Spread/removal parameter identification in a SIR epidemic model

The outbreak of the COVID-19 pandemic in 2020 has renewed the interest in epidemic models, striving to infer fruitful information from the available data. The whole world has faced the urge for a sudden comprehension of the spread of the virus and different approaches are nowadays available to cope with the inherent stochasticity of the phenomenon, the fragmentary fashion of usable data and the identifiability problems related to them. This work proposes a novel approach to identify a basic SIR epidemic model with time-varying parameters, where Susceptibles, Infected and Removed (i.e. recovered and deceased) people are accounted for. The standard deterministic approach trivially exploits the average evolution only, disregarding any other information carried out by the epidemiological data. Instead, by suitably formulating a discrete stochastic framework for the mathematical model, the identification task is carried out by exploiting raw data to compute the higher-order moments evolution and involve them in the identification task. The methodology is applied to the Italian COVID-19 case study and shows promising results obtained according to rough epidemic data, essentially provided by the overall amount of contaminated individuals.