Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the number of secondary cases is often modelled using a negative binomial distribution. However, this may not be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the offspring mean and its overdispersion when the data generating distribution is different from the one used for inference. We find that overdispersion estimates may be biased when there is a substantial amount of heterogeneity, and that the use of other distributions besides the negative binomial should be considered. We revisit three previously analysed COVID-19 datasets and quantify the proportion of cases responsible for 80% of transmission, p (80%) , while acknowledging the variation arising from the assumed offspring distribution. We find that the number of secondary cases for these datasets is better described by a Poisson-lognormal distribution.