We　establish　a　stochastic　HIV/AIDS　model　involving　the　susceptible　with　protection　awareness　within　a　total　population.　The　mechanism　of　dynamic　behaviors　of　the　stochastic　HIV/AIDS　model　with　protection　awareness　are　investigated　in　order　to　control　the　spread　of　HIV/AIDS.　We　firstly　show　that　the　stochastic　model　admits　a　global　positive　solution　with　any　initial　positive　values.　By　constructing　Lyapunov　functions,　the　ergodic　stationary　distribution　under　the　condition　R0s>1,　and　the　extinction　under　the　condition　R0e<1　for　the　stochastic　model　are　further　obtained　respectively.　Moreover,　by　using　positive　preserving　truncated　Euler–Maruyama　method　(PPTEM),　the　related　numerical　simulations　are　performed,　which　demonstrate　the　quantitative　properties　of　persistence　and　extinction　of　the　solution.　Precisely,　the　increasing　of　protection　efficiency　of　the　susceptible　with　protection　awareness　reduces　the　scale　of　the　infected　individuals　with　AIDS;　and　the　continuous　antiretroviral　therapy　(ART)　also　benefits　the　control　of　the　scale　of　the　infected　individuals　with　HIV/AIDS;　the　media　reports　with　more　instructions　and　details　such　as　taking　post-exposure　prophylaxis　(PEP)　within　72　h　to　help　the　individuals　avoid　the　infection　to　meet　the　90%–90%–90%　plan　of　WHO.　©　2023　Elsevier　Ltd