Compared with the existing HIV/AIDS host model that considers only age-since-infection or only spacial diffusion, we propose a new age–space structured model that incorporating both two infection ages, spacial diffusion, and HAART (highly active antiretroviral therapy) to analyze the global dynamics of HIV/AIDS epidemic and study the incident of its transmission among MSM (men who have sex with men) group. We first obtain the well-posedness and positivity of the solution for the model. The generation operator $\mathcal{R}$ is obtained by the process of renewal, followed by the basic reproduction number $R_0$. Then we prove that the disease-free equilibrium is globally asymptotically stable (g.a.s) when $R_0<1$, the space-independent steady state is g.a.s, and the disease will be present when $R_0>1$. Numerical simulations are conducted to reinforce these analytical results. Finally, numerical results show that key model parameters influence the value of $R_0$ effectively, and indicate that the spatial factor plays a crucial role as a control measure and cannot be ignored during the intervention for HIV transmission among MSM group. Moreover, our work suggests that treatment adherence should be improved during the HAART for HIV infected individuals among MSM.

与仅考虑年龄原因感染或仅空间扩散的现有HIV / AIDS宿主模型相比，我们提出了一种新的时空结构模型，该模型将两个感染年龄，空间扩散和HAART（高效抗逆转录病毒治疗）结合在一起分析艾滋病毒/艾滋病流行的全球动态，并研究其在男男性接触者（男男性接触者）人群中的传播事件。我们首先获得模型解的适定性和正性。代算子$\mathcal{[R}$ 是通过续订过程获得的，然后是基本复制号 ${\mathrm{[R}}_0$。然后我们证明无病平衡在以下情况下是全局渐近稳定的（气体）${\mathrm{[R}}_0<\mathrm{1个}$，与空间无关的稳态是气体，当 ${\mathrm{[R}}_0>\mathrm{1个}$。进行数值模拟以增强这些分析结果。最后，数值结果表明关键模型参数会影响模型的值。${\mathrm{[R}}_0$有效地表明空间因素在控制措施中起着至关重要的作用，并且在MSM组之间的HIV传播干预中不可忽视。此外，我们的工作表明，在MSART中针对HIV感染者的HAART期间应提高治疗依从性。