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.
"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