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Research Journal of Pharmacy and Technology
Year : 2016, Volume : 9, Issue : 11
First page : ( 1945) Last page : ( 1950)
Print ISSN : 0974-3618. Online ISSN : 0974-360X.
Article DOI : 10.5958/0974-360X.2016.00399.1

Mathematical study of an sir epidemic model with nonmonotone saturated incidence rate and white noise

Kumar G Ranjith1,*, Narayan K Lakshmi2, Reddy B Ravindra3

1Department of Mathematics, ANURAG Group of Institutions, Hyderabad

2Department of Mathematics, VIGNAN Institute of Tech. & Sci., Hyderabad

3Department of Mathematics, JNTUH College of Engg., Jagityal, Karimnagar

*Corresponding Author E-mail: ranjithreddy1982@gmail.com

Online published on 2 March, 2017.

Abstract

This paper contemplates an SIR epidemic model with non-monotone saturated incidence rate for both deterministic and stochastic models. The stability of disease-free and endemic equilibrium points of the deterministic model have been dealt with first. As far as the stochastic version goes, the global stability of endemic equilibrium is proved under suitable conditions on the strength of the intensity of the white noise perturbation. Furthermore, we find some numerical examples that attest to the analytical findings.

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Keywords

Non-monotone Saturated Incidence rate, stochastic stability, Endemic equilibrium, Lyapunov Function, White noise.

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