Effects of Contact Tracing and Isolation Policies on Epidemic Dynamics

Compartmental models are widely used to analyse epidemiological dynamics, make predictions, and design intervention policies. The COVID-19 epidemic that emerged in December 2019 rapidly led to a global crisis, necessitating the development of various mathematical models to assist policymakers in recommending effective control strategies such as social distancing, contact tracing, and isolation. However, at the early stage of an epidemic, multiple factors may lead to the underestimation or overestimation of the basic reproduction number (R0), which plays a key role in determining the future trajectory of the epidemic and informing control strategies. The aim of this study is to analyse the impact of contact tracing and isolation policies on the potential underestimation of R0 values by employing a compartmental model of Susceptible-Exposed-Presymptomatic-Asymptomatic-Symptomatic-Reported (SEPADR). Theoretical and empirical results show that the implementation of contact tracing and isolation policies at the early stage of the epidemic leads to an underestimation of R0. Furthermore, mathematical relations between the exponential growth rate (r) and the basic reproduction number (R0) are approximately derived in the presence of a contact tracing and isolation policies, thereby generalizing the well-known r-R0 formulae. The long-term behaviour of the model is assessed by simulating various levels of efficiency in contact tracing and isolation policies.