Mathematical Model for an Effective Management of HIV Infection

Abstract

Human immunodeficiency virus infection destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney, and heart, and causes death. Unfortunately, this infectious disease currently has no cure; however, there are effective retroviral drugs for improving the patients' health conditions but excessive use of these drugs is not without harmful side effects. This study presents a mathematical model with two control variables, where the uninfected CD4+T cells follow the logistic growth function and the incidence term is saturated with free virions. We use the efficacy of drug therapies to block the infection of new cells and prevent the production of new free virions. Our aim is to apply optimal control approach to maximize the concentration of uninfected CD4+T cells in the body by using minimum drug therapies. We establish the existence of an optimal control pair and use Pontryagin's principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically to obtain the optimal control pair. Finally, we discuss the numerical simulation results which confirm the effectiveness of the model.

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

“…The dynamical behavior of the population model with time delay has now become a hot topic of research [ 2 ]. Ogunlaran et al [ 3 ] presented an effective strategy to fight against HIV infection in humans by using the compartment models. Duffin et al [ 4 ] studied the dynamics of the immune deficiency virus of the complete course of infection.…”

Mathematical Transmission of HIV/AID with Early Treatment

“…HIV causes a reduction in the number of functional CD4 + T cells thereby making the body unable to fight and prevent cell infections. A lot of mathematical models have been formulated to study the interactions between CD4 + T cells and HIV [3][4][5][6].…”

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions

“…Mathematical modelling provides a powerful tool to describe and analyse many engineering and physical problems. It has also been used to describe some biological processes such as heart beats [15], diffusion of drugs [15], hepatitis C virus [16], management of HIV infection [17], treatment of diabetes [18], clearing the antibiotic resistant infection [19], aortic aneurysm formation [20], and tumor growth and cancer treatment. Studies in the field of cancer biology focus on developing suitable mathematical models involving quantitative approaches to understand various aspects of tumor growth and the response of cancer cells to clinical interventions.…”