IJPAM: Volume 112, No. 4 (2017)

Title

DYNAMICS OF AN SIS EPIDEMIC MODEL WITH
A SATURATED INCIDENCE RATE UNDER TIME
DELAY AND STOCHASTIC INFLUENCE

Authors

Ranjith Kumar G.$^1$, Lakshmi Narayan K.$^2$, Ravindra Reddy B.$^3$
$^1$Department of Mathematics
Anurag Group of Institutions
Hyderabad, INDIA
$^2$Department of Mathematics
Vignan Institute of Engg. & Tech.
Hyderabad, INDIA
$^3$Department of Mathematics
JNTU College of Engg.
Jagityal, Karimnagar, INDIA

Abstract

This paper examines an SIS model with saturated incidence rate and latent period. To start with the stability of the disease-free and endemic equilibrium of the model with and without delay is dealt with. The existence of Hopf bifurcation is analysed and then obtained by regarding the time delay as the bifurcation parameter. Further, the stochastic model is derived from the deterministic epidemic model through the introduction of random perturbations around the endemic equilibrium point and stochastic stability properties of the model are investigated. The examples and simulations are supplied to throw light on results arrived at.

History

Received: January 14, 2016
Revised: November 4, 2016
Published: February 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 92B, 92D, 34D, 70K, 60H
Key Words and Phrases: SIS Model, Hopf bifurcation, saturation incidence rate, stochastic differential equation, reproductive number

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How to Cite?

DOI: 10.12732/ijpam.v112i4.4 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: 2017
Volume: 112
Issue: 4
Pages: 695 - 707


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