Dr. Kristen Abernathy & Dr. Zach Abernathy
College of Arts and Sciences
Department of Mathematics
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In this project, we study the dynamics of HIV under gene therapy and latency reversing agents. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of the basic reproductive ratio. 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 conclude with findings that suggest a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone.
Grant, Andrew B. and Hazelton, Paul, "Optimal control of an HIV model with gene therapy and latency reversing agents" (2020). S.U.R.E Posters. 8.