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Title: Analytical solutions for an avian influenza epidemic model incorporating spatial spread as a diffusive process
Authors: Phontita Thiuthad
Valipuram S. Manoranjan
Yongwimon Lenbury
Mahidol University
South Carolina Commission on Higher Education
Washington State University
Keywords: Mathematics
Issue Date: 1-May-2015
Citation: East Asian Journal on Applied Mathematics. Vol.5, No.2 (2015), 150-159
Abstract: © 2015 Global-Science Press. 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.
ISSN: 20797370
Appears in Collections:Scopus 2011-2015

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