An SIR model for Covid-19
This is a simple example of an SIR model for my Mathematics for Liberal Arts classes at Northern Kentucky University, Spring of 2022.
Let's think about things on the scale of a week. What happens over a week?
With an Ro of 2 (2 people infected for each infected individual, over the course of a week); recovery rate of 1 (every infected person loses their infectiousness after a week), and resusceptible rate of .05 (meaning .05, or a twentieth of the recovered lose their immunity each week), the disease peaks -- does the wave, then waves again before the year is out, then ultimately becomes
"endemic" (that is, it's never going away, which is clear after two years -- that is, a time of 104 weeks). This is like our seasonal flu (only the disease in this simulation doesn't illustrate seasonality -- that requires a more complicated model).
With an Ro of .9, recovery rate of 1, and resusceptible rate of .05, the disease is eliminated.
Masking, social distancing (including quarantining following contact), and quarantines all serve to reduce infectivity. And if we can drive infectivity down far enough, the disease can be eliminated. Other things that help is slowing down the resusceptibility, by vaccinating. Vaccines (in general) impart an immune response that reduces -- or even eliminates -- your susceptibility. We are still learning the extent to which these vaccines impart long-term immunity.
Other tools at our disposal include Covid-19 treatments, which increase the recovery rate, and vaccinations, which reduce the resusceptible rate. These can also serve to help us eradicate a disease, so that it doesn't become endemic (and so plague us forever).
Andy Long
Mathematics and Statistics
Some resources:
- Wear a good mask: https://www.cdc.gov/coronavirus/2019-ncov/your-health/effective-masks.html
- Gotta catch those sneezes: https://www.dailymail.co.uk/sciencetech/article-8221773/Video-shows-26-foot-trajectory-coronavirus-infected-sneeze.html
