# Effective Reproduction Number Re or Rt

by Raywat Deonandan, PhD

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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.

The lecture Effective Reproduction Number Re or Rt by Raywat Deonandan, PhD is from the course Pandemics.

### Included Quiz Questions

1. The average number of secondary cases produced by an existing case in a population of both susceptible and immune people
2. The average number of primary cases per infectious case
3. The total number of new cases per new infectious cases
4. The total number of secondary cases per total population
5. The average number of secondary cases per number of primary cases
1. It is not responsive to calendar time.
2. It reflects that people are infectious for the same length of time.
3. It does not show how many people in a population are immune.
4. It does not show how many people in a population are susceptible.
5. It falsely implies a relatively high death rate.

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