[MUSIC] In the previous activity when we were focused in the beginning of the epidemic, we were looking at a situation where the whole population is susceptible. At that stage, we narrowed things down to a single fundamental driver, the average number of infections that is caused by each infected case. Now, at the epidemic peak, many of you will have released that there is a second actor on the stage. This is the population immunity. Intuitively, people are only infectious for a finite time before they die or recover. This could be days, as in the case of measles, or years, as in the case of HIV. The main point is that, as the epidemic grows, there are more and more people who used to be susceptible but are now immune. The overall effect is that number of susceptible people steadily declines. Eventually the infection becomes a victim of its own success. Imagine an infected person at the beginning of the epidemic. They're surrounded by susceptible people since we've assumed that everyone else has no prior immunity, however, now imagine an infected person late in the epidemic. At this stage, this person is not surrounded by so many susceptible people because immunity is more widespread. Without a new supply of susceptible people in the population, it becomes harder and harder for an infected person to replace themselves by at least one infected person. Now I gave him meaningful look when I said without a new supplier susceptible people. And, that's because I want you to remember that we're thinking of a very simple SIR epidemic here where people become immune and that's it. In a later week, we will look at more realistic situations where susceptibility can go up as well as down, but let's return to that infected person late in the epidemic. Remember that the definition of R naught is the average number of secondary cases in a fully susceptible population where we can also define a similar concept to a partially susceptible population. In other words, where some people are already immune. In this situation, we refer to the effect of reproduction number Reff. You can see that this definition is very similar to that of R naught, except we don't require that the whole population is susceptible. As a result, note that Reff changes over time as the epidemic progresses. In L symbol SIR epidemic, Reff initially has the same value as R naught since everyone is susceptible. But, it steadily declines over time as more and more people become immune. The epidemic slows down, comes to a halt and starts reversing when Reff eventually declines to 1. In other words, each infected person is unable to meet enough susceptible individuals to pass on the infection and thereby replace themselves. And, this is due to a depletion in the pool of susceptibles across the population. So, we asked the question earlier, does everyone get infected? You can see from this curve that the answer is no, It is not necessary for everyone in the population to become immune, in order for the epidemic to reach its peak. And in fact, even once the epidemic has run its course, there are still people who remain susceptible. They've escaped infection altogether. The important thing is even though they're remaining susceptible people, there are too few of them for Reff to be maintained above 1 and this, is what makes an epidemic decline. Many of you will have heard of the concept of Herd immunity which echoes what we have discussed so far. Herd immunity is just a situation where an infection due to the number of immune people in a population. And by now, you will know that in mathematical modeling Herd immunity is the same as saying Reff is less than 1. You have seen how this condition arises during the natural course of an epidemic because a virus affects and immunizes sufficiently many people to reach Herd immunity. But what if we could raise Herd immunity artificially without the need for people to suffer infection, all that much disease? This is the very purpose of vaccination. And when we vaccinate population, we want to increase Herd immunity to a threshold at which any index case is simply unable to precipitate an epidemic. We'll talk about vaccination in a later module, but keep these ideas in mind until then. [MUSIC]