A simple SIR model with a large set of asymptomatic infectives

Gaeta, Giuseppe

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. In the second part of the note, we apply our model to the COVID-19 epidemics in Northern Italy, by numerical simulations based on estimate of certain parameters on the basisof medical evidence, and on fit of the other parameters from data on the first decade of March; the simulations reproduce quite satisfactorily the developements in the subsequent week, at difference with the standard SIR model. Our simulations show that if no actions were taken, the estimates based on this model would be about one third of those based on the SIR model as far as the height of the epidemic peak is concerned, and about half for what concerns the time scale of the epidemics. Moreover, the model suggests that an overwhelming part of the population would be in contact with the virus, most of them with no or very little symptoms. We also consider the situation in which the restrictive measures are taken into account by a"reduction factor", and discuss on the one hand how a prompt isolation of asymptomatic infectives would change the dynamics in this framework, and on the other what the time-scale could be in this context; this both in the"mitigation"scenario, in which the measures taken only reduce the epidemic, and in the"eradication"one, in which the measures raise sufficiently the epidemc threshold, as it appears to have happened in China.