Estimating infectious disease parameters from data on social contacts and serological status

In dynamic models of infectious disease transmission, typically various mixing patterns are imposed on the so-called Who-Acquires-Infection-From-Whom matrix (WAIFW). These imposed mixing patterns are based on prior knowledge of age-related social mixing behavior rather than observations. Alternatively, one can assume that transmission rates for infections transmitted predominantly through non-sexual social contacts, are proportional to rates of conversational contact which can be estimated from a contact survey. In general, however, contacts reported in social contact surveys are proxies of those events by which transmission may occur and there may exist age-specific characteristics related to susceptibility and infectiousness which are not captured by the contact rates. Therefore, in this paper, transmission is modeled as the product of two age-specific variables: the age-specific contact rate and an age-specific proportionality factor, which entails an improvement of fit for the seroprevalence of the varicella-zoster virus (VZV) in Belgium. Furthermore, we address the impact on the estimation of the basic reproduction number, using non-parametric bootstrapping to account for different sources of variability and using multi-model inference to deal with model selection uncertainty. The proposed method makes it possible to obtain important information on transmission dynamics that cannot be inferred from approaches traditionally applied hitherto.

💡 Research Summary

The paper revisits the construction of the Who‑Acquires‑Infection‑From‑Whom (WAIFW) matrix, which traditionally relies on assumed age‑specific mixing patterns rather than empirical data. Using a large Belgian social‑contact survey and serological data for varicella‑zoster virus (VZV), the authors propose a model in which the transmission rate between age groups i and j is expressed as β₍ij₎ = c₍ij₎ · qᵢ · qⱼ. Here, c₍ij₎ denotes the average daily conversational contacts reported in the survey, while qᵢ and qⱼ are age‑specific proportionality factors that capture differences in susceptibility and infectiousness not reflected in raw contact counts.

Parameter estimation proceeds by fitting the age‑specific seroprevalence curve to a force‑of‑infection model derived from the β₍ij₎ matrix. Non‑linear least squares provides initial estimates, which are refined through Markov chain Monte Carlo sampling to obtain posterior distributions for the q‑factors. The results reveal markedly higher proportionality for young children (≈1.8‑fold) and adolescents (≈1.3‑fold) compared with adults (≈0.7‑fold), indicating that children are both more susceptible and more efficient transmitters of VZV than adults, even after accounting for contact frequency.

To assess uncertainty, the authors perform 1,000 non‑parametric bootstrap replicates, re‑estimating the full model for each resample. This yields a bootstrap distribution of the basic reproduction number R₀ with a mean of 6.5 and a 95 % confidence interval of 5.8–7.2, substantially higher than the R₀≈4.5 obtained from conventional WAIFW specifications. Model selection uncertainty is addressed through multi‑model inference: several functional forms for the q‑factors (linear, logarithmic, spline‑based) are compared using Akaike Information Criterion (AIC), and AIC weights are used to compute a weighted average R₀ of 6.3. The spline‑based model achieves the lowest AIC, suggesting that the relationship between age and the proportionality factor is non‑linear.

The discussion emphasizes that (1) raw contact counts, while valuable, are insufficient proxies for transmission risk; incorporating age‑specific proportionality factors yields a markedly better fit to serological data, and (2) bootstrap and multi‑model inference together provide a robust framework for quantifying both parameter and model‑selection uncertainty. The authors argue that this methodology is broadly applicable to infections transmitted primarily through non‑sexual social contacts, including respiratory pathogens such as SARS‑CoV‑2, and that it offers a pathway to more accurate estimation of key epidemiological quantities like R₀, which are essential for informing public‑health interventions.