Types of People
From the virus point of view it sees three types of people:
- Those who it hasn't yet infected [the susceptibles S],
- Those who currently have it [the infectious I],
- and those who used to have it [the removed R].
These type of models are called compartmental models, and people can move between compartments in a logical way.
How the virus spreads (Maths part)
Suppose I have the virus, and am infectious for 8 days. If I meet 15 people in a day and there's an average of 5% chance of transferring the virus during each of those interaction, then over the 8 days I'll give it to roughly 8×15×0.05=6 people [5% is 0.05 as a fraction]. More generally between a start time and end time of measuring:
Please stop and draw this out in your mind or on paper to see why the above makes sense.
So we still need to estimate the number of removed. A reasonable way of estimating it is
The above is pretty much all the maths required as a good starting point to model infectious diseases.