Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

Ibrahim H. I. Ahmed; Peter J. Witbooi; Kailash Patidar

doi:10.1155/2012/275902

Journal of Applied Mathematics (Jan 2012)

Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

Ibrahim H. I. Ahmed,
Peter J. Witbooi,
Kailash Patidar

Affiliations

Ibrahim H. I. Ahmed: Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
Peter J. Witbooi: Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
Kailash Patidar: Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa

DOI: https://doi.org/10.1155/2012/275902
Journal volume & issue: Vol. 2012

Abstract

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We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge-Kutta method.

Published in Journal of Applied Mathematics

ISSN: 1110-757X (Print); 1687-0042 (Online)
Publisher: Hindawi Limited
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://onlinelibrary.wiley.com/journal/4185

About the journal