SIR Model Revisited

It has been about 15 months since I first did my original SIR modeling concerning the progression of Covid 19. That post is here. I thought I would re-visit the model and the data after all the things that have come to pass since that time. In my initial simple model I used a scaled population  (1 being the total U.S. population.) I have subsequently made some numerical changes  such that I could use the actual U.S. population and compare the confirmed cases and the estimates from the CDC.

As was mentioned in a previous post the CDC has esitmated that the total disease burden is off by a factor of 4.0 due to a variety of reasons they have published. That post is here. To my knowledge no one seems to take real issue with their estimates. In my model I used the multiplication factor published by the CDC and re-plotted it. It is shown below the break.

In the graph I also plotted the actual number of confirmed cases multiplied by the factor estimated by the CDC. I was rather surprised by these results. First, the agreement between the CDC esitmated number of cases and my model was fairly close. I really didn't expect that. Second, the implications from the model and the case number estimates. This model has no feature for a vaccine or any sort of prophylactic measures. It's a straight susceptible-infection-recovered model that only assumes that once infected the person will not be re-infected due to gained immunity. The first implication of this, and the simplest, is that nothing that has been done to date has affected the progression of the disease. If this were indeed the case, then some people will have a lot of questions to answer.