Early in the Covid-19 pandemic, we heard a lot about models. We haven’t heard quite as much in recent months. This is especially interesting because models may be even more useful at the current stage of the epidemic than they have been at any time up to now. After all, we now have better information to calibrate models, which means they can be used to help guide decision-making at levels ranging from the decisions of individual persons (Will my Thanksgiving celebration be safe? Do I need to wear a mask?) to organizations (Are my employee protections adequate? Should my company change its policies because of the resurgence?) to the government (all manner of official rules and regulations).
I’ve written previously about what models are useful for. But, what exactly are disease transmission models, anyway?
First, let us say what they are not. Epidemic models are not oracles. From ancient times, an oracle was a wise person who could give prophetic advice. In theoretical computer science, an oracle is a computer program that gives the correct answer to any instance of some class of problems. In both cases, an oracle is one that sees perfectly. Epidemic models are not oracles.
If epidemic models are not oracles, what are they? I suggest they are tools. The Oxford English Dictionary defines “tool” as “A device or implement, especially one held in the hand, used to carry out a particular function”.
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At a zoom conference on the future of epidemic modeling, University of Michigan Professor and epidemic modeler Aaron King suggested that we should think about models as scientific instruments. That is, mathematical models of epidemics are not different in kind to microscopes, thermometers, Geiger counters, oscilloscopes, radio-telescopes and the host of other devices used in the performance of science. Specifically, instruments are devices used to make measurements.
If this is correct, then we should be able to answer how it is that epidemic models measure and what it is they measure. Indeed, Professor King specifically likened a model to the lens or mirrors of a telescope. What lenses and mirrors do is focus parallel rays of light so that what is too faint to be visible without the instrument becomes apparent when viewed through the instrument. Lenses transform the disorganized light into a coherent representation. Epidemic models, Professor King suggested, should be understood to do the same thing with data. By concentrating the information contained in diffuse data sources, a model can provide a crisp picture of the unobservable epidemic.
But models, like lenses, are imperfect. Optical aberrations and image distortion arise in reflected and refracted images from (i) material imperfections, or (ii) the mismatch between an actual lens and a theoretical one that is geometrically perfect. That is, our theoretical model of a lens is an idealization that abstracts away from the minor details and imperfections of real lenses.
In the same way, epidemic models are expected to be imperfect. First, as real lenses always have material imperfections, real people exhibit variations in their individual behaviors, social contact, susceptibility to infection, vulnerability to disease, and a wide range of other factors that affect the progression of an epidemic. Second, just as real lenses are not geometrically perfect, real populations may not follow the idealized geometry of epidemic models.
So, one view is that epidemic models are instruments that may be used to measure the state of the epidemic. But this is probably not all. They can be used to measure other things as well, such as the basic reproduction number, R0, or, even more abstractly, the evidence in support of a hypothesis. They can also be used for purposes other than measuring, such as prediction. So, there may be different kinds of models and they may have different functions. Some models may be multi-purpose tools, and we should understand that multi-purpose tools typically do not perform to the same standard that specialized tools do.
What’s more, there is a part of the original OED definition that we have not looked at carefully enough. A tool, says the OED, is a device, “especially one held in the hand”. Mathematical models are not held in the hand at all. Some may be held in the mind. But, for practical purposes, virtually all models are held within computer systems. So, what are we to make of this part of the definition? Should we discard the definition or conclude that models are not actually tools? The temptation is to think the definition is overly narrow, as we think of gardening tools or woodworking tools as our archetype. However, even if the definition is slightly too narrow, I think it nonetheless points to a deeper truth. Tools only perform their functions when in the service of a tool-user, “held in the hand” so to speak. Tools and tool-users cannot be separated. Moreover, the more skilled the user is with the tool, the better the outcome or product. That is, performance is inextricably linked to skill. We should, therefore, expect that models may not be separated from the modelers that “build” them.
Just because epidemic models are not oracles does not mean they are not working properly. Understanding their purpose, in this case as instruments to measure the state of the epidemic, helps to explain why, their proper use, and when we may expect them to work well.