Global Stability of an SEIRS Model with Impulsive Vaccination and Saturating Incidence Rate

Yang Yang, Cheng Nannan

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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DOI: http://doi.org/10.11591/ijeecs.v12.i9.pp6999-7006

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