Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

Zachary Abernathy,Andrew Grant,Paul Hazelton,Kristen Abernathy

doi:10.3390/mca26040077

Abstract

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

Highlights

Uncovering a functional cure or new preventative methods for the Human Immunodeficiency Virus (HIV) remains a challenge and focus of medical research
In the search for a functional cure that would alleviate the need for lifelong Antiretroviral therapy (ART) medication, recent studies suggested the usage of other methods such as gene therapy and latency reversing agents to help overcome the limitations of ART treatments [1]
For a combination treatment strategy, we find that using upper limits for the latencyreversing agents (LRAs) activation rate of α = 1.8 and ART removal rate of c = 1 reduces the effectiveness of gene therapy required to achieve R0( f ) < 1 to f > 0.8150

Summary

Introduction

Uncovering a functional cure or new preventative methods for the Human Immunodeficiency Virus (HIV) remains a challenge and focus of medical research. Though ART is effective at reducing the viral load to undetectable levels, even short lapses in treatment grant the virus the capability to rapidly rebound within weeks [1]. This can be attributed to the presence of a minute number of latently infected cells that store the genetic information of HIV yet are not actively replicating virions, evading typical ART strategies. In the search for a functional cure that would alleviate the need for lifelong ART medication, recent studies suggested the usage of other methods such as gene therapy and latency reversing agents to help overcome the limitations of ART treatments [1]

Objectives

Results

Conclusion