Estimation of introduction and transmission rates of SARS-CoV-2 in a prospective household study

Abstract

Household studies provide an efficient means to study transmission of infectious diseases, enabling estimation of susceptibility and infectivity by person-type. A main inclusion criterion in such studies is usually the presence of an infected person. This precludes estimation of the hazards of pathogen introduction into the household. Here we estimate age- and time-dependent household introduction hazards together with within household transmission rates using data from a prospective household-based study in the Netherlands. A total of 307 households containing 1,209 persons were included from August 2020 until March 2021. Follow-up of households took place between August 2020 and August 2021 with maximal follow-up per household mostly limited to 161 days. Almost 1 out of 5 households (59/307) had evidence of an introduction of SARS-CoV-2. We estimate introduction hazards and within-household transmission rates in our study population with penalized splines and stochastic epidemic models, respectively. The estimated hazard of introduction of SARS-CoV-2 in the households was lower for children (0-12 years) than for adults (relative hazard: 0.62; 95%CrI: 0.34-1.0). Estimated introduction hazards peaked in mid October 2020, mid December 2020, and mid April 2021, preceding peaks in hospital admissions by 1-2 weeks. Best fitting transmission models included increased infectivity of children relative to adults and adolescents, such that the estimated child-to-child transmission probability (0.62; 95%CrI: 0.40-0.81) was considerably higher than the adult-to-adult transmission probability (0.12; 95%CrI: 0.057-0.19). Scenario analyses indicate that vaccination of adults can strongly reduce household infection attack rates and that adding adolescent vaccination offers limited added benefit.

Fig 1. Lexis diagram of the study population.

Lines show households from the date of inclusion in the study to infection of the first household member (brown dots), completion of the inclusion period without infection (blue dots at time in study of 161 days) or dropout (blue dots with time in study shorter than 161 days). Date of inclusion of the first household was 24 August 2020, and last date of the study was 29 July 2021.

Fig 2. Estimates of the household introduction hazard for adults.

Shown are the posterior median of the introduction hazard per person (blue line) with associated 95% credible envelope (gray area). Household introduction hazards of children and adolescents are obtained by multiplication of the hazard for adults with the relative introduction hazards for children and adolescents. Also presented are the daily number of hospitalisations (yellow dots). To remove weekday effects the number of hospitalisations are represented by a 7-day moving average centered around the current day.

Fig 3. Estimated person-to-person transmission probabilities.

Shown are posterior medians of the infectious contact probabilities, i.e. the probabilities that a transmission event would have occurred from an infected person over its infectious period if the contacted person had not already been infected by another person. Infectious contact probabilities are calculated from the person-to-person transmission rates per infectious period β_ij and the Laplace transform of the scaled infectious period distribution: $\mathbb{P}\left(i\text{infected}\text{by}j\right)=1-{(1+\frac{{\beta }_{ij}}{\alpha })}^{\alpha }$, where α = 50 is the shape parameter of the infectious period probability distribution.

Fig 4. Posterior predictive checks in common households of size four, containing two adults and two children (cf. Table 1).

Shown are the fractions of the households with a given number of secondary infections (black dots) with exact binomial confidence ranges (lines) stratified by primary case (child or adult), together with the corresponding posterior probabilities of secondary cases.

Fig 5. Estimates of the probability of infection of an adult for different household compositions, primary infection (child, adolescent, adult), and vaccination strategies.

(A) no vaccination, (B) vaccination of adults, and (c) vaccination of adults and adolescents (C). Plots represent the posterior distribution (1,000 samples), and black dots indicate posterior medians. Vaccine efficacy for susceptibility is VE_S = 0.9. Notice the difference in scale on the y-axis between (A) and (B)-(C).