Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic

Abstract

Objectives: With the declining numbers of coronavirus disease 2019 (COVID-19) cases in the state of São Paulo, Brazil, social distancing measures have gradually been lifted. However, the risk of a surge in the number of cases cannot be overlooked. Even with the adoption of nonpharmaceutical interventions, such as restrictions on mass gatherings, wearing of masks, and complete or partial closure of schools, other public health measures may help control the epidemic. We aimed to evaluate the impact of the contact tracing of symptomatic individuals on the COVID-19 epidemic regardless of the use of diagnostic testing.

Methods: We developed a mathematical model that includes isolation of symptomatic individuals and tracing of contacts to assess the effects of the contact tracing of symptomatic individuals on the COVID-19 epidemic in the state of São Paulo.

Results: For a selection efficacy (proportion of isolated contacts who are infected) of 80%, cases and deaths may be reduced by 80% after 60 days when 5000 symptomatic individuals are isolated per day, each of them together with 10 contacts. On the other hand, for a selection efficacy of 20%, the number of cases and deaths may be reduced by approximately 40% and 50%, respectively, compared with the scenario in which no contact-tracing strategy is implemented.

Conclusion: Contact tracing of symptomatic individuals may potentially be an alternative strategy when the number of diagnostic tests available is not sufficient for massive testing.

Figure 1. Schematic representation of the model compartments.

Figure 2. Cumulative numbers of reported cases and deaths, number of ICU patients (black dots), and the corresponding fitted model (blue lines). The solid lines and shaded area correspond to median values and 95% probability intervals, respectively.

Figure 3. Cumulative number of cases as a function of time for different numbers of isolated symptomatic individuals per day, isolated contacts, and selection efficacies of (a) 20% and (b) 80%. The solid black line shows the effect that would be observed if no isolation strategy is used.

Figure 4. Cumulative number of deaths as a function of time for different numbers of isolated symptomatic individuals per day, isolated contacts, and selection efficacies of (a) 20% and (b) 80%. The solid black line shows the effect that would be observed if no isolation strategy is used.

Figure 5. Efficacy of the CT strategy, defined as 1 minus the ratio of the number of cases under a CT strategy divided by the number of cases without CT strategy, as a function of time for different combinations of symptomatic individuals isolated per day, number of isolated contacts, and selection efficacies of (a) 20% and (b) 80%.

Figure 6. Cumulative number of isolated individuals as a function of time for different combinations of isolated symptomatic individuals per day, isolated contacts, and selection efficacies of (a) 20% and (b) 80%.

Figure 7. Partial rank correlation coefficients for the number of cumulative cases as the output variable and the following input variables: number of isolated symptomatic individuals (ε_I); selection efficacy (eff); number of contacts (c); initial proportion of infected (f_I), susceptible (f_S), and recovered (f_R) individuals; and asymptomatic-to-symptomatic ratio (r_AS).