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Stability of periodic solutions for an SIS model with pulse vaccination

โœ Scribed by Yicang Zhou; Hanwu Liu

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
701 KB
Volume
38
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

vaccination is an important strategy for the elimination of infectious diseases. A mathematical SIS model with pulse vaccination is formulated in this paper. The dynamical behavior of the model is studied, and the basic reproductive number & is defined. It is proved that the disease-free periodic solution is stable if Ro < 1, and it is unstable if Ro > 1. The global stability of the disease-free periodic solution is studied and sufficient condition is obtained. The existence and stability of the endemic periodic solution are investigated analytically and numerically. @ 2003 Elsevier Ltd. All rights reserved.

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## Commumcated by M Slemrod Abstract--Sufficient conditions are obtained for the existence of positive penodm solutions of the followmg mtegrodtfferentml model of mutuahsm s)ds K2(t) + c~2(t) dl(s)Nl(t -s) ds dN2(t) \_ r2(t)N2(t) . ---~ .... N2(t -a2(t)) , dt [ 1+/0 Jl(S)Nl(t-s)ds where r~,K~,a~