Numerical study of a diffusive epidemic model of influenza with variable transmission coefficient

A diffusive epidemic model for H1 N1 influenza is formulated with a view to gain basic understanding of the virus behavior. All newborns are assumed to be susceptible. Mortality rate for infective individuals in the population is assumed to be greater than natural mortality rate. Latent, infectious...

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Bibliographic Details
Published in:Applied mathematical modelling 2011-12, Vol.35 (12), p.5507-5523
Main Authors: Samsuzzoha, Md, Singh, Manmohan, Lucy, David
Format: Article
Language:English
Subjects:
Biological and medical sciences
Diffusion
Epidemic model
Epidemiology
General aspects
Influenza
Medical sciences
Public health. Hygiene
Public health. Hygiene-occupational medicine
Routh–Hurwitz stability conditions
Splitting method
Transmission coefficient
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Summary:A diffusive epidemic model for H1 N1 influenza is formulated with a view to gain basic understanding of the virus behavior. All newborns are assumed to be susceptible. Mortality rate for infective individuals in the population is assumed to be greater than natural mortality rate. Latent, infectious and immune periods are assumed to be constants throughout this study. The numerical solutions of this model are carried out under three different initial populations distribution. In order to investigate the effect of the disease transmission coefficient on the spread of disease, β is taken to be constant as well as a function of seasonally varying time t and a function of spatial variable x. The threshold quantity ( R 0 ) that governs the disease dynamics is derived. Numerical simulation shows that the system supports the existence of sustained and damped oscillations depending on initial populations distribution, the disease transmission rate and diffusion.
ISSN:0307-904X
DOI:10.1016/j.apm.2011.04.029