Epidemiological measures for assessing the dynamics of the SARS-CoV-2-outbreak: Simulation study about bias by incomplete case-detection

Abstract

During the SARS-CoV-2 outbreak, several epidemiological measures, such as cumulative case-counts (CCC), incidence rates, effective reproduction numbers (Reff) and doubling times, have been used to inform the general public and to justify interventions such as lockdown. It has been very likely that not all infectious people have been identified during the course of the epidemic, which lead to incomplete case-detection. We compare CCC, incidence rates, Reff and doubling times in the presence of incomplete case-detection. For this, an infection-age-structured SIR model is used to simulate a SARS-CoV-2 outbreak followed by a lockdown in a hypothetical population. Different scenarios about temporal variations in case-detection are applied to the four measures during outbreak and lockdown. The biases resulting from incomplete case-detection on the four measures are compared in terms of relative errors. CCC is most prone to bias by incomplete case-detection in all of our settings. Reff is the least biased measure. The possibly biased CCC may lead to erroneous conclusions in cross-country comparisons. With a view to future reporting about this or other epidemics, we recommend including and placing an emphasis on Reff in those epidemiological measures used for informing the general public and policy makers.

Fig 1. SIR model in infectious disease epidemiology.

The population under consideration is divided into three states susceptible (prone to be infected), infected and removed (recovered or dead).

Fig 2. Components of the transmission rate β.

The left panel shows the time dependent part β_t of the transmission rate β during three phases of the pandemic: before lockdown at t = 25 (days), installation of lockdown (from t = 25 to t = 30, between vertical dotted lines) and control of the disease (t > 30). The right panel shows the component β_τ of the transmission rate β as a function of the infection age τ. More details can be found in Section 4 of the S1 File.

Fig 3. Simulated case-detection ratios (CDRs).

CDRs during the pandemic in the four simulated scenarios A to D.

Fig 4. Work flow of the simulation.

Work flow for running the simulation and assessing the bias from incomplete case-detection.

Fig 5. Biases in the simulated scenarios.

Bias (relative error) of the four epidemiological measures in the four simulated scenarios A to D (indicated by the line type): Cumulative case count (top left), incidence rate (top right), effective reproduction number (bottom left) and doubling time (bottom right). A desirable zero bias is indicated by a horizontal solid line at value 0.