Event-specific interventions to minimize COVID-19 transmission

Abstract

COVID-19 is a global pandemic with over 25 million cases worldwide. Currently, treatments are limited, and there is no approved vaccine. Interventions such as handwashing, masks, social distancing, and "social bubbles" are used to limit community transmission, but it is challenging to choose the best interventions for a given activity. Here, we provide a quantitative framework to determine which interventions are likely to have the most impact in which settings. We introduce the concept of "event R," the expected number of new infections due to the presence of a single infectious individual at an event. We obtain a fundamental relationship between event R and four parameters: transmission intensity, duration of exposure, the proximity of individuals, and the degree of mixing. We use reports of small outbreaks to establish event R and transmission intensity in a range of settings. We identify principles that guide whether physical distancing, masks and other barriers to transmission, or social bubbles will be most effective. We outline how this information can be obtained and used to reopen economies with principled measures to reduce COVID-19 transmission.

Keywords: COVID-19; disease transmission; epidemics; interventions.

Fig. 1.

The three types of intervention for reducing $R_{\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}$ in a setting: (Top) reducing transmission $\beta$, (Middle) reducing the number of contacts at a given time $k$, and (Bottom) reducing mixing by increasing $\tau$.

Fig. 2.

The effects of the three types of interventions on $R_{\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}$. At baseline, $k=10,\beta =0.5,T=20$, and $\tau =4$. In each panel, reducing transmission means reducing $\beta$ by half, distancing means reducing $k$ (the number of people in proximity) by half, and “strict bubbles” means ensuring that attendees contact only $k$ individuals over the whole event rather than mixing with others outside their bubble. (Top) No mixing ($\tau =T$); the horizontal axis is the total event duration in hours. (Middle) Mixing occurs every 4 h. (Bottom) A setting with a 10 times lower propensity for transmission ($\beta =0.05$). Here, transmission never “saturates” because $1-e^{-\beta \tau }$ remains small enough that it is approximately $\beta \tau$, which is small.

Fig. 3.

(Left) Transmission rate and (Right) saturation vary over reported events. Median transmission rates range from 0.025 (E11: household survey) to 0.58 (E8: lunch) transmissions per contact per hour. Transmission rates are highest for events involving sharing meals, singing, and speaking (presumably at volume, although we do not have this information). Among the events we described, the choir, birthday parties, call center, and lunch are the most “saturated.”

Fig. 4.

Probability of observing a single choir outbreak with between 30 and 52 new infections given a particular $\lambda$ and $\beta$.

Fig. 5.

Four different kinds of events depending on whether they are (Left) linear (low transmission probability) or (Right) saturating (high transmission probability) and whether they are (Upper) static (same contacts for whole event) or (Lower) dynamic (high turnover of contacts). We select representative parameters for each type of event, determine the number of new infections, and show how the three interventions effect this number. Interventions are reducing transmission (halving $\beta$), introducing distancing (halving $k$), and strict bubbling (setting $\tau =T$). The parameters used for the plots are funeral: $k=10$, $\tau =2$, $T=2$, and $\beta =0.05$; birthday party: $k=9$, $\tau =3$, $T=3$, and $\beta =0.05$; public transport: $k=15$, $\tau =1$, $T=4$, and $\beta =0.05$; and school: $k=20$, $\tau =3$, $T=24$, and $\beta =0.3$.