The calculation of Covid-19 infection rates in churches

Preamble

In a recent post, I looked at the risk of Covid infection on GB trains, based on the spreadsheet calculation methodology of Professor Jimenez and his team at the University of Colorado – Boulder. This method is based solely on aerosol transmission, which is now regarded as being of much more significance than transmission by surface contamination, and the risk of the latter can be easily reduced by normal hygiene precautions. In this post, I apply the same methodology specifically to the case of churches and include a downloadable EXCEL spreadsheet that might be of use to others. There is a level of self-interest of course, as I am a minister at an Anglican church which will shortly be faced with decisions concerning the nature of worship as the Covid restrictions are removed.  Essentially the spreadsheet gives a numerical value for the risk of Covid infection with specified amelioration methods in place (social distancing, masks, no singing etc.) and allows a rational assessment of safety to be made.

At the outset, it needs to be made clear that there are very many assumptions in the methodology of Jimenez, with some of the parameters not well specified, and the base values of risk that the model gives must be regarded as indicative only and it is best used in a comparative sense. In what follows, I first describe the input and output parameters of the spreadsheet, and then look at how it might be used to compare risk levels for different situations.

Download the spreadsheet from here

The spreadsheet

The spreadsheet is quite simple and straightforward, and requires no specific expertise to use. A screenshot is given above. The brown cells are input parameters, and the blue cells the output parameters The former are as follows.

• Length, width and height of worship area. The model effectively assumes that the worship area is a three-dimensional box. This is clearly not usually the case, and some degree of judgement will be required in assigning the length, width and height. All dimensions are in metres.
• Duration of worship is specified in hours.
• The ventilation with outside air is specified in air changes per hour. For most old churches that have been well maintained, this will be small and a value of 1.0 can be assumed. For particularly drafty churches, this could be rather higher (at say 3.0). For air-conditioned worship areas a value of 10.0 is appropriate.
• For the decay rate of the virus and the deposition to surfaces standard parameters are assumed. Normally the value for additional control measures will be zero unless there is filtering of recirculated air.
• The number in the choir and congregation are self-explanatory. Ministers should be included in the latter. Because of lack of reliable data on breathing rates and virus emission rates in children, no breakdown by age is required. This is probably a conservative assumption.
• The fractions of time that the choir sings and the fraction of time that the congregation sings are both values between 0 and 1.0. The choir fraction is when they are singing alone – it is assumed they will join with the congregation when the latter sing.
• The fraction of population that is immune is taken to be the proportion of the population that have received a full course of vaccinations, multiplied by 0.9 to allow for virus escape. At the time of writing in the UK, this parameter has a value of around 0.5.
• The parameter that allows for virus transmission enhancement due to variants has a base value of 1.0, a value of 1.5 for the alpha variant, and a value of 2.0 for the delta variant.
• A choice of values for masks efficiency for both breathing in and out are given.
• The fraction of the congregation with masks is a number between 0 and 1.0.
• The probability of being infective is taken from regional ONS data. For example, if the ONS figure of those infected is 1 in 500, then the probability will be 1/500 = 0.002.
• The hospitalization and death rates of those infected can also be taken from ONS data and have small values just above 0.0. At the time of writing the hospitalization rate is around 0.02 (2%) and the death rate is almost negligible and is taken as 0.001 (0.1%).

The next set of parameters in the spreadsheet are those that emerge from the calculation process and are not of direct interest to users. These lead on to the output parameters, which are as follows.

• The probabilities of covid infection, hospitalisation and death of a person attending the service of worship.
• These probabilities expressed as risk – for example a risk of 1 in 1000 of infection.
• The number of covid cases, hospitalisations and deaths arising from attending the service.

Comparing risk

The absolute values of probability and risk must only be regarded as approximate. Indeed, Jimenez emphasises that there is a great deal of uncertainty around many of the assumed parameter and urges caution in the interpretation of the results. At best, the results will be accurate to within an order of magnitude. The main utility of the model would seem to be to assess changes in risk – for example, any particular congregation may be comfortable with a certain set of Covid amelioration methods (no singing, masks etc.) and the method can be used to see how this risk might change as these measures are relaxed.

As an example of this, let us consider a church (which is not dissimilar to the one where I am a minister), where the congregation is currently capped at 60, there is 100% marks wearing, and only the choir of 6 sings. For the current infection rate of 1 in 150, this gives a risk of infection of 1 in 18100 for a one-hour service. This level of risk would seem to be acceptable to the congregation. Indeed, for one person attending similar services each week for one year, the risk of covid infection is close to the UK risk of injury in a vehicle accident in a year.

Firstly, suppose that a capacity of 100 is allowed (i.e. social distancing regulations are abolished). This increases the risk of infection to 1 in 11800. Now suppose that in addition masks are no longer required. This leads to a risk of infection of 1 in 4100. Allowing congregational singing raises the risk further to 1 in 1600. As all these figures are dependent upon regional infection rate, they also allow for the congregation to decide at what infection level restrictions can be removed. Should the infection level fall to 1 in 1000, then the overall risk with no amelioration measures decreases from 1 in 1600 to 1 in 11300. Whilst these figures are themselves only approximate, they nonetheless give any congregation the information to make a rational choice of how to proceed as restrictions are eased.

Closing comment

In order to make the spreadsheet as easy to use as possible, I have deliberately kept it simple and have not included too many options. However, if anyone has any suggestions for improvements / useful additions, then please contact me on c.j.baker@bham.ac.uk.