# MODELING AND ANALYSIS OF AN EPIDEMIC MODEL WITH CLASSICAL KERMACK-MCKENDRICK INCIDENCE RATE UNDER TREATMENT

• Kar, T.K. (DEPARTMENT OF MATHEMATICS, BENGAL ENG. AND SCI. UNIV.) ;
• Batabyal, Ashim (DEPARTMENT OF MATHEMATICS, BALLY NISCHINDA CHITTARANJAN VIDYALAYA) ;
• Agarwal, R.P. (DEPARTMENT OF MATHEMATICS, FLORIDA INSTITUTE OF TECHNOLOGY)
• Accepted : 2009.12.07
• Published : 2010.03.25

#### Abstract

An epidemic model with Classical Kermack-Mckendrick incidence rate under a limited resource for treatment is proposed to understand the effect of the capacity for treatment. We have assumed that treatment function is strictly increasing function of infective individuals and becomes constant when the number of infective is very large. Existence and stability of the disease free and endemic equilibrium are investigated, boundedness of the solutions are shown. Even in this simple version of the model, backward bifurcation and multiple epidemic steady states can be observed with some sets of parameter values. Hopf-bifurcation analyses are given and numerical examples are provided to help understanding.

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