29 March 2020
I made the point a few days ago that extremely simple exponential curve-fitting has done astonishingly well in predicting the progression COVID-19.
Adam Adamou, Director of the London Mathematical Laboratory, makes precisely the same point with rather more detail and sophistication:
A few key points:
- Simple exponential models work well in the early stages because they mirror the mechanics of disease spread (each infected person infects more than one person).
- They are limited: they can’t predict when the curve will bend, for example.
- The models that follow real underlying disease mechanics, like SIR models, more closely mirror disease mechanics including the achievement of herd immunity. But key inputs are not knowable early on, and the models are exceptionally sensitive to these inputs.
- Over time, we are able to estimate these variables with more accuracy and can transition to “better” epidemiological models.
Indeed, here’s one such simple model / paper (cited by Adamou) which predicts that NHS capacity in the UK will be strained and then exceeded in “1-2 weeks” (this was on the 22nd of March):
As someone who has built such exponential models, it’s extremely important to point out what they do, and don’t predict.
These models simply answer the following question mathematically: “If the exponential growth we have seen so far continues on an exponential path, what will happen?”
Of course, there are many ways that we can change that outcome. Stringent control measures, changes to individual habits (self-imposed social distancing, washing hands), achieving herd immunity, developing a vaccine, etc. would all make the future different than the past.
But the fact that even where we have seen stringent measures put in place (Italy, Spain, France, Germany), the curve is taking time to bend to a slower-growth path, should alert us that the time to act is now (actually, it was in late January / early February) and that we need to risk doing too much rather than not doing enough.