Numerical modelling of an SIR epidemic model with diffusion
Journal article
Authors/Editors
Strategic Research Themes
No matching items found.
Publication Details
Author list: Chinviriyasit S., Chinviriyasit W.
Publisher: Elsevier
Publication year: 2010
Journal: Applied Mathematics and Computation (0096-3003)
Volume number: 216
Issue number: 2
Start page: 395
End page: 409
Number of pages: 15
ISSN: 0096-3003
eISSN: 1873-5649
Languages: English-Great Britain (EN-GB)
View in Web of Science | View on publisher site | View citing articles in Web of Science
Abstract
A spatial SIR reaction-diffusion model for the transmission disease such as whooping cough is studied. The behaviour of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by linearization and by using Lyapunov functional. Our result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small. These results are verified numerically by constructing, and then simulating, a robust implicit finite-difference method. Furthermore, the new implicit finite-difference method will be seen to be more competitive (in terms of numerical stability) than the standard finite-difference method. ฉ 2010 Elsevier Inc. All rights reserved.
Keywords
Disease-free equilibrium, Finite-difference method, Reaction-diffusion system, SIR model, Whooping cough
Contact Information