The Stochastic Approach for SIR Epidemic Models: Do They Help to Increase Information from Raw Data?

The recent outbreak of COVID-19 underlined the need for a fast and trustworthy methodology to identify the features of a pandemic, whose early identification is of help for designing non-pharmaceutical interventions (including lockdown and social distancing) to limit the progression of the disease. A common approach in this context is the parameter identification from deterministic epidemic models, which, unfortunately, cannot take into account the inherent randomness of the epidemic phenomenon, especially in the initial stage; on the other hand, the use of raw data within the framework of a stochastic model is not straightforward. This note investigates the stochastic approach applied to a basic SIR (Susceptible, Infected, Recovered) epidemic model to enhance information from raw data generated in silico. The stochastic model consists of a Continuous-Time Markov Model, describing the epidemic outbreak in terms of stochastic discrete infection and recovery events in a given region, and where independent random paths are associated to different provinces of the same region, which are assumed to share the same set of model parameters. The estimation procedure is based on the building of a loss function that symmetrically weighs first-order and second-order moments, differently from the standard approach that considers a highly asymmetrical choice, exploiting only first-order moments. Instead, we opt for an innovative symmetrical identification approach which exploits both moments. The new approach is specifically proposed to enhance the statistical information content of the raw epidemiological data.