HIV dynamics under multi-drug combination therapy: mathematical modelling and data fitting

The Manual of National Free AIDS Antiviral Drug Treatment (version 2023), compiled by the National Center for AIDS/STD Control and Prevention, China CDC, recommends that the preferred first-line treatment regimen for drug-naive, HIV-infected individuals be a combination of tenofovir disoproxil fumarate (TDF), lamivudine (3TC) and efavirenz (EFV). Now two questions arise: why should multi-drug combination therapy be used to suppress the viral load in patients? What are the impacts of different medication regimens on the viral load dynamics? To this end, we consider a within-host HIV infection model coupling viral dynamics and pharmacokinetics, where the time evolution of drug concentration is described by a two-compartment model with extravascular drug delivery route. Based on the actual data, we apply the Markov-chain Monte-Carlo (MCMC) method containing the Metropolis-Hastings (M-H) algorithm to estimate the unknown parameters in pretreatment model of HIV infection and pharmacokinetics model, respectively. Subsequently, based on the estimated parameters, numerical results suggest that: (i) in the case of monotherapy, the viral load in patients can be completely suppressed if the first-line treatment regimen is strictly followed, but the impact of medication adherence on antiviral response is more obvious; (ii) in the case of multi-drug combination therapy, the impact of medication adherence on antiviral response is diminished compared to monotherapy; (iii) early initiation of the first-line treatment helps to ensure the success of treatment. This study reveals the time evolution of viral load under antiviral therapy, evaluates the effectiveness and potential risks of treatment, and provides guidance for the clinical treatment.