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.)

SIR Model: High Transmission Rate and Fixed Recovery Rate

So if I reduce the transmission rate I can replot everything and it shows as below. I've put it in a video format so I can watch the change. What it means is that there are still significant numbers of the population available for infection. What we have done though is spread out in time the infectious and reduce the strain on the health care system.

SIR Model: Reduced Transmission Rate with Fixed Recovery Rate

It does not mean we will necessarily avoid any new infections or deaths as time goes on. Not if the disease stays present in the population. Thus, the predictions of a second wave. Remember also, the recovery portion of the model assumes that immunity is gained and previous members of the population do not re-enter the susceptible population. On to the next model, which is one of my own devising.

In this model I assume a disease that is latent in the population with some goodly portion of the population available for infection. As the infection becomes active or starts to be transmitted new members of the population are infected. This is shown below.

My Re-Infection Model

The red line is infection activity and the blue line is members of the population infected. Two things are notable. The first is that the infections rapidly grow and then decay according to the original SIR model. The second thing to note is that the infections continue cycle after cycle as long as there is a significant susceptible population.

Well, I have plowed this field enough for now, but I am certain to re-visit it at a later date. The spreadsheet for a simple SIR Model is available for download in the Open Calculators section of the Google Drive.