IJPAM: Volume 103, No. 1 (2015)

DYNAMIC PROPERTIES FOR
AN EPIDEMIC MODEL WITH PARTIAL IMMUNITY

Lili Wang$^1$, Rui Xu$^2$
$^{1,2}$Institute of Applied Mathematics
Shijiazhuang Mechanical Engineering College
97 Heping West Road, Shijiazhuang, P.R. CHINA


Abstract. In this paper, an epidemic model with waning preventive vaccine is formulated. The analysis of the model is presented in terms of the basic reproduction number. If the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are obtained for the global attractiveness of the endemic equilibrium. Numerical simulations are carried out to illustrate the main results.

Received: January 31, 2015

AMS Subject Classification: 34K20, 34K60, 92D30

Key Words and Phrases: global stability, epidemic model, vaccination, compound matrices

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DOI: 10.12732/ijpam.v103i1.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 37 - 60


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