A mathematical modeling study of the effectiveness of contact tracing in reducing the spread of infectious diseases with incubation period

Abstract

In this work, we study an epidemic model with demography that incorporates some key aspects of the contact tracing intervention. We derive generic formulae for the effective reproduction number $R_e$ when contact tracing is employed to mitigate the spread of infection. The derived expressions are reformulated in terms of the initial reproduction number $R_0$ (in the absence of tracing), the number of traced cases caused by a primary untraced reported index case, and the average number of secondary cases infected by traced infectees during their infectious period. In parallel, under some restrictions, the local stability of the disease-free equilibrium is investigated. The model was fitted to data of Ebola disease collected during the 2014–2016 outbreaks in West Africa. Finally, numerical simulations are provided to investigate the effect of key parameters on $R_e$. By considering ongoing interventions, the simulations indicate whether contact tracing can suppress $R_e$ below unity, as well as identify parameter regions where it can effectively contain epidemic outbreaks when applied with a given level of efficiency.