The multi-compartment si(Rd) model with regime switching: An application to covid-19 pandemic

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Abstract

We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.

Original languageEnglish
Article number2427
JournalSymmetry
Volume13
Issue number12
DOIs
Publication statusPublished - 15 Dec 2021

Keywords

  • Infection modelling
  • Real data
  • Regime switching in ordinary differential equations
  • SARS-COVID-19
  • SIR type models

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