Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process
Year: 2015
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 150–159
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.201114.080415a
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 2 : pp. 150–159
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Travelling wave solutions reaction-diffusion equations avian influenza epidemic.