Abstract—The SEIR model for the transmission dynamics of influenza is extended by the addition of second-order space derivatives to enable the geographic spread of the disease in a population which has not been vaccinated against it. The resulting system of four reaction-diffusion equations is solved by a convergent finite-difference technique which is first-order accurate in time and second-order accurate in space. The resulting methods are analyzed for local truncation errors and stability. The numerical results verify that the proposed method is more competitive in terms of numerical stability than the standard finite-difference method.

Index Terms—SEIR model, reaction-diffusion system, finite-difference method, initial condition, influenza, infectious diseases.

The authors are with the Department of Mathematics, King Mongkut’s University of Technology Thonburi, Thung Khru, Bangkok 10140 Thailand (e-mail: atitjc@hotmail.com, iwirwong@kmutt.ac.th).

Cite: Atit Jaichuang and Wirawan Chinviriyasit, "Numerical Modelling of Influenza Model with Diffusion," International Journal of Applied Physics and Mathematics vol. 4, no. 1, pp. 15-21, 2014.