Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy

Abstract

In Italy, 128,948 confirmed cases and 15,887 deaths of people who tested positive for SARS-CoV-2 were registered as of 5 April 2020. Ending the global SARS-CoV-2 pandemic requires implementation of multiple population-wide strategies, including social distancing, testing and contact tracing. We propose a new model that predicts the course of the epidemic to help plan an effective control strategy. The model considers eight stages of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H) and extinct (E), collectively termed SIDARTHE. Our SIDARTHE model discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed individuals is important because the former are typically isolated and hence less likelyto spread the infection. This delineation also helps to explain misperceptions of the case fatality rate and of the epidemic spread. We compare simulation results with real data on the COVID-19 epidemic in Italy, and we model possible scenarios of implementation of countermeasures. Our results demonstrate that restrictive social-distancing measures will need to be combined with widespread testing and contact tracing to end the ongoing COVID-19 pandemic.

Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and applications

“…: Recovery rate of class I T (t) k 1 : Contact rate p : Proportion that a contact is su¢ cient enough to lead to transmission w : Transmission coe¢ cient for the infected classes : Recruitment rate into class S (t) 1 : Rate of vaccination…”

“…The consideration of these statistics prompted researchers from Turkey and South Africa to undertake research in di¤erent …elds of science, technology and engineering in the last 3 months, since their future is left uncertain. As the virologists are focusing their attention in developing a vaccine that could be used to prevent the spread of the deadly virus; mathematicians rely on modelling techniques to produce multi-scenarios models that could be utilized to foresee the future [1][2][3][4][5][6]. Therefore, as mathematicians our role is to use and apply mathematical tools, particularly mathematical models, on suggested scenarios that could be helpful in predicting the future.…”

Simplified model of Covid-19 epidemic prognosis under quarantine and estimation of quarantine effectiveness

“…Consequently, on the basis of eq. ( 3 ), the parameter of SIR model can be estimated as the number of new registered cases of infection to number of active cases ratio: ( 4 ) where is the rate of new infected cases ( 5 ) which can be estimated by counting new cases of infection, and usually is measured by number of registered new cases per time period ( 6 ) The number of daily new infected cases is defined as ( 7 ) So, expected number of new cases in next day could be predicted by the today number of active infected individuals multiplied by the infectious rate ( 8 ) In general, the infectious rate is time dependent and usually can be described by a complex function with additional parameters that must be daily calibrated according to last epidemiological data. Behaviour of the infectious rate during quarantine may differ in different countries, which reduces possibilities to build correct model of the infectious rate on the basis of epidemiological data from other countries.…”

“…Most popular epidemic dynamics models of Covid-19 are based on transmission model for a directly transmitted infectious disease, such as standard compartment models of disease SIR [5,6], or more advances derivates, such as SEIR and similar models [7][8][9][10]. Many of the models, which are used to forecast the COVID-19 epidemic, do not accurately capture the transient dynamics of epidemics; therefore, they give poor predictions of both the epidemic's peak and its duration [11], because calibration of parameters are based on dynamics of such non-reliable epidemiological data as number of active infectious cases.…”

Monitoring and Tracking the Evolution of a Viral Epidemic Through Nonlinear Kalman Filtering: Application to the Covid-19 Case

“…In this case, it is a matter of determining how the coefficients that define this equation evolve over time. In the case of epidemics, among the most popular models are those derived from the SIR (Susceptible-Infected-Recovered) model, [3], such as the one used for example in [4] to analyze the evolution of Covid-19 in Italy.…”