Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 869603, 13 pages
Research Article

Travelling Waves of a Diffusive Epidemic Model with Latency and Relapse

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 21 December 2012; Accepted 25 February 2013

Academic Editor: Zhen Jin

Copyright © 2013 Zhiping Wang and Rui Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An SEIR epidemic model with relapse and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of the feasible steady states to this model is discussed. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.