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 available resources of the pre-pandemic national health systems were inadequate to cope with the huge number of infected subjects needing health care and with the rapidity of the infection spread characterizing the COVID-19 outbreak. Indeed, an adequate allocation of the resources could produce in principle a strong reduction of the infection spread and of the hospital burden, preventing the collapse of the health system. In this work, taking inspiration from the COVID-19 and the difficulties in facing the emergency, an optimal problem of resource allocation 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 of various 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 the virus, the level of infectivity of the infectious subjects and the recovery from the disease. The subgroups are selected within the total population based on some peculiar characteristics, like for instance age, work, social condition, geographical position, etc., and they are connected by a network of contacts that allows the virus circulation within and among the groups. The proposed optimal control problem aims at defining a suitable monitoring campaign that is able to optimally allocate the number of swab tests between the subgroups of the population in order to reduce the number of infected patients (especially the most fragile ones) so reducing the epidemic impact on the health system. The proposed monitoring strategy can be applied both during the most critical phases of the emergency and in endemic conditions, when an active surveillance could be crucial for preventing the contagion rise.