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

Abstract : Controlling an epidemiological model is often performed using optimal control theory techniques for which the solution depends on the equations of the controlled 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 controlled 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 a manner that the number of infected individuals is asymptotically reduced and the number of individuals under PrEP medication remains 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.
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https://hal.archives-ouvertes.fr/hal-03453203
Contributor : Loïc MICHEL Connect in order to contact the contributor
Submitted on : Saturday, November 27, 2021 - 10:57:26 PM
Last modification on : Friday, August 5, 2022 - 2:54:51 PM

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Loïc Michel, Cristiana Silva, Delfim Torres. Model-free based control of a HIV/AIDS prevention model. Mathematical Biosciences and Engineering, AIMS Press, In press, 19 (1), pp.759-774. ⟨10.3934/mbe.2022034⟩. ⟨hal-03453203⟩

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