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

Juping Zhang; Zhen Jin; Yakui Xue; Youwen Li

doi:10.1155/2009/490437

Discrete Dynamics in Nature and Society (Jan 2009)

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

Juping Zhang,
Zhen Jin,
Yakui Xue,
Youwen Li

Affiliations

Juping Zhang: Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China
Zhen Jin: Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China
Yakui Xue: Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China
Youwen Li: Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China

DOI: https://doi.org/10.1155/2009/490437
Journal volume & issue: Vol. 2009

Abstract

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

Published in Discrete Dynamics in Nature and Society

ISSN: 1026-0226 (Print); 1607-887X (Online)
Publisher: Hindawi Limited
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://www.hindawi.com/journals/ddns/

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