As a country we continue to struggle with our handling of the pandemic. It’s a good thing that a vaccine is coming since we don’t seem to be able to properly manage the infection rate any other way. During the upcoming holiday season I’m concerned about our path as I see people continue to gather, travel, and socialize during the holidays without the knowledge of how to do it safely.
Even though SES is officially under contract, getting the funding in place to support test reactor work is slow going. That has always been the case, but after a year of no revenue, the wait is a painful reminder of how far behind the company finances are and how much of the savings have disappeared. Even with no ability to invoice for work, the costs of maintaining the company continue. I’m still holding out hope that we’ll resolve the funding in the near term so there can be some revenue before the holidays.
As I’ve been sitting around waiting for funding to come in, I’ve taken a renewed interest in our handling of the pandemic. My interest has been driven by a couple of factors, namely how my kids will continue their schooling at home for the foreseeable future and how to safely interact with people outside of my bubble. It led me down a number of rabbit holes. On my quest I’ve found a lot of information available that can help us make risk informed decisions, but little of it has made it into the public discourse. Armed with a plethora of publicly available data and a better understanding of the risk drivers associated with infection, I’ve become more comfortable managing my exposure. The sad part is that it’s not that complicated – which is why I’m so frustrated that public messaging hasn’t been more clear. We should all be armed with the knowledge and act accordingly.
I’m not sure why the messaging has been so poor. Perhaps the leadership of our institutions thinks that that level of information is not easily digestible and subject to mis-interpretation, or they think that if we understand there is risk we’ll all be frightened. Both seem to pre-assume the interest level and decision making capability of well informed people, so I’m going to take a stab as rectifying this situation. For this newsletter I’m going to lay out a simple approach to understanding the risk levels and give some preliminary results relating the risk of various activities to each other so we can all make better decisions together.
Two personal experiences and some time on my hands led me to understand the actual risks associated with COVID-19: my children’s current school situation, and my participation in a brass quintet. The first experience has been regularly documented and well understood by most, so I won’t bore you with details. Our family chose to keep our children learning virtually for the time being as there was no clear indication of what the risk might be to our bubble, which includes older grandparents.
The second experience is a little unique in that I am a member of a brass quintet that would normally rehearse once a week indoors. Given the increasing number of COVID cases and indications that it will only get worse, this type of activity with people outside of my bubble seems like too large of a risk. Or is it?
As I thought about it, I really didn’t have a basis for concern about meeting with other people indoors other than anecdotes that these settings spread the virus. But what is it about the settings that’s concerning? Is it the number of people? The space between them? Disinfection of surfaces? I don’t like to tell people that we have to cancel rehearsals without understanding why or whether there is something that can be done to minimize the risk acceptably.
As many of my readers know, I’m a big advocate of risk-based decision making. As an engineer, there is no absolute answer and every decision takes on some element of risk. Understanding the magnitude of the risk is the first step is making a good decision before considering other factors such as importance of the activity. To support my personal risk-based decision making, I went down the path of looking for studies and anecdotes that can be used to build a simple model. The sections below step through my process to develop my simplified model, but if you just want to see the result, you can click the bottom below to scroll down to them and skip all of the boring stuff.
At this stage, it’s unconscionable that people still don’t have a clear picture of how this virus is transmitted. I’ve gone through numerous articles posted by reputable organizations and the information is out there. I’ll summarize what should be evident and common knowledge (but it’s not).
What I take away from this is that we need to keep our fluids to ourselves and wash our hands with soap. Regular cleaning of surfaces is likely sufficient, as long as we don’t provide a pathway to ingestion before hand washing.
This information certainly points to the efficacy of masks and why they have been promoted. Social distancing will also prevent some of the larger expelled particles from being transmitted between people as they settle, but aerosol sized particles will stay suspended.
That brings us to the discussion about the ubiquitous cloth masks. It seems likely that they will do a great job stopping larger droplets that contain virus from being spread between people – almost regardless of distance. What they won’t do is prevent aerosolized virus from being ingested for two reasons: in most cases the cloth weave won’t be sufficiently dense to filter such a small particle and even if it were, without a tight seal, air will come in around the mask, seeking the path of least resistance. Cloth masks do seem to prevent the spread by larger droplets pretty effectively. And as these droplets can contain a large number of viroids and contaminate surfaces, this is an important mitigation measure. But we haven’t been mitigating aerosol spread with this control. The result is that mask mandates significtly reduce transmission in some aspects, we still have a means of transmission not addressed.
