Mathematics in Engineering

2021, Issue 2: 1-39. doi: 10.3934/mine.2021013
Research article

A simple SIR model with a large set of asymptomatic infectives

• 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.

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

Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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