COVID-19 April 03, 2020 and Colorado Special Edition

All data continues to proceed as it has for many days now.  The initial high exponential growth has given way to more moderate but still exponential growth.  Doubling time for infections is now at 4.5 and doubling time for deaths is 3.0 days.  The forecast for reach 10,000 dead will happen by the end of the day on the 5th.  The decadaling time for deaths is currently 10.2 days, so if the trend continues we will reach 100,000 dead a little over 10 days later.  The graphs are below.

I have taken a little time to look at using more advanced models to fit the data.  Why am I familiar with all this stuff?  At the age of about 13 years I received an Apple II clone computer on which I taught myself the BASIC programming language.  After mastering the language, one of the first "real" programs I wrote was a predator-prey model, and continued to add complexities to that model over time.  My first foray into numerical computing and modeling was in the area of population biology.  Eventually, that gave way to an interest in modeling of other natural systems, and I have been modeling fluids and atmospheres for the last several decades.

The next level of model complexity beyond the exponential model is arguably the Gompertz model .  There are three parameters that are set in that model: the initial population, the final population, and the growth rate.  I've applied this model to both the US and Colorado.  I've set the initial population of infections to the observed value at the start of recorded infections in the US or Colorado, as appropriate.  I then adjusted the growth rate and final population to obtain a good fit, as determined by eyeballing the Gompertz curve compared to the observed data.  There is a wide variation of parameters that give a reasonable fit to the US data, and that tells me that the data is not yet sufficiently constraining to obtain much quantitative information.  All that can be said is that the exponential model has broken down (which is already self-evident).  Where the US data goes is difficult to predict in the longer-term.  Short-term trends can be used for short-term predictions.

The spread of reasonable parameters for Colorado was more limited.  The Gompertz model compared to the data is shown in two figures below.  One uses the semi-log scale and the other uses linear scales.  The fit, judging by eye, is good, and here's what the model indicates.  The total number of infections in Colorado will hit approximately 70,000.  We will hit the following milestones on the following days: 10,000 on April 12; 20,000 on April 22; a maximum number of new daily cases (1,133 new daily cases totaling 26,476) on April 27, at which point the number of new cases will finally start to decrease each day; 30,000 on April 30; 40,000 on May 10; 60,000 on June 8.  The 70,000 cases are reached asymptotically, which is to say it takes an infinity amount of time to get there.  Note that the plots below only go through early May.

I want to emphasize this model is extremely uncertain, and I would not put great faith into the exact number or dates.  But, unlike the exponential model which grows unrealistically forever, the Gompertz model exhibits a realistic growth and then flattening.  I will update this model periodically as new data comes in and we'll see how it does.  As a very rough estimate, it does predict that the worst for Colorado is yet to come, but that by mid- to late-May, the worst will be behind us.