I've seen media reports over the last couple of weeks that the IHME model, which is widely used by the government and policymakers, revised their death toll down to 60,000 by August. I'm usually loathed to criticize other modelers, especially when they are almost certainly experts, whereas I am not. But, I don't see how the IHME has any basis in reality. I think it's fair to criticize a weather forecaster that predicts warm and sunny skies when a simple look out the window shows that it's pouring rain. And I say this as a weather forecaster. We are now at over 42,000 deaths in the US. Just 18,000 short of 60,000. And we aren't even through April. The daily death rate is over 2,000 per day. Even if it drops to half that, we will hit 60,000 in May, not August. A lot can change by August. I don't know what the numbers will be three months from now, especially as social distancing policies change. One thing I am nearly certain of, however, is that the death toll is going to be over 60,000 within weeks, not months.
For clarity, I want to distinguish the modeling I'm doing from what most of the other experts are doing. (Again, I am not an expert modeling infectious diseases). I am simply fitting a mathematical function to the historical data and using that to extrapolate out into the future. I am not trying to explicitly simulate the rate of spread or how contagious the disease is (i.e., the R0 factor). The advantage to this method is that it relies upon the underlying data itself with the implicit assumption that the infection spread is governed by the laws of nature, that the future is a function of the past, and that the laws of nature follow some smooth mathematical function. I have chosen to use the Gompertz curve, because it has been shown to empirically reproduce the historical rise and fall of many biological populations. The Gompertz curve is a solution to a very simple population biology model. Thus my "modeling" implicitly rather than explicitly incorporates a very simple numerical model. But I don't really care about that. From my perspective, I'm just fitting a curve to the data without care of WHY that is happening. It just is. And for now, it seems to be doing a rather good job.
In contrast, most of the models discussed in the media and which are used by government officials are solutions to a bunch of complex mathematical equations that are explicitly trying to simulate the growth and decay of infection based upon quantitative measures of infection. These models require specific inputs, many of which are poorly constrained. For example, the R0 is a key parameter and the solutions are very dependent on small changes to the poorly constrained value. The models also require knowledge of when an infection started, which even now is uncertain by as much as a month or more. Population density and a measure of the interaction between people can also be important in these models. The advantage of these models is that you can plug in a range of values and see what happens. You can understand how sensitive the system is to changes in R0 or other parameters. You can UNDERSTAND how the system behaves. These models answer a lot more of the "why", which I completely ignore. Most of these models should work very well if the input values are reasonably constrained. But they aren't, and thus there is a very wide range of outcomes predicted between models and within individual models.
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