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Pulse vaccination in the periodic infection rate SIR epidemic model

Zhen Jin·Mainul Haque·Quanxing Liu
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Abstract

A pulse vaccination SIR model with periodic infection rate $β(t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence, bifurcation and global stability. It has been shown that the infection-free periodic solution is globally stable provided $R_0 < 1$ and is unstable if $R_0>1$. Standard bifurcation theory have been used to show the existence of the positive periodic solution for the case of $R_0 \to1^+$. Finally, the numerical simulations have been performed to show the uniqueness and the global stability of the positive periodic solution of the system.

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Zhen Jin, Mainul Haque, Quanxing Liu. 2006-06-09. Pulse vaccination in the periodic infection rate SIR epidemic model. https://doi.org/10.1142/s1793524508000370

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