TY - JOUR
T1 - Analytical Solutions for an Avian Influenza Epidemic Model incorporating Spatial Spread as a Diffusive Process
AU - Phontita Thiuthad, Valipuram S. Manoranjan & Yongwimon Lenbury
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 - <p style="text-align: justify;">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.</p>