Abstract
<p style='text-indent:20px;'>We consider a compartment mathematical model for a SARS-CoV-2 epidemic involving five classes considered to be essential to depict the feature of the epidemic. A first goal is to approach by an optimal control technique the identification of two essential transmission rates in the model, that is the average number of individuals infected in unit time by an infected symptomatic and by an asymptomatic, respectively. These are provided by the first-order conditions of optimality corresponding to the minimization problem introduced for formulating the identification objective. The discussion of the asymptotic stability of the system done for the case when life immunity is gained reveals an asymptotic extinction of the disease, with a well determined reproduction number.</p>
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