Considering multiple effects of spatial factors (spatial heterogeneity and mobility) and temporal heterogeneity (the periodic administration of the drug) in HIV infection and treatment, we formulate a time periodic reaction–diffusion equation model to study the HIV viral dynamics. The basic reproduction number $R_0$ is derived and the global threshold dynamics is explored in terms of $R_0$. When $R_0<1$, the infection-free periodic solution is globally attractive. When $R_0>1$, the model system is uniformly persistent. The global stability analysis is also performed in the critical case of $R_0=1$ with spatial heterogeneity but without time periodicity. The global asymptotic stability of the infection steady state for the spatial homogeneous model is discussed. Furthermore, numerical simulations reveal that (i) the value of $R_0$ depends on spatial heterogeneity, which indicates that different human individuals or different organs in one individual may have different infection states even if the drug efficacy is the same; and (ii) the 2-LTR level at the steady state may increase and the steady-state viral load may decrease dramatically if raltegravir is administered from the beginning of thetreatment.

考虑到在HIV感染和治疗中空间因素（空间异质性和流动性）和时间异质性（药物的定期给药）的多重影响，我们制定了时间周期性反应扩散方程模型来研究HIV病毒动力学。基本复制数${\mathrm{[R}}_0$ 导出，并根据以下方面探索全局阈值动态 ${\mathrm{[R}}_0$。什么时候${\mathrm{[R}}_0<\mathrm{1个}$，无感染的定期解决方案在全球具有吸引力。什么时候${\mathrm{[R}}_0>\mathrm{1个}$，模型系统是统一持久的。在以下情况下也进行全局稳定性分析：${\mathrm{[R}}_0=\mathrm{1个}$具有空间异质性但没有时间周期性。讨论了空间齐次模型的感染稳态的全局渐近稳定性。此外，数值模拟显示（i）${\mathrm{[R}}_0$取决于空间异质性，这表明即使药物功效相同，不同的人类个体或一个个体中的不同器官也可能具有不同的感染状态；（ii）如果从治疗开始就使用raltegravir，则稳态下的2-LTR水平可能会增加，稳态病毒载量可能会急剧下降。