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

Abstract

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.