The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence

Juping Zhang, Zhen Jin, Yakui Xue and Youwen Li

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-18

Abstract:

An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number 𠑅 ∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if 𠑅 ∗ < 1 . The infection-free periodic solution is unstable and the disease is uniform persistent if 𠑅 ∗ > 1 . Our theoretical results are confirmed by numerical simulations.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:490437

DOI: 10.1155/2009/490437

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