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Research Journal of Pharmacy and Technology
Year : 2017, Volume : 10, Issue : 10
First page : ( 3305) Last page : ( 3311)
Print ISSN : 0974-3618. Online ISSN : 0974-360X.
Article DOI : 10.5958/0974-360X.2017.00586.8

Stability Analysis of an SIRS Model with Saturated Incidence Rate and Treatment

Reddy K Madhusudhan1,*, Narayan K Lakshmi2, Reddy B Ravindra3

1Department of Mathematics, Vardhaman College of Engineering, Hyderabad, India

2Department of Mathematics, Vignan Institute of Technology & Sciences, Hyderabad, India

3Department of Mathematics, JNTUH College of Engineering, Kukatpally, Hyderabad, India

*Corresponding Author E-mail: kmsreddy.vce@gmail.com

Online published on 26 March, 2018.

Abstract

This research article attempts a study of SIRS epidemic model where saturated incidence rate under treatment forms a mathematical condition, the assumption being that there are two distinct possibilities informing the rate at which treatment rate is administered: one which remains unvarying over a period of time regardless of the number of infected individuals receiving treatment; another where the proportion at which treatment is provided is determined by the number of individuals directly affected by the epidemic. The existence and stability of equilibrium points are explored for both the cases. The analytical results are in fine agreement with numerical simulations.

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Keywords

SIRS epidemic model, saturated incidence rate, basic reproduction number, treatment, global stability.

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