Asymptotic behavior and stability of a stochastic model for AIDS transmission

A stochastic model for AIDS transmission is presented in this paper. The existence and uniqueness of its solution is proved, and the solution belongs to an interval satisfying the actual condition. Furthermore, the disease equilibrium can be demonstrated to be existent, and both its almost surely exponential stability and its pth moment exponential stability can be concluded. Based on parameter analysis, the first quadrant can be integrated into several parts according to the comparison between almost surely exponential stability and pth moment exponential stability. And the potential meaning of the stability is further demonstrated. Finally, based on the above theoretical analysis, some conditions for AIDS to decrease and then to die out are obtained by computer simulation.