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Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process

Published online by Cambridge University Press:  28 May 2015

Phontita Thiuthad ,
Valipuram S. Manoranjan  and
Yongwimon Lenbury
Phontita Thiuthad
Affiliation:
Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama 6 Road, Bangkok 10400, Thailand Centre of Excellence in Mathematics, CHE, 328 Si Ayutthaya Road, Bangkok 10400, Thailand
Valipuram S. Manoranjan
Affiliation:
Department of Mathematics, Washington State University, Pullman WA 99164, USA
Yongwimon Lenbury*
Affiliation:
Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama 6 Road, Bangkok 10400, Thailand Centre of Excellence in Mathematics, CHE, 328 Si Ayutthaya Road, Bangkok 10400, Thailand
*
*Corresponding author. Email addresses: thiuthadp@hotmail.com (P. Thiuthad), mano@wsu.edu (V.S. Manoranjan), scylb@yahoo.com (Y. Lenbury)
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Abstract

We consider a theoretical model for the spread of avian influenza in a poultry population. An avian influenza epidemic model incorporating spatial spread as a diffusive process is discussed, where the infected individuals are restricted from moving to prevent spatial transmission but infection occurs when susceptible individuals come into contact with infected individuals or the virus is contracted from the contaminated environment (e.g. through water or food). The infection is assumed to spread radially and isotropically. After a stability and phase plane analysis of the equivalent system of ordinary differential equations, it is shown that an analytical solution can be obtained in the form of a travelling wave. We outline the methodology for finding such analytical solutions using a travelling wave coordinate when the wave is assumed to move at constant speed. Numerical simulations also produce the travelling wave solution, and a comparison is made with some predictions based on empirical data reported in the literature.

Keywords

34D2035C0792B05Travelling wave solutionsreaction-diffusion equationsavian influenza epidemic
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 2 , May 2015 , pp. 150 - 159
Copyright
Copyright © Global-Science Press 2015 

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