Modelling of HIV viral load and 2-LTR dynamics during high active antiretroviral therapy in a heterogeneous environment

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 thresh-old 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.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates a diffusive HIV infection model with space-dependent parameters, different infection stages, and different classes of antiretroviral drugs. The combined effect of spatial heterogeneity, viral diffusion, and treatment intensification on the long-term dynamics of the model is examined. The results show the impact of spatial heterogeneity and viral diffusion on the basic reproduction ratio and viral load, as well as the effectiveness of different types of antiretroviral drugs.