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 methodologyto identify the features of a pandemic, whose early identification is of help for designingnon-pharmaceutical interventions (including lockdown and social distancing) to limit the progressionof the disease. A common approach in this context is the parameter identification from deterministicepidemic models, which, unfortunately, cannot take into account the inherent randomness of theepidemic phenomenon, especially in the initial stage; on the other hand, the use of raw data within theframework of a stochastic model is not straightforward. This note investigates the stochastic approachapplied to a basic SIR (Susceptible, Infected, Recovered) epidemic model to enhance information fromraw 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 agiven region, and where independent random paths are associated to different provinces of the sameregion, which are assumed to share the same set of model parameters. The estimation procedure isbased 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, exploitingonly first-order moments. Instead, we opt for an innovative symmetrical identification approachwhich exploits both moments. The new approach is specifically proposed to enhance the statisticalinformation content of the raw epidemiological data.