Abstract
Simple SummaryTwo 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.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.
Highlights
The advance of the disease caused by the corona virus SARS-CoV-2 (COVID-19)surprised world population in the early 2020 as its rapid spread and virulence affected the lives of millions of people and caused thousands of deaths
Covid-19 data are available from 24 February for Italy, and the data available for Spain is from 1 January, but we have decided that the first analysis period will be from
We will show the parameter β adjusted by linear regression for the different regions of Spain and Italy based on the SIR models which derive the Equations (8)
Summary
The advance of the disease caused by the corona virus SARS-CoV-2 (COVID-19)surprised world population in the early 2020 as its rapid spread and virulence affected the lives of millions of people and caused thousands of deaths. While there is a great number of different models we can use to describe a disease like this [4,5,6], due to the limited data at the time of writing this paper, we have chosen a SIR model, which fits better the available data. The network of interactions that define the spread of an infectious disease is modelled with differential equations It involves different types of infected subpopulations, or susceptible to be infected [13,14,15], as well as the transitions
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