Exposure and respiratory infection risk via the short-range airborne route

Abstract

Leading health authorities have suggested short-range airborne transmission as a major route of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). However, there is no simple method to assess the short-range airborne infection risk or identify its governing parameters. We proposed a short-range airborne infection risk assessment model based on the continuum model and two-stage jet model. The effects of ventilation, physical distance and activity intensity on the short-range airborne exposure were studied systematically. The results suggested that increasing physical distance and ventilation reduced short-range airborne exposure and infection risk. However, a diminishing return phenomenon was observed when the ventilation rate or physical distance was beyond a certain threshold. When the infectious quantum concentration was less than 1 quantum/L at the mouth, our newly defined threshold distance and threshold ventilation rate were independent of quantum concentration. We estimated threshold distances of 0.59, 1.1, 1.7 and 2.6 m for sedentary/passive, light, moderate and intense activities, respectively. At these distances, the threshold ventilation was estimated to be 8, 20, 43, and 83 L/s per person, respectively. The findings show that both physical distancing and adequate ventilation are essential for minimising infection risk, especially in high-intensity activity or densely populated spaces.

Keywords: COVID-19; Interrupted jet; Physical distance; Short-range airborne transmission; Ventilation rate; Wells-riley model.

Graphical abstract

Fig. 1

Schematic diagram of the expired jet using a two-stage jet model.

Fig. 2

Idealised breathing cycles. (a) Sinusoidal cycles; (b) square cycles. We considered an ideal 4-s breathing cycle in this idealised model.

Fig. 3

A simple model of the continuum from short-range to long-range inhalation routes. (a) A simple jet model assuming the expired jet is steady (a1) or interrupted (a2); (b) The jet zone with a variable distance x in (a), and the room zone. The jet model may be modelled using the ideal steady jet model of (a1) and the two-stage jet model of (a2).

Fig. 4

The assumed worst condition in which a susceptible person inhales exactly when the exhaled air of the infected person arrives at his/her mouth.

Fig. 5

The time-varying streamwise penetration distance of the geometric centre of the expired jet estimated using the two-stage model for light activity (exhalation/inhalation rate, 0.2 L/s). The streamwise penetration distance of the starting jet $x\sim t^{\frac{1}{2}}$ and the streamwise penetration distance of the puff $x\sim t^{\frac{1}{4}}$ after the 2-s exhalation phase.

Fig. 6

Comparison of the measured and predicted streamwise and radial penetration distances for an interrupted jet. (a) Streamwise penetration distance as a function of dimensionless time; (b) normalised radial penetration distance as a function of the streamwise penetration distance.

Fig. 7

An ideal model of the development of expiratory interrupted jet flows for 8 s during light activity (exhalation/inhalation rate, 0.2 L/s). The transparent level of yellow and red colours illustrates flow dilution. The jet tip was estimated using Equations (3) and (9). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 8

The measured and predicted dilution factors vary with the distance from the discharge orifice. Prediction using the steady and two-stage jet models was made with five activity intensities and the discharge orifice as 0.02 m. The representative inhalation/exhalation rates listed in Table 1 were used. Note that for the steady jet model, the dilution factor is 1 when the distance is less than 0.12 m. The jet or puff flow in Ghaem-Maghami and Johari [29] and Behera et al. [28] was injected into an isothermal and isobaric chamber. The former was accompanied by a weak co-flow (a 0.5% of jet velocity) while the latter had no co-flow.

Fig. 9

The measured and predicted exposure index $C_x/C_r$ varies with the distance from source manikin. Prediction using the two-stage jet model was made with three ventilation rates: 30, 50, and 70 L/s per person. In the legend, each case is shown with [#L/s per person, & L/s, $ s], in which # refers to the ventilation rate, & refers to the exhalation rate, and $ refers to the breathing duration. The air distribution design was displacement ventilation in the studies [30,[31], [32]]; downward ventilation in the studies [33,34]; and mixing ventilation in the study [35]. In data of displacement ventilation, the heads of the source and the target manikins are suspected to be within the upper mixing zone. These measurement data were first summarised by Chen et al. [36].

Fig. 10

The predicted normalised concentrations of the expired flow at different distances and ventilation rates of 1–10 L/s per person and infinity for standard activity (exhalation rate, 0.1 L/s). The results of the new two-stage jet model and the steady-state jet model are shown and compared.

Fig. 11

Estimated short-range airborne infection risk varies with distance and ventilation rate, and the partial derivatives of infection risk against distance and ventilation rate. (a) Estimated short-range airborne infection risk, $P$, as a function of the distances and ventilation rates for standard activity (infectious quantum concentration, 0.1 quanta/L and exposure time, 42 s, assuming a 2-h total exposure period with four close-contact events per hour and 5.4 s/per close-contact event). In the inserted figure, the partial derivative of infection risk is shown against distance $\frac{\partial P}{\partial x}$. (b) The estimated short-range airborne infection risk $P$ at threshold distance $x=0.7$ m and, in the inset figure, the partial derivative of infection risk against the ventilation rate $\frac{\partial P}{\partial q_e}$ are shown.

Fig. 12

Estimated short-range infection risk $P$ for four activity intensities and the corresponding physical distance threshold, with ventilation rates ranging from 0.1 to 500 L/s per person, and a partial derivative of infection risk against the ventilation rate $\frac{\partial P}{\partial q_e}$ using the equations presented in Supplementary Information C3.