Abstract
In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically.
Highlights
Human immuno deficiency virus (HIV-1) is a lentivirus that causes acquired immuno deficiency syndrome (AIDS), a condition in humans in which the immune system gets to fail, leading to life-threatening opportunistic infections
In the literary study, many mathematical models have been formulated in order to understand the dynamics of HIV infection (Ali & Zaman, 2016; Ali, Zaman, & Algahtani, 2016; Perelson & Nelson, 1999) and optimal control methods have been applied to the derivation of optimal therapies for this HIV infection
Lenhart, and McNally (1998) used an optimal control which represents the percentage effect the chemotherapy has on the fundamental interaction of the CD4T cells with the virus
Summary
Human immuno deficiency virus (HIV-1) is a lentivirus that causes acquired immuno deficiency syndrome (AIDS), a condition in humans in which the immune system gets to fail, leading to life-threatening opportunistic infections. Infection with HIV-1 occurs by the transfer of blood, semen, vaginal fluid, or breast milk. Within these bodily fluids, HIV-1 is present as both free virus particles and virus within infected immune cells. Butler, Kirschner, and Lenhart (1997) used a single control representing the percentage effect the chemotherapy has on viral infectivity (this would simulate a drug such as AZT). Fister, Lenhart, and McNally (1998) used an optimal control which represents the percentage effect the chemotherapy has on the fundamental interaction of the CD4T cells with the virus. The physical meaning of our control problem is to minimize the infected cells measure and free virus particles amount and maximize the healthy cells density in blood by implementing the two control variables
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