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.

The first step is to tread the ground paved by the work of so many other people, and I started with the SIR model. That is the Susceptible-Infectious-Recovered Model which is a very simple view of disease transmission and recovery. It's premise is simple: the total population is susceptible to the disease and given long enough will contract it and eventually people will recover. Graphically it is shown below.

SIR Model

At the beginning the total population (1) of the red line is available for infection. As time goes on people contract the disease and eventually recover, the green line. The blue line, the infectious, is the number of people available to infect others. If there is no recovery the red line and blue line would go to 0 and 1 respectively. It would look like this.

SI Model

With recovery though there is an assumption that the person becomes immune to the disease and is removed for all time (t) from the population of susceptible people. The mathematics behind this is all straightforward solutions to partial differential equations, and there is nothing particularly complex about it. Having said that it took some effort on my part to set the problem up and go through the solution process and making sure I understand it.

Now I noted the simple model says nothing about environmental factors, population density, regional variations, race or ethnicity, gender, immune system response and a whole slew of other factors that in the real world will drive disease transmission and recovery. Still this is the first step in understanding the problem.

I've said nothing about the R0, the recovery rate, or anything else. I picked constants that give a good view of the graph for the given time scale. I hope to expand on this and add some real world effects to it in future posts. This is a start.