Abstract
HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin's Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.
Highlights
There is an ever-changing need for new and useful treatment regimes that will provide assistance and relief in all aspects of the human condition
According to the Joint United Nations Programme on Human immunodeficiency virus (HIV) and AIDS (UNAIDS), there were 36.7 million people living with HIV/AIDS in 2016, 1.6 million of which live in Kenya [1]
This study has addressed some of the shortcomings noted from the in-host HIV dynamics models by applying three control variables representing the three drug regimes on the market, that is, the fusion inhibitor, reverse transcriptase inhibitors, and the protease inhibitors, in the in vivo HIV model
Summary
There is an ever-changing need for new and useful treatment regimes that will provide assistance and relief in all aspects of the human condition. Gaff and Schaefer [6] applied optimal theory in evaluating mitigation strategy that would be highly effective in minimizing the number of people who get infected by an infection The study applied both vaccinations and treatment as control variables for their various model. Like Hattaf and Yousfi [16], the study applied the two control strategies, that is, RTIs and the PIs. the study failed to put into account both the latently infected cells and the noninfectious virus that results due to the use of RTIs and PIs, respectively. The study failed to put into account both the latently infected cells and the noninfectious virus that results due to the use of RTIs and PIs, respectively Failure to include such important variables in the model underscores the adequacy of the model in representing the actual HIV in-host mechanism. The study will apply optimal control theory together with Pontryagin’s Maximum Principle in solving the objective function with the aim of establishing the optimal treatment strategy
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