Parameterization of control functions in the problem of modeling HIV infection therapy

D. S. Grebennikov^abc, A. I. Lyfenko^d, A. M. Timokhin^c, R. S. Savinkov^abc, G. A. Bocharov<sup>abc

a</sup> Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia
^b Branch of Moscow Center of Fundamental and Applied Mathematics at INM RAS, Moscow, Russia
^c I. M. Sechenov First Moscow State Medical University of the Ministry of Health of the Russian Federation (Sechenov University), Moscow, Russia
^d Lomonosov Moscow State University, Moscow, Russia

Abstract: Mathematical modeling is actively used to study the mechanisms of human immunodeficiency virus of type 1 (HIV-1) infection. Current HIV-1 therapy involves the regular, lifelong use of multiple antiviral drugs. However, this therapy is associated with varying degrees of side effects due to toxicity, drug interactions, resistance development, and high cost. Mathematical models of HIV-1 infection and optimal control methods can be used to develop effective regimens for applying multiple antiretroviral drugs, taking into account the immune status of HIV-1-infected patients. In this study, we identify the pharmacodynamic parameters of drugs based on a previously constructed stochastic model of the processes that determine viral replication in infected cells. We also study the efficiency of standard therapy for various HIV-1 infection regimens using a system dynamics model. The results of the study indicate the need to take into account differences in the body's response to therapy based on the criterion of efficiency, which actualizes the task of selecting individual therapy regimens using optimal control methods based on physiologically approved models of HIV-1 infection.

Keywords: mathematical modeling, HIV, parameter identification, pharmacodynamics, stochastic model, optimal control.

UDC: 517.929, 517.958

DOI: 10.22363/2413-3639-2025-71-4-585-603