COVID-19 Superspreading Suggests Mitigation by Social Network Modulation

Although COVID-19 has caused severe suffering globally, the efficacy of nonpharmaceutical interventions has been greater than typical models have predicted. Meanwhile, evidence is mounting that the pandemic is characterized by superspreading. Capturing this phenomenon theoretically requires modeling at the scale of individuals. Using a mathematical model, we show that superspreading drastically enhances mitigations which reduce the overall personal contact number and that social clustering increases this effect.

Figure 1

The characteristics of superspreading. (a) Simulated infection network characterized by superspreading, with a dispersion parameter $k=0.1$, within what has been observed for COVID-19 [4, 5]. Superspreaders appear as hubs, while most individuals are “dead ends,” meaning that they do not transmit the disease. The epidemic mainly grows by spreading from one superspreader to the next. (b) The dispersion parameter $k$ provides a measure of superspreading, with lower $k$ values corresponding to a greater heterogeneity. With a $k$ value of 0.1 for COVID-19, approximately 10% of the population has the infectiousness to cause 80% of transmission. SARS and MERS are also characterized by a significant heterogeneity [14, 15], while pandemic influenza is believed to be more homogeneous [18]. (c) Simulated infection network without superspreading (all individuals have equal infectiousness). Here, most individuals spread the disease to a few others, leading to a branched structure.

Figure 2

The reproductive number. Distributions of individual reproductive number $R$ and value of $R_0$ for different dispersion parameters and number of social contacts during an infectious period. This figure is based on the analytical framework described in the main text. See Supplemental Material [19] for details on the calculation. (a) Distribution of $R$ for a disease where all individuals have equal infectiousness. (b) Distribution of $R$ for a disease characterized by superspreading (dispersion parameter $k=0.1$). (c) Basic reproductive number $R_0$ as a function of social connectivity and dispersion. The dashed line represents $R_0=1$. These calculations take into account the Poisson distributed contact number and the fact that each infectious person will have one insusceptible person in their network (the individual from whom the infection originated), even when computing the basic reproductive number. Details on an analytic computation of $R_0$ for fixed ($\delta$-distributed) contact number can be found in Supplemental Material [19].

Figure 3

The epidemic trajectory of a heterogeneous disease is highly sensitive to mitigation. Epidemic trajectories as a function of the number of people that each person interacts with during an infectious period. (a) Time evolution in the absence of any infection heterogeneity. (b) Time evolution for a disease with dispersion parameter $k=0.1$, roughly representative of COVID-19.

Figure 4

Final attack rate (total fraction of the population infected) as a function of network connectivity and transmission heterogeneity. In (a), we investigate an Erdös-Renyi network, with the same degree distribution as in Fig. 2. (b) explores a network where each person is assigned to two groups of people, leading to a highly clustered network. The black regions indicate conditions where the disease cannot spread in the population. On the right-hand side, small fragments of the networks in question are shown. Each of the two contour plots in this figure are based on 1500 runs of the model. A detailed description of the algorithm used to generate the clustered network is included in Supplemental Material [19].