COMPLEXITY AND ASYMPTOTICAL BEHAVIOR OF A SIRS EPIDEMIC MODEL WITH PROPORTIONAL IMPULSIVE VACCINATION

Guang-Zhao Zeng () and Lan-Sun Chen ()
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Guang-Zhao Zeng: Department of Mathematics, Shaoguan University, ShaoGuan, GuangDong, 512005, China
Lan-Sun Chen: Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing, 116024, China

Advances in Complex Systems (ACS), 2005, vol. 08, issue 04, 419-431

Abstract: This paper considers an SIRS epidemic model with proportional impulsive vaccination, which may inherently oscillate. We study the ratio-dependent impulsive control and obtain the conditions about the basic reproductive number for which the epidemic-elimination solution is globally asymptotic. On the other hand, if the epidemic turns out to be endemic, we study numerically the influences of impulsive vaccination on the periodic oscillation of a system without impulsion and find sophisticated phenomena such as chaos in this case.

Keywords: SIRS epidemic model; proportional impulsive vaccination; globally asymptotic; chaos; quasi-periodic solution (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219525905000580

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