This is where public policy and communication have fallen apart. The public policy restricting indoor gatherings, even with a mask mandate is directly addressing the aerosol transmission path. The fact that this is not stated clearly leads to people thinking that these controls are bogus as there is no clear understanding by the populace why this is helpful. We’ll talk about how public policy implicitly incorporates the concept of aerosol spread, even though that is never explained.
When I went to develop the model, I started with the discussion above. After looking it over, I realized that we can positively control spread through large droplets and surfaces to a point where it is unlikely any significant virus will be ingested through mask wearing and hand washing. The only other transmission mechanism to consider is aerosol. Luckily this is a fairly well understood field of study that has been backed up by years of experimentation for other aerosol agents.
In its essence, aerosol ingestion will occur when we take in a breath. The number of viroids in the air we breath in will somehow indicate our likelihood of getting infected.
The first part of the model is just to determine the concentration of virus particles in the air. That includes knowing the number of infected people in a space, how much virus they shed and at what rate, the space air mixing and air change rate, etc. Most of this information can be either assumed or is based on pretty simple math.
Determining the likelihood of infection is the larger lift. In general, the academic community has coalesced around a simple equation supported with a history of testing.
The probability of infection is a function of the viroid dose (d) divided by some critical amount of viroid (infectious dose) that will make you sick (k). There are other variations, but they are all essentially the same. This specific formulation came from Reference 1. The next section will talk about this equation in more detail.
For purposes of this model, we’re going to make some simplifying assumptions that make our life easier:
For a finite time step of our simulation, the concentration of virus particles can be determined by the equation below.
We are doing a virus particle balance divided by the volume of the space in the current time step. The first term in the numerator multiplies the number of infected people in the space (n) by their respiration rate, the length of the time step, and the viral load density in respirations. Add to this is the number of viroids (nv) from the previous time step that were already in the space. The second term determines the amount of virus removed by multiplying the fresh air introduced through the volumetric air change rate (ACHV) with the viroid concentration from the previous time step.
There is no real certainty on the density of viroids in the aerosol expelled by infected people. But that doesn’t matter since we’re going to use the results of this calculation as a comparison between scenarios. What does matter is the relative number of particles expelled associated with certain activities. This is where the study performed for the International Coalition of Performing Arts (Reference 2) comes in handy. They measured the number of particles released into the air for various activities, mostly related to playing instruments and singing, but it creates a basis for common sense understanding of the relative magnitudes.
The equation to be used was already introduced. We can adapt this to calculate the probability for infection at each time step by using the total inhaled viroid from the time entering the space as the dose input (d) . That can be calculated by:
Note that this assumes you entered the space when the infected person entered the space. The infectious dose number is really the only unknown quantity in the equation left. There is much debate on what this number should be, and even how many viroids are required to form a Plaque Forming Unit, which would be the basis for infection. Also at issue is that different doses may lead to different levels of infection. Much like the assumption about viral load in an infected person, we’re using this simulation as a single point comparison between scenarios, so the complexity is unnecessary (thankfully). Even more to our point, the actual infectious dose is not the subject of our study, so we can choose any value we want, as long as we leave it the same for every simulation. In our case, we’ll use it to establish a benchmark condition.
Building a spreadsheet incorporating the equations above and some values for the virus density based on Colorado study, we can establish an infectious dose as a benchmark. From that point we can use the resulting infectious dose determined to study the relative risk for other situations.
The guidance we’ve heard from contact tracing is that you have to be around someone infectious for 15 minutes before it’s worth tracing. Let’s assume our health organizations have our best interests in mind and that means there’s at most a 1% chance that we would have been infected by such an encounter. Even more to the point, we’re going to consider this encounter to be within the 6ft distance in a space with little moving air. Therefore the air volume of concern is 12 ft2 up to six feet high with no air replacement. We’ll combine this with the results from Reference 2 for a theatre major reading a script, which is around .2 parts/ml. Using these inputs we vary the infectious dose number until we show a 1% chance of infection at 15 minutes.
