Optimal Treatment Strategies for HIV with Antibody Response

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.