Risk Analysis for AIDS Control Based on a Stochastic Model with Treatment Rate

A stochastic model with treatment rate for AIDS transmission and control is presented by taking the treatment of HIV patients into account. We prove the existence of the equilibrium and analyze the asymptotic behavior of the model. We then discuss the effect on the model with the change of the treatment rate and the contact rate by considering knowledge, attitudes, and behavior of HIV patients. Through the numerical solution of the stochastic differential equation, we obtain the risk probability when the proportion of the population infected with HIV against total population exceeds a given control aim under different situations. The condition for AIDS to decrease and even to die out is demonstrated by simulation. Consequently, some strategies can be developed to prevent AIDS from breaking out at a certain risk level.