Now we'll talk a bit about the natural history of infectious diseases, and the different distributions or periods that govern how diseases progress in people. So there are a few key distributions in the course of infection we'll talk about. The latent period, the incubation period and the generation time or serial interval. So to illustrate these with this course of infection, I've cartoon out in the bottom. We start with this happy person. He hasn't been infected yet. Time goes by and he's infected, and for all these periods this is when the clock starts, but he's not infectious yet. He can infect other people and he doesn't have symptoms yet, he doesn't know he's sick. He has the silent pathogen that's infected him and it is riding with him, and he doesn't know he has it yet, and he doesn't know he's going to get sick. After a while, he's still asymptomatic, but he becomes infectious, and we denote that here by the fat smiley face turning to red. So this period between when he's infected, and when it becomes infectious is called the latent period. So after a bit more time, he's going around infectious but he doesn't know he's infectious, he's just infecting people left and right but has no idea he's sick because he doesn't have any symptoms yet, but eventually he turned sad, because he developed symptoms. So that time between when he was infected, that initial infectious event, and when he developed symptoms, that's called the incubation period. On average though, there some amount of time between when he was infected and when he actually infects another person, because even though he was infectious before, he may not have actually infected anyone. So eventually he's going along, he's sick, he's infectious and encounters this other lady here who he infects, and of course she hasn't gone through her latent period or incubation period yet, so she's neither infectious or know she's infected, but that time between when our original person was infected, and when you new infects this other person or the average time between the amount original person was infected, and when he infect s someone else is called the generation time. So let's talk a little bit more about these distributions. As I said, the latent period is the time from being infected to becoming infectious. It requires assumptions to measure because we don't really have a direct measure of infectiousness. So it can be measured by pathogens shedding. For instance, we could swab people's noses on every day of their flu infection, see how much flu viruses is in it, and make an assumption about how much virus had to be there before they infected other people. It could be the timing of infection events among contacts. So for instance, if we had one of those households studies we were talking about before, and we had our index case, and we saw people exposed to the index case becoming infected on different days, we might be able to estimate the timing of the infection. The third way it can be measured is by sophisticated mathematical models, that look at disease patterns and try to estimate these unseen or latent periods. Largely the latent period when it comes to control, and we'll talk about this later is important in its relation to the incubation period, particularly whether it's longer or shorter than the incubation period. So as I said the incubation period is the time from being infected to developing symptoms, and it can be measured if we have an estimate of the time of exposure, and the time of symptom onset, and usually we're not able to get the time of exposure exactly. There have been a few experimental infection studies where they've actually given people diseases and directly measured it, but usually we have to say, okay, there's, here's a start period and here's an end period where somebody could have been infected because say, maybe they were traveling to an area where the disease occurred, and now here's when they become sick, and then we use statistical techniques to say, "All right, the average timing in that period and the timing of when they become sick, how does the period look?" The incubation period is partially important because it tells us when cases are picked up by surveillance. Think about if there's an epidemic and I go out, and do active symptoms surveillance in the community. I go door to door and start asking people, are they sick? Or perhaps I set up a screening program at the airport to ask people who are coming into my country if they've developed symptoms of a disease. I'll only catch those people if they're actually sick or have actually developed symptoms, that is they've already completed their incubation period for the disease. It's also important for passive surveillance. So that is when people come into hospitals and clinics, and we detect them that way because people don't go to the doctor just, they're walking down the street, "I think I'll go to the doctor today see if I'm infected with any pathogens." Now you wait till you get sick and then you go to the doctor. So everybody we see for that surveillance system, the incubation period will have completed, and this will become important when we start talking about control. So the generation time is the time between subsequent generations of infection, and this is a little bit more tricky of a concept. So this is the average time from me being infected to infecting others. So this light is not directly observable because like I said before we don't really observe the actual moment of infection, but we can approximate the generation time by the serial interval, which is the time between symptom onset on subsequent generations of infection. That is, this is the time between me developing symptoms, and the time between the people who I infect develop symptoms. So that is difficult to measure, but in contrast with the actual timing of infection events, we could conceive of a study where we might actually be able to measure it. So the generation time is important because it has a close relationship with the basic reproductive number or the reproductive number that we talked about earlier in dictating the speed at which epidemics grow. So let's think about that a little bit. So imagine we have a disease of a basic reproductive number of two, and a disease of a basic reproductive number of three. So your intuition might be that, that disease with a basic reproductive number of three, would always grow faster than the disease with a basic reproductive number of two, but now let's imagine their generation times are different, and this is what I illustrate here. On the top, we have a disease for basic reproductive number of two and a generation time of two days. So after one day or on the first day, there's a single case, two days later we have two cases, and then each of those two cases calls two more cases. So two days later we have four cases, and so that's on day four. So then on day six we have eight cases, then on day eight we have 16 cases, and then on day 10, we have 32 cases. So now imagine as illustrated on the bottom, that we have a disease that has a reproductive number of three but a generation time of five-days. So we still start with a single case in our first day but now it takes five days before we have three cases, and on day 10, each of those three cases will have cost three more cases, and that'll give us nine total cases. So by day 10 in the less transmissible disease as measured by the reproductive number, we have well over three times as many, 32 cases compared to the more transmissible disease, the one of the reproductive number of three, where we only have nine cases, and this is because of the different generation time. However, ultimately over the course of the entire epidemic, if it's not controlled, this disease that causes three cases in each generation, will infect more people than the disease that infects two cases in each generation. So all of these key periods; the incubation period, latent period and the generation time, tend to follow long tailed distributions. So that as illustrated on the right, means that most people are around the single central tendency, so have are on the shorter end of the length of the period but then there's a very long tail, and there are people who may have generation times or incubation periods 2, 3, 4 even 10 times as long as the average. So in other words, for the incubation period, this means while most people will develop symptoms in a short time, few will take much longer to do so. So, statistically examples of the long tailed distributions include the log-normal distribution and the gamma distribution. One of the reasons this is important is because we're not always interested in the median time or the meantime at which people get sick. We might be interested at periods when say, 90 percent of people have developed symptoms or 95 percent of people develop symptoms, so that long tail is often important when we're thinking about these diseases. To summarize the key points from this section, the incubation period is the time for an infection to symptom onset. The latent period is the time from infection to becoming infectious, and the generation in time is the time between subsequent generations of infection, and it's approximated by the serial interval, the time between symptom onset in each of those generations. The generation time combined with the reproductive number, determines how fast an epidemic will grow. All three distributions tend to have long right tail, so some people have very long periods compared to the average. So as an exercise, let's consider a few diseases. Measles has an R nought of 12 and a generation time of 12 days. Influenza has an R nought of two and a generation time of around four days. In the epidemic and a completely naive population, that means everyone's susceptible, So R nought matters not R. How many people would have be infected after 24 days, and assume that there isn't enough immunity to make, the reproductive number changed at all, that is R nought will be present in each generation. Now imagine 50 percent of the population was immune at the start of the epidemic, how many people would be infected after 24 days now?
