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Contact Tracing (CT) is one of the measures taken by government and healthofficials to mitigate the spread of the novel coronavirus. In this paper, weinvestigate its efficacy by developing a compartmental model for assessing itsimpact on mitigating the spread of the virus. We describe the impact on thereproduction number ${\mathcal{R}_0}$ of COVID-19. In particular, we discussthe importance and relevance of parameters of the model such as the number ofreported cases, effectiveness of tracking and monitoring policy, and thetransmission rates to contact tracing. We describe the terms "perfecttracking", "perfect monitoring" and "perfect reporting" to indicate that tracedcontacts will be tracked while incubating, tracked contacts are efficientlymonitored so that they do not cause secondary infections, and all infectedpersons are reported, respectively. We consider three special scenarios: (1)perfect monitoring and perfect tracking of contacts of a reported case, (2)perfect reporting of cases and perfect monitoring of tracked reported cases and(3) perfect reporting and perfect tracking of contacts of reported cases.Furthermore, we gave a lower bound on the proportion of contacts to be tracedto ensure that the effective reproduction, ${\mathcal{R}_c}$, is below one anddescribe ${\mathcal{R}_c}$ in terms of observable quantities such as theproportion of reported and traced cases. Model simulations using the COVID-19data obtained from John Hopkins University for some selected states in the USsuggest that even late intervention of CT may reasonably reduce thetransmission of COVID-19 and reduce peak hospitalizations and deaths.

How Efficient is Contact Tracing in Mitigating the Spread of Covid-19? A Mathematical Modeling Approach