Optimal Resource Allocation for Fast Epidemic Monitoring in Networked Populations

The COVID-19 pandemic highlighted the fragility of the world in addressing a global health threat. The availableresources of the pre-pandemic national health systems were inadequate to cope with the huge number ofinfected subjects needing health care and with the rapidity of the infection spread characterizing the COVID-19outbreak. Indeed, an adequate allocation of the resources could produce in principle a strong reduction of theinfection spread and of the hospital burden, preventing the collapse of the health system. In this work, takinginspiration from the COVID-19 and the difficulties in facing the emergency, an optimal problem of resourceallocation is formulated on the basis of an ODE multi-group model composed by a network of SEIR-like submodels.The multi-group structure allows to differentiate the epidemic response of different populations or ofvarious subgroups in the same population. In fact, an epidemic does not affect all populations in the same way,and even within the same population there can be epidemiological differences, like the susceptibility to thevirus, the level of infectivity of the infectious subjects and the recovery from the disease. The subgroups areselected within the total population based on some peculiar characteristics, like for instance age, work, socialcondition, geographical position, etc., and they are connected by a network of contacts that allows the viruscirculation within and among the groups. The proposed optimal control problem aims at defining a suitablemonitoring campaign that is able to optimally allocate the number of swab tests between the subgroups of thepopulation in order to reduce the number of infected patients (especially the most fragile ones) so reducing theepidemic impact on the health system. The proposed monitoring strategy can be applied both during the mostcritical phases of the emergency and in endemic conditions, when an active surveillance could be crucial forpreventing the contagion rise.