Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks; an application to COVID-19

We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases. We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing. The model is fitted to data reported for the early spread of COVID-19 in South Korea, Brazil, and Venezuela. The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries. Using the fitted values, we estimate the effective reproduction number $R_e$ and investigate its responses to varied control scenarios of contact tracing. Alongside the positivity of solutions, and a stability analysis of the disease-free equilibrium are provided.