On realized serial and generation intervals given control measures: The COVID-19 pandemic case

Abstract

The SARS-CoV-2 pathogen is currently spreading worldwide and its propensity for presymptomatic and asymptomatic transmission makes it difficult to control. The control measures adopted in several countries aim at isolating individuals once diagnosed, limiting their social interactions and consequently their transmission probability. These interventions, which have a strong impact on the disease dynamics, can affect the inference of the epidemiological quantities. We first present a theoretical explanation of the effect caused by non-pharmaceutical intervention measures on the mean serial and generation intervals. Then, in a simulation study, we vary the assumed efficacy of control measures and quantify the effect on the mean and variance of realized generation and serial intervals. The simulation results show that the realized serial and generation intervals both depend on control measures and their values contract according to the efficacy of the intervention strategies. Interestingly, the mean serial interval differs from the mean generation interval. The deviation between these two values depends on two factors. First, the number of undiagnosed infectious individuals. Second, the relationship between infectiousness, symptom onset and timing of isolation. Similarly, the standard deviations of realized serial and generation intervals do not coincide, with the former shorter than the latter on average. The findings of this study are directly relevant to estimates performed for the current COVID-19 pandemic. In particular, the effective reproduction number is often inferred using both daily incidence data and the generation interval. Failing to account for either contraction or mis-specification by using the serial interval could lead to biased estimates of the effective reproduction number. Consequently, this might affect the choices made by decision makers when deciding which control measures to apply based on the value of the quantity thereof.

Fig 1. Infectivity measure.

Infectivity Measure over the infectious period (blue line) and day of symptom onset (dashed orange line).

Fig 2. Control measure—Time to diagnosis.

(A) Average and 95% confidence intervals for the mean realized serial and generation intervals and (B) associated realized standard deviations (B) for diagnosis before the onset of symptom (Before Symptom), coincident with symptom onset (Upon Symptoms) and gamma-distributed delays to diagnosis (Gamma distr.—Baseline).

Fig 3. Undiagnosed population—Prevalence.

(A) Average and 95% confidence intervals for the mean realized serial and generation intervals and (B) associated realized standard deviations when all the infectives are diagnosed (0%), 31% of infectives are not diagnosed (31%) and 86% of the infectives are not diagnosed.

Fig 4. Difference between mean serial and generation intervals and realized incubation periods.

(A) Difference between mean serial and generation interval and (B) between the realized incubation period of infectors and infectee when the time to diagnosis varies among: 1 day before symptom onset (BeforeSymptom), at symptom onset (UponSymptom), after a gamma-delay from symptom onset (AfterSymptom). (C) Probability that infectious individuals make at least one effective contact during their infectious period, for a varying incubation period length.