A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures

SIMPLE SUMMARY: Two different mathematical models are proposed in order to describe the spreading of COVID-19 through the different provinces and regions of Spain and Italy. The models will divide the populations of both countries in three categories: the subpopulation susceptible to be infected of the disease, the subpopulation which is already infected and thus is infectious, and the subpopulation which has already recovered from the disease so is considered immune. The transmission rate is calculated within these models while considering the different locations and, more importantly, the lockdown measures implemented during 2020. The efficiency of these measures is compared between the areas of infection and the different levels of lockdown. ABSTRACT: Two discrete mathematical SIR models (Susceptible-Infectious-Recovered) are proposed for modelling the propagation of the SARS-CoV-2 (COVID-19) through Spain and Italy. One of the proposed models is delay-free while the other one considers a delay in the propagation of the infection. The objective is to estimate the transmission, also known as infectivity rate, through time taking into account the infection evolution data supplied by the official health care systems in both countries. Such a parameter is estimated through time at different regional levels and it is seen to be strongly dependent on the intervention measures such as the total (except essential activities) or partial levels of lockdown. Typically, the infectivity rate evolves towards a minimum value under total lockdown and it increases again when the confinement measures are partially or totally removed.