Managing virus propagation: A spatiotemporal inverse problem approach for controlling COVID-19 spread

In this work, we are interested in a spatiotemporal SIR mathematical model. We assume that the transmission rate [Formula: see text], which is a fundamental parameter of the model, is unknown. To reconstruct it, we base on an output of the system which is none other than the prevalence function [Formula: see text] (the density of infected people at time [Formula: see text] and in position [Formula: see text], where [Formula: see text] belongs to [Formula: see text] the considered country), the case where [Formula: see text] in which the sub-regions [Formula: see text] constitute a regional division of [Formula: see text] and [Formula: see text] the indicator function of the subset [Formula: see text] is also studied. With the parameter [Formula: see text] being the most important factor characterizing the propagation of the epidemic, we devote the second part of our work to optimize the controlled transmission rate [Formula: see text] and by minimizing an appropriate functional. To achieve this work, we use the forward–backward sweep method (FBSM) and Matlab to illustrate our theoretical results through examples.