What has gone around may come back around: reinfection in the extended stochastic multi-region control of infodemics and seasonal coronaviruses

Abstract

In this paper, we study an optimal control approach against seasonal coronaviruses by adding terms of reinfection to dynamics of the optimization constraint and which is mainly defined by a stochastic multi-region SIRS control differential system. In fact, in addition to the problem of infodemics spread, we take into account that protective immunity against such viruses is short-lasting as there is a risk of reinfection, while the immunization process control against the epidemic could be realized through any available actions either by following those who suggest long-term awareness in response of any surprising COVID-19-like in future or those who recommend some potentially effective medical intervention such as vaccines or antiviral drugs, while other strategists, especially in times of global epidemic emergencies, could not see any alternative approach to the closure policies in order to limit the movement of infected people. In front of all these different possibilities to intervene, we let our control functions open to define any of such considerations and we analyze some of their advantages on preventing the viruses spread through different numerical scenarios associated to a boolean variable whose values directly define the cases of uncontrolled and controlled regions but being interconnected by the factor of mobility.