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.

Planetary Orbital Eccentricity Updated

In my previous post on the subject I mentioned how I didn't have the eccentricity of the Earth's orbit quite right yet. I have pretty much corrected that. The old data set and the new are shown below the break.

No not that Climatology

Well, back to writing some posts. A fellow I know needed me to help him move some cattle. That meant quite a bit of time in the saddle, and then hauling winter feed to the new location. Oh great I get to ride drag, and no that doesn't mean riding in women's clothes. It's where you get to smell the cow flatulence all day and eat dust for hours on end at the back of the drive.

I have worked with a lot of people over the years in what I call planetary sciences. This also includes atmospheric research. Over the years I have built a number of instruments and conducted experimental studies in support of this type of work so I naturally developed an interest in the subject. One aspect of this field is obviously the climate of earth both in the past and the present. The present day arguments over modern climate change don't hold much interest for me but the past or paleoclimate studies do. 

What Do You Believe?

Given our last election and some of the rather unusual events I thought I would create a mathematical model to explore this strange space. So the first thing to do is to express the thing in some form and see if it makes sense. An exponential model first comes to mind such as:

How About a Nice Curve Fit?

I've been meaning to do this for some time. That is developing a Windows based system for fitting equation of state terms to experimental data, rather then relying on other people's fitting routines. One of the more common equations of state (P-v relationship) people like to use in the explosives world is the Jones-Wilkins-Lee (JWL) equation of state. There are others but I won't go into them for now. One form of the JWL equation of state for the products of detonation is given by:

The data to fit to has to be in an Excel file and can be imported directly into the application. The data file needs to be in the form displayed. The pressure units are in GPa.

Down The Rabbit Hole

Charles Dodgson who wrote the wonderful book Alice's Adventures in Wonderland under the pen name Lewis Carroll was a mathematician by training and practice. His book was admirably illustrated by Sir John Tenniel. Dodgson  made some good strides in mathematical logic, linear algebra, and matrix operations. Of course, who doesn't remember who Alice spotted one fine day and decided to follow. 

 

Our notorious white rabbit, and so down his rabbit hole we go to do some exploring. Namely data, mathematics, curve fitting, and models,  all of which would be familiar territory for Dodgson. I was planning to post on a completely different matter when I realized I have been remiss, and that I needed to better define some things. 

SIR Model Revisited

I've gone back and cleaned up my basic SIR Model as described in a previous post. I have added some features and put some more thought into it. I hope to describe it here and what might be some of the ramifications. Given the current state of political affairs here in the United States and being the election season it has helped me wade through some of the effluvia that is always present in politics. Especially concerning this matter.

Show Me The Model

I've been exploring the model space and it's a dark, cold place. You can get lost out there. I developed a basic SIR model for disease transmission and recovery and set out to turn the knobs on the values. Recall the original model looked like the graph below. What you can see is that the blue line is very nearly at zero and the green line is approaching 1000 or the total population that I used.

The blue line being very nearly zero means there are very few members of the population left that are susceptible to the disease. The red line indicates the infectious which are the people currently suffering from infection and potential death. "Flattening the curve" is spreading out the red line in time which can be accomplished by reducing the transmission rate (social distancing.)

That Took A Bit of Work

In my "What This Blog is About" page I mention about doing something yourself and then explaining it to someone else so you can really start to understand something. I have been asked a number of times my take on the Covid 19 business, and I have tried to stay honest and say I don't know enough about it to offer up much in the way of an opinion. I have been trying to rectify that ignorance and have made the first steps. This is my description of what I know to this point and what I have done.