a impulsive vaccination SEIRS epidemic model with constant input, saturation incidence rate and exposed period, and the threshold valueσ=1 is obtained at which disease is eliminated. By using the impulsive differential equation theory, it is proved that whenσ<1, the disease-free periodic solution is globally asymptotically stable, and that whenσ>1,the system is uniformly persistent. On these grounds, it is shown that impulsive vaccination can bring obvious effects on the dynamics behaviors of the system.
Keywords
SEIRS model; Impulsive vaccination; Treatment rate; Reproduction number; Global stability
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PDFDOI: http://doi.org/10.11591/tijee.v12i9.3840
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