From the hospital scale to nationwide: observability and identification of models for the COVID-19 epidemic waves

Two mathematical models of the COVID-19 dynamics are considered as the health system in some country consists in a network of regional hospital centers. The first macroscopic model for the virus dynamics at the level of the general population of the country is derived from a standard SIR model. The second local model refers to a single node of the health system network, i.e. it models the flows of patients with a smaller granularity at the level of a regional hospital care center for COVID-19 infected patients. Daily (low cost) data are easily collected at this level, and are worked out for a fast evaluation of the local health status thanks to control systems methods. Precisely, the identifiability of the parameters of the hospital model is proven and thanks to the availability of clinical data, essential characteristics of the local health status are identified. Those parameters are meaningful not only to alert on some increase of the infection, but also to assess the efficiency of the therapy and health policy.