Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control

Abstract

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), the etiological agent of the Coronavirus Disease 2019 (COVID-19) disease, has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used-appropriately and less appropriately-to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, often dominated by a small number of individuals, and heavily influenced by superspreading events (SSEs). The distinct transmission features of SARS-CoV-2, e.g., high stochasticity under low prevalence (as compared to other pathogens, such as influenza), and the central role played by SSEs on transmission dynamics cannot be overlooked. Many explosive SSEs have occurred in indoor settings, stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, produce processing facilities, fish factories, cruise ships, family gatherings, parties, and nightclubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity to effectively contain outbreaks with targeted interventions to eliminate SSEs. Here, we describe the different types of SSEs, how they influence transmission, empirical evidence for their role in the COVID-19 pandemic, and give recommendations for control of SARS-CoV-2.

Fig 1. Poisson and NB-distributed secondary infections.

Figure shows a schematic of an NB branching process and example distributions of NB and Poisson distributions of secondary infections. Both distributions have R₀ = 2.6 [28], and the NB has dispersion parameter k = 0.16 [25] with 100,000 draws. The code required to generate this figure can be found in S1 Data. NB, negative binomial.

Fig 2. Example trajectories of NB and Poisson branching processes.

Figure shows example trajectories (in number of active infections versus generation) of NB and Poisson branching processes and cumulative infection sizes after 6 generations of spread. Both simulations start with 1 infection and have the same R₀ = 2.6. For NB branching process, we assume dispersion parameter k = 0.16, same as SARS-CoV-1 [24,33]. We run all simulations 10,000 times. Dashed red lines represent theoretical values in the large-population limit $\mathit{I}={\mathit{R}}_{\mathbf{0}}^{\mathit{n}}$, where I is number of active infections, and n is number of generations. Solid blue lines are the mean values of all simulations including those that have not taken off, which overlap with the theoretical values when the susceptibles are not depleted. Solid orange lines are the mean value for simulations that took off, and the outbreaks appear more explosive in the first few generations in the NB simulations. Both number of active cases and cumulative infections are in log₁₀ scale. The code required to generate this figure can be found in S1 Data. NB, negative binomial; SARS-CoV-1, Severe Acute Respiratory Syndrome Coronavirus 1.

Fig 3. Controlling outbreaks and the effect of “cutting the tail”.

(A) Values of R_eff under different thresholds of maximum number of secondary infections and the probability of keeping the maximum number of secondary infection thresholds. We compare 3 scenarios with R₀ = 1.5, 2.0, and 3.0, where lower R₀ represents the consequence of population-wide mild to moderate NPIs. The NB distribution is truncated at the max number of secondary cases, and the distribution is renormalized after the truncation. Contours highlight R_eff = 1 boundary. Lower R₀ facilitates the extinction of outbreak, and increases the probability of success controlling the outbreak, especially when the probability of reducing hotspot transmission is low. If the vast majority of transmission inside hotspots can be eliminated under all R₀ scenarios, a control target of less than 10 secondary infections can bring R_eff to close to unity. (B) Probability of an outbreak successfully taking off with 1 seed infection under NB and Poisson distributions, as well as an NB distribution with cutoff number of secondary infections of 10 and with 100% efficiency. The stochastic branching process simulations are run 10,000 times with R₀ ranging from 0.8 to 3.0. The success of outbreak is defined as having more than 20 infections at generation 6. Dispersion parameter k for NB is 0.16. Data are calculated using methods based on probability-generating functions [50]. The code required to generate this figure can be found in S2 Data. NB, negative binomial; NPI, non-pharmaceutical intervention.