Abstract
In this paper, we propose an optimal control problem for an HIV infection model with cellular and humoral immune responses, logistic growth of uninfected cells, cell-to-cell spread, saturated infection, and cure rate. The model describes the interaction between uninfected cells, infected cells, free viruses, and cellular and humoral immune responses. We use two control functions in our model to show the effectiveness of drug therapy on inhibiting virus production and preventing new infections. We apply Pontryagin maximum principle to study these two control functions. Next, we simulate the role of optimal therapy in the control of the infection by numerical simulations and AMPL software.
Highlights
IntroductionAcquired immune deficiency syndrome (in short, AIDS) is caused by a type of lentivirus called human immunodeficiency virus (HIV)
Acquired immune deficiency syndrome is caused by a type of lentivirus called human immunodeficiency virus (HIV)
We propose a new mathematical model of HIV, which is an extension of the model developed in [16, 17]
Summary
Acquired immune deficiency syndrome (in short, AIDS) is caused by a type of lentivirus called human immunodeficiency virus (HIV). One way is to use drugs that help the immune system to prevent the spread of HIV infection. Antiretroviral therapy, used to treat HIV in most countries, can restore the immune system and prevent opportunistic infections. These treatments reduce the production of new infections and the rate of HIV transmission. Protease inhibitor (PI) prevents virus production from infected cells [20, 21] Since these treatments are singly detrimental to the patient, an optimal therapy for the treatment of HIV infection using a combination of multiple appropriate treatment strategies is needed.
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