I'm Franz Wiesbauer.

I'm an internist, trained in epidemiology and public health at Johns Hopkins and the

founder of Medmastery.

Today we're going to learn how to predict if an epidemic is going to spread fast and

wide or not.

This is super timely.

The new coronavirus called SARS-CoV-2 might very well become a pandemic.

So let's see what will factor into that.

There are a couple of things you need to know.

Let's first talk about the basic reproductive ratio called R naught.

It applies to a situation where everyone in the population is susceptible and no

control measures are taken.

So we're talking about a population that has no immunity to the pathogen.

They're seeing the virus or bacteria for the very first time.

R naught, gives you the number of new cases that an existing case can generate

over time, on average.

So let's take an arbitrary population and say that this guy has the disease and

transmits it to this guy over here.

And this guy transmits it to that guy.

So on average, one case gives the disease to one other person.

So R naught is equal to one.

In the scenario where R naught is equal to one, the population of infected

individuals stays constant.

Now let's look at another fictitious population where one infected person

infects three other individuals on average.

So R naught is equal to three.

So this guy gives it to these three people, and these three people give it to

three more people in turn.

I think you can already tell that what we're looking at here is an exponential

growth curve that looks something like this.

So the number of infected patients increases.

So as we've seen, when R naught is equal to one, the group size will stay constant.

When R naught is greater than one, the group of infected individuals will grow.

And what will happen if R naught is below one?

Well, I think you guessed it.

If that happens, the population of infected individuals will get smaller and

smaller over time.

Let's now look at the variables that influence R naught.

One would be the route of transmission.

So R naught will vary depending if the route of transmission is fecal-oral or if

it's airborne via droplets.

For example, both modes of transmission have been described for the new

coronavirus.

Another factor that influences the value of R naught is the epidemiological system

in which the pathogen is transmitted.

So R naught will be slightly different in various geographic regions with different

social and cultural behaviors, for example.

Here's a quick formula - how you can think of R naught.

It basically depends on the susceptible population that an infected person is

going to encounter per time unit, let's say per days, times the average duration

of infectiousness in days, times the average probability that transmission will

take place per unit of contact.

So each time an infectious individual interacts with another susceptible person.

Which is largely a measure of pathogen virulence - the ability of a pathogen to

cause disease.

It has been estimated by various authors that R naught for COVID-19 is somewhere

between two and three.

Let's compare that to the values of R naught seen during flu pandemics.

During the 1918 influenza pandemic, R naught was 1.8.

In 1957 it was 1.65.

In 1968 it was 1.8 again.

And in 2009 it was 1.46.

So when it comes to R naught, SARS-CoV-2 is quite a bit more scary than influenza,

isn't it?

So what else do we need to know in order to tell if an epidemic is going to spread

fast and wide apart from R naught?

Well, we need to know what is called the serial interval.

What is the serial interval?

Well, let's say this guy, Bob, infected this girl, Pam, with the new coronavirus.

The serial interval would correspond to the time it takes between symptom onset in

Bob to symptom onset in Pam.

Essentially the serial interval is a measure of how fast the disease spreads

from one person to the next.

Let's take the example of a fictitious population of 1000 uninfected individuals

who have never been exposed to the coronavirus, let's say.

Let's assume that this guy enters the population because he has just returned

from Wuhan, China.

Now I will make up some numbers for demonstration purposes.

Let's say R naught was five and the serial interval was 10 days.

So in the first 10 days, this guy infects five people, they develop disease.

After 10 more days, each of these individuals infects five more people in

turn, and they develop the disease.

So we have now 25 people, and after 10 more days, each one of those 25 people

infects five people each.

So we end up with 125 new infected individuals in the last 10 day period.

So overall, we end up with 156 infected individuals in this population of a

thousand.

So what's the incidence of disease?

That's 156 per 1000 per 30 days, or 5.2 per 1000 per day.

Let's take a different serial interval and see what happens.

Let's now say that the serial interval is 30 days instead of 10.

Now that initial case, infects five people over the entire month, so we end up with

six infected cases.

So what's the incidents now?

Six cases per 1000 per 30 days corresponds to 0.2 per 1000 per day.

So you see, changing the serial interval really makes a big difference.

So what's the serial interval for the novel coronavirus?

Well, different authors describe different numbers.

It's generally thought to be somewhere around 7.5 days, maybe even shorter.

For comparison, the serial interval for influenza has been estimated at somewhere

between 2.2 and 2.8.

So here are the R naughts and serial intervals of previous flu pandemics.

And if we compare that to those of the SARS-CoV-2 we see that the coronavirus has

a worse R naught, meaning that one patient infects more individuals than is the case

for influenza.

On the other hand, the serial interval for the coronavirus is longer, which might buy

us some time.

So I hope you now understand why with the low reproductive ratio and a high serial

interval, you'll get an epidemic that will propagate more slowly.

Whereas with a higher reproductive ratio and a low serial interval, you'll get a

much more threatening epidemic that will propagate much faster.

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