This paper is concerned with a diffusive HIV infection model with space-dependent parameters, different infection stages and different classes of antiretroviral drugs, in which the cells are assumed to be comparatively immobile and the viruses obey Fickian diffusion in a continuous bounded domain with a smooth boundary. The aim of this paper is twofold: first, to investigate the combined effect of spatial heterogeneity, viral diffusion and high active antiretroviral therapy on the long-term dynamics of the model; second, to evaluate the effect of treatment intensification with the integrase inhibitor raltegravir on the viral load and 2-LTR dynamics in patients with uninterrupted antiretroviral therapy in a spatially heterogeneous environment. Through mathematical analysis, the basic reproduction ratio is explicitly calculated and determined as a threshold to predict whether the infection is cleared up in the cases of spatial heterogeneity and homogeneity. Besides, the results of numerical simulations show that: (i) both spatial heterogeneity and viral diffusion affect the basic reproduction ratio and the time evolution of viral load at each location; (ii) protease inhibitors may be more effective in reducing viral load than reverse transcriptase inhibitors, although both have the same effect on the basic reproduction ratio; (iii) treatment intensification with raltegravir induces a very minor decrease in viral load and a minor increase in 2-LTR, which implies that ongoing viral replication may not be the source of the persistence of low-level viral load.

本文研究了一个具有空间依赖性参数、不同感染阶段和不同类别的抗逆转录病毒药物的扩散性 HIV 感染模型，其中细胞被假定为相对不动，病毒服从 Fickian 扩散在连续有界域内平滑边界。本文的目的有两个：第一，研究空间异质性、病毒扩散和高效抗逆转录病毒治疗对模型长期动力学的综合影响；其次，评估整合酶抑制剂拉替拉韦强化治疗对在空间异质环境中接受不间断抗逆转录病毒治疗的患者的病毒载量和 2-LTR 动力学的影响。通过数学分析，在空间异质性和同质性的情况下，明确计算并确定基本繁殖率作为预测感染是否被清除的阈值。此外，数值模拟结果表明：（i）空间异质性和病毒扩散都会影响每个位置的基本繁殖率和病毒载量的时间演变；(ii) 蛋白酶抑制剂在降低病毒载量方面可能比逆转录酶抑制剂更有效，尽管两者对基本繁殖率的影响相同；(iii) 使用拉替拉韦强化治疗会导致病毒载量的轻微降低和 2-LTR 的轻微增加，这意味着持续的病毒复制可能不是低水平病毒载量持续存在的原因。