Stability and optimal control of a cytokine-enhanced general HIV infection model with antibody immune response and CTLs immune response

In this article, a cytokine-enhanced viral infection model with cytotoxic T lymphocytes (CTLs) immune response and antibody immune response is proposed and analyzed. The model contains six compartments: uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, viruses, CTLs and antibodies. Different from the previous works, this model not only considers virus-to-cell transmission and cell-to-cell transmission, but also includes a new infection mode, namely cytokine-enhanced viral infection. The incidence rates of the healthy CD4+T cells with viruses, infected cells and inflammatory cytokines are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. Firstly, we prove that all the solutions of the model are nonnegative and uniformly bounded. Then, five key parameters with strong biological significance, namely the virus basic reproduction number R0, CTLs immune response reproduction number R1, antibody immune response reproductive number R2, CTLs immune competitive reproductive number R3 and antibody immune competitive reproductive number R4 are derived. Then, by using Lyapunov’s method and LaSalle’s invariance principle, we have shown the global stability of each equilibrium. In addition, the numerical simulation results also show that the theoretical results are correct. Finally, we formulate an optimal control problem and solve it using Pontryagins Maximum Principle and an efficient iterative numerical methods. The results of our numerical simulation show that it is very important to control the infection between viruses and cells and between cells and inflammatory cytokines for controlling HIV.