Covid-19 superspreading. lessons from simulations on an empirical contact network

Abstract

Infectious individuals who cause an extraordinarily large number of secondary infections are colloquially referred to as superspreaders. Their pivotal role for the transmission of Covid-19 has been exemplified by now infamous cases such as the Washington choir practice, where one infectious individual caused 52 secondary infections [1]. In order to formally analyse superspreading, we denote by Z the individual reproduction number. In a fully susceptible population, the mean mZ is known as the basic reproduction number R0. Based on branching arguments and assuming a well-mixed population, the distribution of Z is typically modelled by a negative binomial distribution whose variance mZ(1+mZ=kZ) is characterised by the dispersion parameter kZ [2]. Empirical evidence suggests that Covid-19 exhibits a particularly wide distribution of Z, with the right tail representing superspreading events. In situations without interventions, the dispersion parameter kZ was estimated in the range 0.04 - 0.2 [3, 4]. Some studies even found evidence for a fat tailed Z-distribution, possibly a power law with the exponent close to 1 [5, 6]. The underlying mechanisms for the emergence of this level of heterogeneity are difficult to establish. A priori, network effects could play a role, as suggested in [5]. A more frequent line of reasoning focuses on physiological or biological factors: wet pronunciation, loud speech, frequent coughing or higher viral loads could result in some infected individuals being inherently more prone to spread the disease than others during an encounter with a susceptible individual [7]. Combining both lines of thought, the study in [8] shows that individual variation in infectiousness indeed leads to higher variance of Z on some standard static network models. However, no previous study has investigated heterogeneities of the Z-distribution on empirical contact networks. Therefore, we provide preliminary simulation results based on one realistic temporal social contact network and gather further evidence that the key to finding Z-distributions in alignment with empirical data is to allow for individual variation in infectiousness.