Abstract
The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the distribution of the number of secondary cases is skewed and often modeled using a negative binomial distribution. However, this may not always 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 mean and variance of this distribution when the data generating distribution is different from the one used for inference. We also analyze COVID-19 data from Hong Kong, India, and Rwanda, and quantify the proportion of cases responsible for 80% of transmission, p_{80%}, while acknowledging the variation arising from the assumed offspring distribution. In a simulation study, we find that variance estimates may be biased when there is a substantial amount of heterogeneity, and that selection of the most accurate distribution from a set of distributions is important. In addition we find that the number of secondary cases for two of the three COVID-19 datasets is better described by a Poisson-lognormal distribution.
Highlights
The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases
In general we find that when overdispersion increases, estimates tend to become more biased when the considered offspring distribution does not correspond to the data generating distribution
Since most studies that aim to quantify variation in disease transmission have assumed the offspring distribution to follow a negative binomial, we investigated the impact of incorrectly assuming this distribution as an approximation to the underlying transmission process
Summary
The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases. When variation in disease transmission is present, large outbreaks can occur even if R0 is less than one To account for this heterogeneity, the individual number of secondary cases can be described by a random variable, whereas R0 represents the expected value for an entire susceptible population. Most studies investigating the amount of heterogeneity in disease transmission have assumed a Poisson process with rate given by the individual reproduction numbers, assumed to follow a Gamma distribution, resulting in a negative binomial offspring distribution[3,11]. In this way, heterogeneity has often been quantified using the k parameter, with k the negative binomial dispersion parameter. This has allowed comparison between studies, where lower values of k indicate increased heterogeneity in transmission, and possibly a larger amount of superspreading
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