Analysis and optimal control of the impact of large people mass fluxes on epidemics spread

In the paper, the problem of the effects of people motion between two separated population under epidemic spread is considered, referring in particular the COVID-19 case. Model, analysis and design of an optimal switching control emulating the different steps of containment intervention strategies are presented. In particular, the case of an asymmetric people flow is studied, considering one small population receiving a people flow from a second one, more numerous. While the analysis is carried on in the general case, the hypothesis that the small outgoing flux of individuals from the largest population does not change its steady state conditions. After equilibrium and stability analysis of the proposed mathematical model, the philosophy of the switching control is discussed, the control is designed and the results of numerical simulations are reported to support the effectiveness of the proposed approach.