Basic Reproduction Number R0

00:00 Hello. In this video, we'll tackle that all important topic of the R nought (R0), the basic reproduction number.

00:06 Also the R(t), the effective reproduction number.

00:10 And from it, we'll learn about the herd immunity threshold.

00:13 All these important topics, and terms you probably heard a lot about in the news lately.

00:19 We'll learn about the limitations of the R nought, a little bit about how to compute it, and learn as well about some of the basic reproduction numbers and herd immunity thresholds for some of the famous diseases throughout history.

00:32 I hope you enjoy it.

00:34 The basic reproduction number, the R nought, as it sometimes called R0 is used to measure the transmission potential of a disease.

00:45 How likely it is to find fast penetration through a society or population.

00:51 You see average number of new infections produced by an existing infection.

00:56 And the zero in R0 and nought refers to the fact that at this point, zero people are immune in the population.

01:06 Therefore, everybody is susceptible.

01:10 We compute the R nought by dividing the number of new cases by the number of existing cases within the duration of the subjects infection.

01:19 Now, what does that mean duration of subjects infection? You're infectious, so long as you can pass the disease on to somebody else.

01:28 And you're no longer infectious if you've recovered, or if you're dead.

01:32 So, the duration of infection is not the same as calendar time.

01:35 It will vary from individual to individual.

01:38 And technically, there are a handful of different and exotic ways of computing the R nought for a population.

01:46 But this is the general idea of how the math is done.

01:50 For example, if the R0 for COVID-19, in a given population is 3, we'd expect every existing case, every existing person with the disease to produce 3 new secondary infections.

02:04 This assumes, of course, that everybody around the infected people are susceptible, and that the disease is penetrating homogeneously through the population, which isn't always true.

02:16 R0 excludes the new cases produced by the secondary cases.

02:20 We only care about the people that the existing people will directly infect.

02:26 We don't count the people that are subsequently infected by the new people who are infected, or else this goes on forever.

02:33 We only care about the first layer of infections.

02:37 So, let's look at some scenarios.

02:39 Consider if two people are infected at the beginning of an outbreak.

02:43 How does that look if the R0 is two, one, or less than one? So, if R0 is 2 at the beginning of the outbreak, we have 2 infected people, shown here as 2 green individuals.

02:57 At Time 1, those 2 individuals have stopped being infectious.

03:03 They've stopped being infectious because they've either recovered or they're dead.

03:07 Neither case they're not infecting people anymore.

03:10 But before that happened, they managed to infect 2 people each.

03:15 So, now, we have a total of 4 people who are infected.

03:19 At Time 2, those 4 people have infected an additional 8 people.

03:23 But those four people are now either recovered or dead.

03:26 At Time 3, those 8 people have now infected 16 people, and the original 8 are now recovered or dead.

03:35 And at Time 4, those 16 people have now infected 32 individuals.

03:43 And now the epidemic is out of control.

03:47 As you can see, the R0 is 2 in 4 time intervals, we now have a very high number of infected people.

03:54 Consider now if the R0 were 1.

03:58 So, we start out with 2 infected people, shown here again, with our 2 green people.

04:03 At Time 1, those 2 people are no longer infectious.

04:07 They're either recovered or they're dead, but they have each infected 1 new people.

04:12 So we still have 2 infected people in the population.

04:15 At Time 2, of those 2 people are now either recovered or they're dead.

04:20 They have infected 2 more people.

04:22 At Time 3, we have 2 people. At Time 4, we have 2 people.

04:25 In other words, when the R0 is 1, we always have the same number of infected people in the population.

04:32 We have steady state.

04:35 If the R0 is less than 1, let's say 0.5.

04:38 What happens there? Well, at Time 0, we have 2 people again who are infected, but on average those 2 people infect 1 person.

04:48 So, 0.5 each gives us 1 person.

04:51 And the original 2 are now either recovered or dead.

04:54 At Time 2, that 1 person is not capable of infecting 0.5 people because 0.5 is not a person, so the epidemic stops.

05:06 If R0 is less than 1, the epidemic goes away.

05:09 Huge differences in these three scenarios.

05:12 So we watch the reproduction number very carefully to determine how likely an infection is to really take off in a population.

05:23 So again, with the R0 is 2, we start out with 1 person, who gives it to 2, who gives it to 4, who gives it to 16, who gives it to 32.

05:31 It takes off quickly.

05:32 if R0 is greater than 1, we technically have exponential growth, which is a serious consideration.

05:40 So, in this slide, this summarizes what we know.

05:45 If R0 is greater than 1, the epidemic is worsening.

05:48 If it's equal to 1, it's holding steady.

05:50 And if it's less than 1, it's diminishing.

05:53 It's affected by several factors: Course, the rate of contacts in the population.

05:59 So, if you can't get access to people, you can't infect them.

06:03 And this is an important observation because that gives us a tool to stop transmission prevent contact, you prevent transmission.

06:12 What's the probability of infection being transmitted during contact? So, some diseases are less likely than others to actually find purchase in your body, if you're exposed to them.

06:25 So that matters.

06:26 And the duration of infectiousness.

06:29 So, the more time you have to infect people, the more likely you are to infect them.

06:34 If you're only infectious for a few hours, well, you probably won't encounter a lot of people in those few hours.

06:40 But if you're infectious for many days or weeks, you're going to encounter a lot of people and have many opportunities to transmit this infection.