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. 2009 Dec 6;6 Suppl 6(Suppl 6):S791-800.
doi: 10.1098/rsif.2009.0305.focus. Epub 2009 Oct 7.

Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards

Catherine J Noakes  1 , P Andrew Sleigh
Affiliations

Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards

Catherine J Noakes et al. J R Soc Interface. .

Abstract

Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks. The most common approach for assessing risk is to use the Wells-Riley equation to relate infectious cases to human and environmental parameters. While it is a simple model that can yield valuable information, the model used as in its original presentation has a number of limitations. This paper reviews recent developments addressing some of the limitations including coupling with epidemic models to evaluate the wider impact of control measures on disease progression, linking with zonal ventilation or computational fluid dynamics simulations to deal with imperfect mixing in real environments and recent work on dose-response modelling to simulate the interaction between pathogens and the host. A stochastic version of the Wells-Riley model is presented that allows consideration of the effects of small populations relevant in healthcare settings and it is demonstrated how this can be linked to a simple zonal ventilation model to simulate the influence of proximity to an infector. The results show how neglecting the stochastic effects present in a real situation could underestimate the risk by 15 per cent or more and that the number and rate of new infections between connected spaces is strongly dependent on the airflow. Results also indicate the potential danger of using fully mixed models for future risk assessments, with quanta values derived from such cases less than half the actual source value.

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Figures

Figure 1.
Figure 1.
Schematic representation of simple zonal model for three adjacent zones. Solid black arrows indicate ventilation extract, solid grey arrows indicate interzonal flows, dashed black arrows indicate infection source within the zone.
Figure 2.
Figure 2.
Hypothetical ward layout used in the study showing possible ventilation supply/extract (black arrows) and interzonal mixing (grey arrows).
Figure 3.
Figure 3.
Comparison of variability from mean results in stochastic and deterministic fully mixed models. Error bars show 1 s.d. from the mean, with grey capped error bars for the stochastic model and black uncapped error bars for the deterministic model.
Figure 4.
Figure 4.
Effect of air mixing on the total rate of infection. Error bars show 1 s.d. from the mean value. Solid line denotes βo = 27 m3 min−1; open triangle denotes βo = 9 m3 min−1; filled diamond denotes fully mixed.
Figure 5.
Figure 5.
Effect of ventilation regime on the risk of infection over a 170 h period. Mean data obtained from 100 simulation runs. (a) Infections in bay 1. (b) Infections in bay 2. (c) Infections in bay 3. Filled diamonds, case A; open squares, case B; filled triangles, case C; crosses, case D; open triangles, case E; open diamonds, case F.
Figure 6.
Figure 6.
Schematic of ventilation flows in regimes D and C. Location of infector indicated by star. Black arrows indicate ventilation flow; grey arrows indicate interzonal mixing flows.
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References

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