Mathematical modelling of host-disease-drug interactions in HIV disease

The human immunodeficiency virus (HIV) has resisted nearly three decades of efforts targeting a cure. Sustained suppression of the virus has remained a challenge, mainly due to the remarkable evolutionary adaptation that the virus exhibits by the accumulation of drug-resistant mutations in its genome. Current therapeutic strategies aim at achieving and maintaining a low viral burden and typically involve multiple drugs. The choice of optimal combinations of these drugs is crucial, particularly in the background of treatment failure having occurred previously with certain other drugs. An understanding of the dynamics of viral mutant genotypes aids in the assessment of treatment failure with a certain drug combination, and exploring potential salvage treatment regimens. Mathematical models of viral dynamics have proved invaluable in understanding the viral life cycle and the impact of antiretroviral drugs. However, such models typically use simplified and coarse-grained mutation schemes, that curbs the extent of their application to drug-specific clinical mutation data, in order to assess potential next-line therapies. Statistical models of mutation accumulation have served well in dissecting mechanisms of resistance evolution by reconstructing mutation pathways under different drug-environments. While these models perform well in predicting treatment outcomes by statistical learning, they do not incorporate drug effect mechanistically. Additionally, due to an inherent lack of temporal features in such models, they are less informative on aspects such as predicting mutational abundance at treatment failure. This limits their application in analyzing the pharmacology of antiretroviral drugs, in particular, time-dependent characteristics of HIV therapy such as pharmacokinetics and pharmacodynamics, and also in understanding the impact of drug efficacy on mutation dynamics. In this thesis, we develop an integrated model of in vivo viral dynamics incorporating drug-specific mutation schemes learned from clinical data. Our combined modelling approach enables us to study the dynamics of different mutant genotypes and assess mutational abundance at virological failure. As an application of our model, we estimate in vivo fitness characteristics of viral mutants under different drug environments. Our approach also extends naturally to multiple-drug therapies. Further, we demonstrate the versatility of our model by showing how it can be modified to incorporate recently elucidated mechanisms of drug action including molecules that target host factors. Additionally, we address another important aspect in the clinical management of HIV disease, namely drug pharmacokinetics. It is clear that time-dependent changes in in vivo drug concentration could have an impact on the antiviral effect, and also influence decisions on dosing intervals. We present a framework that provides an integrated understanding of key characteristics of multiple-dosing regimens including drug accumulation ratios and half-lifes, and then explore the impact of drug pharmacokinetics on viral suppression. Finally, parameter identifiability in such nonlinear models of viral dynamics is always a concern, and we investigate techniques that alleviate this issue in our setting.