your way of explaining is so cool, soothing to the ears and easy to understand ! I watched your video a few months ago, I wanted to revise SIR and looked through some other videos today but they were not as good as yours. I then searched over and over again to get back to your videos....
Thank you, Dane! I'm sure I heard that idea from someone at some point in university differential equations classes, and wish I could cite it, but I don't recall where I first saw the idea.
Great video. Simplified for better understanding. Just a question? At time t=0, do we have infected individual(s).! If not, then how does the susceptible get infected, that is, where does the infection come from?
This model is from 1927. It assumes that an infected person immediatly gets contageous. Same wirh the recovered or dead. Strange that no model with time constants was developed since. A particular aspect of corona is that it can be contageous 3 days before any symptoms are there. None of this can be imbedded in this model. In our present situation, we see that also the parameters beta and gamma vary with time, as new contact restricting measures are introduced. So modelling our current pandemia is flawed by all these restrictions. Wonder how politicians can draw the right conclusions from this.
Thank you, Ram. In many descriptions the term used for the R compartment is "removed" rather than recovered. We assume that there are not additions to the overall population, but the important thing for the model is that whether recovered or removed, it is assumed that the individual cannot infect others.
The model allows one to use any number of individually infected individuals. However the number needs to be non-zero, or the model will not ever evolve (which makes sense since if no one is infected, it will not spread). The smaller the initial number the slower the initial growth will be but because the initial growth is exponential, the infective population will eventually become significant. This is all easier to see on a log scale. If you use non-normalized equations (which I would if I redid the videos) I'd probably experiment with 10 to 1000 initially infected individuals if you have a population size of, say, 300,000,000 people. It depends what aspects of disease spread you want to use the model to understand. Starting with a bigger number basically amounts to starting the simulation later in the pandemic. If I recorded these videos again, I would use raw numbers rather than numbers scaled down to fraction of the population size. I was just processing what was happening around me at the time and threw the video together to help myself process.
This loose speaking about S and I can be really misleading when further parameters get derived. The graph in the beginning shows clearly that S is NOT the number of suszeptibles, as stated, but it is the RATIO of susceptibles to total population, as these values are normalized between 0 and 1. Therefore beta cannot be the contacts per infected per day. Instead of repeating what all the books say, a more thoughtful handling of the subject would be, what I expect of a RU-vid contribution. Otherwise I can just look it up in Wiki, where the same thoughless stuff is described. And, lastly, Runge Kutta is not a trick for solving but the standard method for solving.
