Effective Reproduction Number Re or Rt

00:00 Now, we've talked now about the base reproduction number the R nought.

00:05 But there's something called the effective reproduction as well sometimes called R, or Re, or Rt or Re as a function of (t).

00:15 It goes through many names.

00:17 Rt is commonly used these days.

00:20 So, remember, the R nought, the zero in the R nought refers to zero people immune in the population.

00:27 As time goes on, some people will become immune or not susceptible.

00:34 So, the effect of reproduction is the average number of secondary cases produced by an existing case in a population that is made up of both susceptible people and not susceptible people.

00:46 So, to get that, we simply multiply the R0 by the fraction of the population that is still susceptible.

00:57 The ones who not yet immune.

00:58 So, over time, as immunity accumulates, the Rt should come down.

01:04 There are some limitations to the reproduction number.

01:09 Remember, it's not responsive to calendar time.

01:15 Different people are infectious for different lengths of time.

01:18 So, we measure, the time period we care about is the length of time one is infectious.

01:25 So, considered two diseases.

01:26 Disease A is highly infectious over a short period of time, and Disease B is less infectious, but over a long period of time.

01:34 Disease A will take off more quickly.

01:37 He'll have a higher incidence at the peak, and it will be much shorter.

01:41 So, here's a couple of curves that consider this.

01:45 Some diseases, people become more or less infectious as time goes on.

01:51 So, consider the example of a disease where someone is infectious, the same amount throughout the duration of their infection.

02:00 In other words, you get infected today, you recover a week from now, but in between now and a week from now, you are capable of infecting the same number of people all the time.

02:13 You are shedding the same amount of virus.

02:15 You are just as dangerous now as you are at the end of your infectious period.

02:20 We call that a flat curve, if we were to graph your infectiousness over time.

02:27 On the other hand, if we consider someone who is highly infectious in the beginning, but less infectious later on as the disease progresses, well, that looks a bit differently if we were to graph this.

02:40 Well, the amazing thing here is the area under each of these curves is exactly the same.

02:45 As a result, the attack rate remains exactly the same.

02:50 What does that tell us? It tells us that reproduction number isn't the only thing that determines the dynamics of an epidemic.

02:59 The shape of the infectiousness function also matters too.

03:04 And you might see in an epidemic curve, something looking like this peaked curve here, where we have a sudden explosion of cases that comes down rapidly.

03:16 Or we might see something resembling the flat curve here where we have a rapid rise but a steady state looking state of affairs that comes down later on.

03:26 They both describe the same level really of seriousness in the population because the attack rates are the same but they look differently graphically.