Analysis of HIV therapy in the liver using optimal control and pharmacokinetics

Abstract

The main burden in treating human immunodeficiency virus (HIV) infection currently, is the side effects of the antiretroviral therapy (ART) used, because each treatment is toxic to the liver. This study uses optimal control theory applied to a mathematical model that describes the dynamics of HIV infection in the liver. The optimal controls are presented as therapy efficacy of reverse transcriptase inhibitors (RTIs), integrase inhibitors (INs) and protease inhibitors (PIs). An objective function is defined with an aim to investigate the optimal control strategy that minimises toxicity, viral load and cost of first-line and second-line HIV regimen. Results indicate that, in the first-line regimen with INs, a patient has to take medication for at least 98% of the treatment time and the regimen should be close to 100% efficacious regardless of the intervention cost. For second-line regimen, the period of drug administration of PIs largely depends on the weight constants. Inclusion of INs in the first-line regimen yields better HIV DNA suppression, as they are more efficacious than NRTIs. Of all drugs studied, nevirapine is highly efficacious but most toxic. The study recommends routine transaminase tests because results indicate liver enzyme elevation even with very low viral load. Numerical results with pharmacokinetic parameters further indicate an increase in HIV load at initiation of therapy, due to viral redistribution in plasma.