Model-free based control of a HIV/AIDS prevention model

TL;DR

This paper introduces a real-time, model-free control method for HIV/AIDS prevention that effectively reduces infection numbers without requiring explicit system equations, outperforming traditional optimal control techniques.

Contribution

The paper presents a novel model-free control algorithm for epidemic management, enabling real-time feedback control without explicit system models, specifically applied to HIV prevention.

Findings

The model-free control reduces HIV infection numbers asymptotically.

It maintains PrEP medication below a fixed threshold.

It outperforms classical optimal control in simulations.

Abstract

Controlling an epidemiological model is often performed using optimal control theory techniques for which the solution depends on the equations of the control system, objective functional and possible state and/or control constraints. In this paper, we propose a model-free control approach based on an algorithm that operates in 'real-time' and drives the state solution according to a direct feedback on the state solution that is aimed to be minimized, and without knowing explicitly the equations of the control system. We consider a concrete epidemic problem of minimizing the number of HIV infected individuals, through the preventive measure pre-exposure prophylaxis (PrEP) given to susceptible individuals. The solutions must satisfy control and mixed state-control constraints that represent the limitations on PrEP implementation. Our model-free based control algorithm allows to close the loop between the number of infected individuals with HIV and the supply of PrEP medication 'in real time', in such manner that the number of infected individuals is asymptotically reduced and the number of individuals under PrEP medication is below a fixed constant value. We prove the efficiency of our approach and compare the model-free control solutions with the ones obtained using a classical optimal control approach via Pontryagin maximum principle. The performed numerical simulations allow us to conclude that the model-free based control strategy highlights new and interesting performances compared with the classical optimal control approach.