## ← 03-18 Herd Immunity

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Showing Revision 2 created 10/24/2012 by Amara Bot.

1. Let's have another look at the SIR Model to learn about
2. an important phenomenon and that's Herd Immunity.
3. On the right-hand side of the I equation, the factor I appears in every term.
4. If we factor it out, this is what happens.
5. This helps us to investigate what happens when a huge percentage of all persons is vaccinated.
6. We model vaccination by taking persons from susceptible to recovered,
7. which means that the number of susceptible person decreases
8. if the size of the population says constant.
9. When the number of susceptible persons shrinks, the first term in the left parenthesis decreases
10. and eventually if you vaccinate enough people, the complete expression is going to become negative.
11. The rate of change is negative, this means that the number of the infectious persons
12. is decreasing over the cause of time, more susceptible people get infected.
13. The number of susceptible person decreases which means that this first term here gets even smaller
14. which means that the expression in the right parenthesis gets even more negative.
15. The number of susceptible persons can only decrease
16. when enough people have been vaccinated, we can never have an epidemic.
17. This is called Herd Immunity.
18. Not everybody is vaccinated, but if the number of people who are vaccinated is large enough,
19. we can not have an epidemic nonetheless.