We investigate a stochastic SI epidemic model in the complex networks. We show that this model has a unique global positive solution. Then we consider the asymptotic behavior of the model around the disease-free equilibrium and show that the solution will oscillate around the disease-free equilibrium of deterministic system when . Furthermore, we derive that the disease will be persistent when . Finally, a series of numerical simulations are presented to illustrate our mathematical findings. A new result is given such that, when , with the increase of noise intensity the solution of stochastic system converging to the disease-free equilibrium is faster than that of the deterministic system.
Jinqing Zhao. Maoxing Liu. Wanwan Wang. Panzu Yang. "The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation." Abstr. Appl. Anal. 2014 (SI01) 1 - 14, 2014. https://doi.org/10.1155/2014/610959