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In this article we propose a compartmental model for the dynamics ofCoronavirus Disease 2019 (COVID-19). We take into account the presence ofasymptomatic infections and the main policies that have been adopted so far tocontain the epidemic: isolation (or social distancing) of a portion of thepopulation, quarantine for confirmed cases and testing. We model isolation byseparating the population in two groups: one composed by key-workers that keepworking during the pandemic and have a usual contact rate, and a second groupconsisting of people that are enforced/recommended to stay at home. We refer toquarantine as strict isolation, and it is applied to confirmed infected cases.In the proposed model, the proportion of people in isolation, the level ofcontact reduction and the testing rate are control parameters that can vary intime, representing policies that evolve in different stages. We obtain anexplicit expression for the basic reproduction number $\mathcal{R}_0$ in termsof the parameters of the disease and of the control policies. In this way wecan quantify the effect that isolation and testing have in the evolution of theepidemic. We present a series of simulations to illustrate different realisticscenarios. From the expression of $\mathcal{R}_0$ and the simulations weconclude that isolation (social distancing) and testing among asymptomaticcases are fundamental actions to control the epidemic, {and the stricter thesemeasures are and the sooner they are implemented,} the more lives can be saved.Additionally, we show that people that remain in isolation significantly reducetheir probability of contagion, so risk groups should be recommended tomaintain a low contact rate during the course of the epidemic.

A model for COVID-19 with isolation, quarantine and testing as control measures