Abstract
Numerical analysis and optimization tools are used to suggest improved therapies to try and cure HIV infection. An HIV model of ordinary differential equation, which includes immune response, neutralizing antibodies, and multidrug effects, is improved. For a fixed time, single-drug and two-drug treatment strategies are explored based on Pontryagin’s maximum principle. Using different combinations of weight factor pairs combining with special upper-bound pairs for controls, nine types of treatment policies are determined and different therapy effects are numerically simulated with a gradient projection method. Some strategies are effective, but some strategies are not particularly helpful for the therapy of HIV/AIDS. Comparing the effective treatment strategies, we find a more appropriate strategy with maximizing the number of uninfected CD4+T-cells and minimizing the number of active virus.
Highlights
Up to date, drug treatments are still available control methods of HIV/AIDS
The existence for the optimal control problem is proved, the optimality system is derived, and a gradient projection method is applied to numerically simulate different therapy effects
On the basis of combinations of weight factors and upper-bounds for controls, we establish some of much interesting or even strange treatment strategies including four types of single-drug controls and five types of twodrug controls, where a large weight coefficient means a high cost of the corresponding drug
Summary
Drug treatments are still available control methods of HIV/AIDS. Reverse transcriptase inhibitors (RTIs) can inhibit HIV RNA from being converted into DNA, blocking integration of the viral code into the target cell. Mathematical models are often used to study HIV/AIDS spread and host-drug-virus interactions to make assumptions and to suggest new methods for its optimal control. Karrakchou et al [3] proposed an infectious model which described the interaction of HIV virus and the immune system of the human body to investigate the fundamental role of chemotherapy treatment in controlling the virus reproduction and to determine the optimal methodology for administering antiviral medication therapies to fight HIV infection. Garira et al [4] studied an optimal control problem including immune response and multidrug effects for HIV multitherapy enhancement. We use numerical analysis and optimization tools to suggest improved therapies to try and cure HIV infection for an improved HIV model of ordinary differential equation, which includes immune response, neutralizing antibodies, and multidrug effects.
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