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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 583648, 8 pages
Research Article

Modeling and Analysis of Epidemic Diffusion with Population Migration

Department of Management Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Received 15 June 2013; Revised 24 July 2013; Accepted 30 July 2013

Academic Editor: Zhiwei Gao

Copyright © 2013 Ming Liu and Yihong Xiao. 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 improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion.