Here, you can see a word cloud of different terms that people tend to come up with when thinking about three factors that drive an epidemic. But which of these are really fundamental drivers? Remember, we're interested in the basic building blocks rather than other variables that simply modify our fundamental drivers. If we think about it, there are just two important things going on, and we can reduce both of those to a single core concept. First, the epidemic can only happen if the pathogen is infectious enough. For the moment, let's put aside the question of how much that should be. The main point is that you don't get an epidemic with a pathogen that just isn't good at getting from one host to another. So what we're interested in is the rate of infection. Second, even if a pathogen can transmit from one person to another, remember that there's a certain duration for which people are infectious. This period comes to an end either because infected people die or recover, but whatever the reason, the infectious period is the only window of opportunity that the pathogen has to pass from one person to another. So there we have it. Our index case can only cause an epidemic if he or she is passing on the infection quickly enough and for long enough. You'll notice that all other variables in the word cloud are simply ways of modifying these drivers. For example, population density or contact rates, just determine how closely people are brought together to determine the rate of infection. At this stage, you may realize that we've already seen these quantities in mathematical terms. If you can remember how, then great. But if not, don't worry. We will come back to this in future lectures. For now, though, the important thing is this, can we bring these two factors together into one criterion for an epidemic to occur? In doing so, can we clarify what we mean by infecting people quickly enough and long enough to start an epidemic? It's often a bad idea to anthropomorphize diseases, but let's do it anyway. If you are a pathogen infecting a single person, then, to avoid extinction, you would want that person to infect at least one other person. In turn, you would want each of those secondary cases to pass on the infection to at least one other person. Again, some may infect more, some may infect less, but what we're concerned with is the average. So when we say that a pathogen needs to transmit quickly enough and for long enough, what we're really saying is that the average number of onward infections per infectious case should be greater than one. If it isn't, then infected people fail to replace themselves and the pathogen goes extinct without causing an epidemic. This is a concept that appears in many other places in nature and society. For example, think of nuclear chain reactions. These are caused by the radioactive decay or break up of unstable atoms such as uranium. Each atom breaking up can cause a number of other atoms, n, to do so as well, and we get an explosive chain reaction as long as n is greater than one. Another well-known example is in social media. When we talk of a video going viral, what we usually mean is that every person seeing this video is passing it on to at least one other person. In infectious disease modeling, this number is important enough that it has its own name. It is called the basic reproduction number or R naught for short. It is defined as the average number of secondary infections caused by a single infected case in a fully susceptible population. So in answer to our question, what is the single criterion for an epidemic, we can answer by saying that an epidemic occurs when R naught is greater than one and that epidemics either fail to takeoff or fizzle out when R naught is less than one. All remaining variables simply modify R naught. Now, let's explore what happens to the prevalence when R naught is greater than one. You can see that we get rapid growth. The prevalence multiplies by a fixed amount with each day or week, and this is what we call exponential growth. It is the same thing with chain reactions and viral videos. When an individual person or atom is replaced by more than one individual on average, you get exponential growth. This is exactly what we see in the early stage of the epidemic. I encourage you to look up different examples of exponential growth in other areas of nature and society so that you can get a feeling for what's going on in this early epidemic phase. However, this cannot go on forever, and the epidemic curve eventually reaches a maximum before it starts to decline. In the next activity, we will again consider exactly what is driving this behavior.