Geophysical Recipe to Model the Covid-19 Epidemic

The coronavirus pneumonia epidemic, caused by SARS-CoV-2, was classified by the World Health Organization as a public health emergency of international concern on January 30th, 2020. The new SARS-CoV-2 was named coronavirus disease 2019 (COVID-19). Countries have reacted with different actions to control the source of infection, to inhibit the way of transmission and to protect the susceptible population. Italy has been strongly impacted by the diffusion of the contagion with about 30000 fatalities at mid-May 2020. The SEIR (Susceptible-Exposed-Infectious-Removed) model predicts the time-evolution of the epidemic phenomenon, based on the analysis of the infection and recovery rates. The prediction is based on the solution of a system of differential equations, usually solved according to a deterministic method. We propose a probabilistic approach, often used in geophysics, to solving the SEIR model of COVID19 epidemic diffusion in Italy and in its most impacted northern regions. Particularly, we solve the differential equations of the SEIR model by adopting a metaheuristic method, the Particle Swarm Optimization (PSO) algorithm, belonging to the family of computational swarm intelligence (Kennedy and Eberhart, 1995). The similarities with geophysical problems are many: the geophysical measures are replaced by official data on the spread of the infection, there is a consolidated predictive model and the goal is to estimate the model coefficients, in order to satisfy the experimental data. Like the geophysical inverse problem, the SEIR differential equations represent an ill-posed problem, whose solution is not unique. The advantage of the PSO approach is that the adaptive exploration of the space domain of the solutions decreases the risk of being trapped into a local minimum and it iteratively searches for the global minimum as the final solution. Moreover, the PSO method provides several scenarios so that the a-posteriori reliability of the model-solution can be evaluated (Godio and Santilano, 2018). The modelling was carried out by using observed data up to the mid of April with a 30-day prediction.