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arXiv · 2304.11114

Optimal control of a reaction-diffusion model related to the spread of COVID-19

Pierluigi Colli·Gianni Gilardi·Gabriela Marinoschi·Elisabetta Rocca
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Abstract

This paper is concerned with the well-posedness and optimal control problem of a reaction-diffusion system for an epidemic Susceptible-Infected-Recovered-Susceptible (SIRS) mathematical model in which the dynamics develops in a spatially heterogeneous environment. Using as control variables the transmission rates $u_{i}$ and $u_{e}$ of contagion resulting from the contact with both asymptomatic and symptomatic persons, respectively, we optimize the number of exposed and infected individuals at a final time $T$ of the controlled evolution of the system. More precisely, we search for the optimal $u_{i}$ and $u_{e}$ such that the number of infected plus exposed does not exceed at the final time a threshold value $\Lambda$, fixed a priori. We prove here the existence of optimal controls in a proper functional framework and we derive the first-order necessary optimality conditions in terms of the adjoint variables.

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Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. 2023-04-21. Optimal control of a reaction-diffusion model related to the spread of COVID-19. https://arxiv.org/abs/2304.11114

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