A simple SIR model with a large set of asymptomatic infectives

Giuseppe Gaeta; Giuseppe Gaeta

doi:10.3934/mine.2021013

Mathematics in Engineering

2021, Volume 3, Issue 2: 1-39. doi: 10.3934/mine.2021013

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Research article

A simple SIR model with a large set of asymptomatic infectives

Giuseppe Gaeta ^{1,2
,
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1.
Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, I-20133 Milano, Italy
2.
SMRI, 00058 Santa Marinella, Italy

Received: 19 May 2020 Accepted: 23 May 2020 Published: 01 June 2020

There is increasing evidence that one of the most difficult problems in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives. We develop a SIR-type model taking into account the presence of asymptomatic, or however undetected, infective, and the substantially long time these spend being infective and not isolated. We discuss how a SIR-based prediction of the epidemic course based on early data but not taking into account the presence of a large set of asymptomatic infectives would give wrong estimate of very relevant quantities such as the need of hospital beds, the time to the epidemic peak, and the number of people which are left untouched by the first wave and thus in danger in case of a second epidemic wave. In the second part of the note, we apply our model to the COVID-19 epidemics in Northern Italy. We obtain a good agreement with epidemiological data; according to the best fit of epidemiological data in terms of this model, only 10% of infectives in Italy is symptomatic.
- COVID,
- epidemiological models,
- SIR model,
- asymptomatic transmission,
- nonlinear dynamics
Citation: Giuseppe Gaeta. A simple SIR model with a large set of asymptomatic infectives[J]. Mathematics in Engineering, 2021, 3(2): 1-39. doi: 10.3934/mine.2021013

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Abstract

There is increasing evidence that one of the most difficult problems in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives. We develop a SIR-type model taking into account the presence of asymptomatic, or however undetected, infective, and the substantially long time these spend being infective and not isolated. We discuss how a SIR-based prediction of the epidemic course based on early data but not taking into account the presence of a large set of asymptomatic infectives would give wrong estimate of very relevant quantities such as the need of hospital beds, the time to the epidemic peak, and the number of people which are left untouched by the first wave and thus in danger in case of a second epidemic wave. In the second part of the note, we apply our model to the COVID-19 epidemics in Northern Italy. We obtain a good agreement with epidemiological data; according to the best fit of epidemiological data in terms of this model, only 10% of infectives in Italy is symptomatic.

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