We present an epidemiological model, which extend the classical SEIR model by accounting for the presence of asymptomatic individuals and the effect of isolation of infected individuals based on testing. Moreover, we introduce two types of home quarantine, namely gradual and abrupt one. We compute the equilibria of the new model and derive its reproduction number. Using numerical simulations we analyze the effect of quarantine and testing on the epidemic dynamic. Given a constraint that limits the maximal number of simultaneous active cases, we demonstrate that the isolation rate, which enforces this constraint, decreases with the increasing testing rate. Our simulations show that massive testing allows to control the infection spread using a much lower isolation rate than in the case of indiscriminate quarantining. Finally, based on the effective reproduction number we suggest a strategy to manage the epidemic. It consists in introducing abrupt quarantine as well as relaxing the quarantine in such a way that the epidemic remains under control and further waves do not occur. We analyze the sensitivity of the model dynamic to the quarantine size, timing and strength of the restrictions.

Department of Applied Mathematics and Statistics Faculty of Mathematics Physics and Informatics Comenius University Mlynská dolina 84248 Bratislava Slovakia

Faculty of Medicine Masaryk University Kamenice 753 5 625 00 Brno Czech Republic

Mathematical Institute of the Silesian University Na Rybníčku 1 746 01 Opava Czech Republic

University of Texas at Dallas 800 W Campbell Richardson TX 75080 USA

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