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Mathematical Problems in Engineering
Volume 2015, Article ID 365049, 8 pages
Research Article

Global Stability of a Variation Epidemic Spreading Model on Complex Networks

College of Information Science and Engineering, Central South University, Hunan, Changsha 410083, China

Received 20 September 2015; Accepted 18 November 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 De-gang Xu et al. 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.


Epidemic spreading on networks becomes a hot issue of nonlinear systems, which has attracted many researchers’ attention in recent years. A novel epidemic spreading model with variant factors in complex networks is proposed and investigated in this paper. One main feature of this model is that virus variation is investigated in the process of epidemic dynamical spreading. The global dynamics of this model involving an endemic equilibrium and a disease-free equilibrium are, respectively, discussed. Some sufficient conditions are given for the existence of the endemic equilibrium. In addition, the global asymptotic stability problems of the disease-free equilibrium and the endemic equilibrium are also investigated by the Routh-Hurwitz stability criterion and Lyapunov stability criterion. And the uniform persistence condition of the new system is studied. Finally, numerical simulations are provided to illustrate obtained theoretical results.