LAUSR

Abstract To screen for virus carriers and for infected individuals to actively seek treatment are the key factors to curb the spread of HIV/AIDS. We propose a stochastic HIV/AIDS model to evaluate their effect. First, we theoretically prove that the solution of the stochastic model is positive and global. Second, we obtain the existence of an ergodic stationary distribution if R 0 S > 1 , and we establish sufficient conditions R 0 ′ 1 for disease extinction. We provide examples and numerical simulations to verify our theoretical results. Finally, we analyze the impact of the above two factors on the dynamical behavior of the stochastic system, and draw conclusions regrading disease prevention and elimination.