For the next simulation, let’s consider the situation advocated by my state government for social gatherings. No gatherings of over 10 people is about all it says. Assume we all take this as 10 people over for Thanksgiving. We would consider that the expelled particles might be a little higher in this condition, similar to a monologue without a mask, around 0.3 parts/ml. We’ll assume that this is an average and people aren’t intentionally sneezing into food or people’s faces so we’re not depositing large particles on surfaces and food. Most house ventilation systems are generally zoned, and for this simulation we’ll use an area of 1000 ft2 for this gathering. Note that we’re assuming good air mixing and the recommended air change rate for residences of .35 air changes per hour (ACH). This shows us that the risk relative to our benchmark case is very low. As a matter of fact, it would take a gathering over two hours before our chances of infection would warrant contact tracing if there was one infectious, asymptomatic person in attendance. If I was making public policy, this would seem like a good basis for any recommendations, so it’s likely our model is closely duplicating the intent of the government mandate, even though they won’t tell us why it exists.
Let’s consider going to get some supplies. As our basis for comparison we’ll consider a standard grocery store of 20,000ft2 with 15 foot ceilings. Per Reference 3, the fresh air requirement is .06CFM/ft2 for such a facility, which results in a value of .24 ACH. We have to consider that at least 10 people currently in the facility are sick, or were there recently. I don’t think that’s a stretch considering what I’ve seen when I go shopping. Let’s assume everyone is being good and wearing a mask and not overly exerting themselves so the expelled particles are low, approximately our 0.2 parts/ml baseline. Based on all of this information, you could be in the store from the time it opened for the first six hours until the probability of infection would rise to the level of getting contract tracing.
Consider an elementary school classroom. In this case, we have to assume that at least two students are infectious without being symptomatic. Similar to the supermarket case, the rate of expelling particles is low (.2) because of mask policies and the teacher being the only speaker for much of the class. The standard size for a classroom is around 900 ft2, and the ACH from Reference 3 is at least 1.25 based on an elementary school student loading. Plugging all that in we get that we get a little over three hours of classroom time before we hit that contact tracking threshold.
Let’s consider my case of a brass quintet. This one is unique, but luckily we have the expelled particle rates from Reference 1 to guide us. Assuming we’re using bell covers, we should expect a rate of around .4 parts/ml on average. We would normally practice in a large church sanctuary of 3200 ft2 with high ceilings. Even with the ventilation running, we’re probably only mixing half of that space though. Our real challenge is the fresh air. It’s not clear what the ACH requirements are for religious facilities as the method of calculation in Reference 3 can yield either .6CFM/ft2 or .06CFM/ft2. Let’s consider the worst case. That would yield an ACH of 0.18. Plugging all that in we get that that it takes a little over two hours in that environment to get to a probability of infection that would normally trigger contact tracing.
The point of this whole exercise is to understand our risk more broadly and how various situations relate to each other. It does not actually tell us how likely we are to get infected, but does inform the riskiness of various types of interactions. Thinking about the model and playing with it really brings to light our primary risk factor; the density of the virus in our inhaled air. That’s controlled by many things, but the rate at which we get new air is the primary driver and controls the long term infection probability. This is why outside activities are so safe and indoor activities with poor ventilation are so dangerous. But with the model we can make some more real-world observations about relative risk such as:
Clearly this is not my primary field of expertise and others are better leveraged to do this work. Which begs the question on why we haven’t seen more of it? People don’t actually understand real risk numbers, but they do understand that the risk when it’s compared to other activities. If you tell them that if you’re talking to someone six feet away for 15 minutes, you are at less risk of catching COVID than being at church for an hour and a half with a mask on, that might get some attention. Similarly, people may be less fearful to get back out there if there is an understanding that we are using appropriate controls that have a real impact on the risk level of going shopping, taking kids to school, etc.
Other than doing this modeling “for real” and perhaps even establishing real numbers for infectious dose so we know the actual risk, there are controls we can easily put in place to greatly minimize risk of infection.
Unlike most newsletters I have references. I looked at a lot more than this to satisfy myself that there was consistency of approach and there weren’t any big holes in the references I did use.
This newsletter was about risk. I’ve spoken about this lots of times but understanding that every decision (or non-decision) has an associated risk really puts it into perspective. I’m not sure the quip today really connects, but I thought I’d put it here anyway.
Doing nothing means you accept the consequence of inaction without the satisfaction of action.