A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data

We propose a transmission model to estimate the main characteristics of influenza transmission in households. The model details the risks of infection in the household and in the community at the individual scale. Heterogeneity among subjects is investigated considering both individual susceptibility and infectiousness. The model was applied to a data set consisting of the follow-up of influenza symptoms in 334 households during 15 days after an index case visited a general practitioner with virologically confirmed influenza. Estimating the parameters of the transmission model was challenging because a large part of the infectious process was not observed: only the dates when new cases were detected were observed. For each case, the data were augmented with the unobserved dates of the start and the end of the infectious period. The transmission model was included in a 3-levels hierarchical structure: (i) the observation level ensured that the augmented data were consistent with the observed data, (ii) the transmission level described the underlying epidemic process, (iii) the prior level specified the distribution of the parameters. From a Bayesian perspective, the joint posterior distribution of model parameters and augmented data was explored by Markov chain Monte Carlo (MCMC) sampling. The mean duration of influenza infectious period was estimated at 3.8 days (95 per cent credible interval, 95 per cent CI [3.1,4.6]) with a standard deviation of 2.0 days (95 per cent CI [1.1,2.8]). The instantaneous risk of influenza transmission between an infective and a susceptible within a household was found to decrease with the size of the household, and established at 0.32 person day(-1) (95 per cent CI [0.26,0.39]); the instantaneous risk of infection from the community was 0.0056 day(-1) (95 per cent CI [0.0029,0.0087]). Focusing on the differences in transmission between children (less than 15 years old) and adults, we estimated that the former were more likely to transmit than adults (posterior probability larger than 99 per cent), but that the mean duration of the infectious period was similar in children (3.6 days, 95 per cent CI [2.3,5.2]) and adults (3.9 days, 95 per cent CI [3.2,4.9]). The posterior probability that children had a larger community risk was 76 per cent and the posterior probability that they were more susceptible than adults was 79 per cent.