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 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.
Highlights
There is increasing evidence that one of the main difficulties in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
We have investigated two questions: (A) How a reduction in the removal time for asymptomatic infectives, i.e. in τ = η−1, would affect – according to the A-SIR model – the dynamics and the basic epidemiological outcomes of it in the regime where the epidemic is taking place; (B) In the case r is small enough to make the population below the epidemic threshold, what are the basic epidemiological outcomes predicted by the model, again depending on various parameters including η
Motivated by the peculiar features of the COVID epidemics, we have considered a SIR-type model, called ASIR model, taking into account the presence of a large set of asymptomatic infectives
Summary
There is increasing evidence that one of the main difficulties in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. This comparison is made by means of numerical simulations for realistic values of the parameters, but with no reference yet to any concrete case. The symbol ⊙ will signal the end of a Remark
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