Volume 5, Issue 2
Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process

Phontita Thiuthad, Valipuram S. Manoranjan & Yongwimon Lenbury

East Asian J. Appl. Math., 5 (2015), pp. 150-159.

Published online: 2018-02

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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

Travelling wave solutions, reaction-diffusion equations, avian influenza epidemic.

  • AMS Subject Headings

34D20, 35C07, 92B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-150, author = {}, title = {Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.201114.080415a}, url = {http://global-sci.org/intro/article_detail/eajam/10788.html} }
TY - JOUR T1 - Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process JO - East Asian Journal on Applied Mathematics VL - 2 SP - 150 EP - 159 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.201114.080415a UR - https://global-sci.org/intro/article_detail/eajam/10788.html KW - Travelling wave solutions, reaction-diffusion equations, avian influenza epidemic. AB -

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.

Phontita Thiuthad, Valipuram S. Manoranjan & Yongwimon Lenbury. (1970). Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process. East Asian Journal on Applied Mathematics. 5 (2). 150-159. doi:10.4208/eajam.201114.080415a
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