Ben Sparks, who, ironically, is the person who lives closest to me.

He's only about 40 miles.

Uh, think he's that way.

Uh, but he's a home at the moment.

So am I.

But we're gonna have a talk via technology.

Hopefully.

And what are we talking about?

Ben?

What are we gonna try and discuss?

I think there's a lot of videos and check out there about how mathematicians are modeling this spread off the covert 19 virus.

And it's kind of like this sort of house in days for mathematical model is, despite it being a horrible circumstance, everybody is curing upto.

Ask the mathematicians opinion on what's gonna happen next, and I guess it's a shower.

Mathematical modeling is what helps us predict what happens in the world in general.

What I wanted to show you was a way of using one of the standard models of disease spread on free piece of software that people could just try themselves and see that the modeling that people are doing to predict this is is kind of accessible.

I see you've got the honoree brown paper needs must we've got to do something properly.

Number five actually don't have any physical brown paper I could find.

So I had to, you know, get a screen grab of brown paper and put it in joji brah, which I'm gonna use to show you a model off a disease spread.

Hope that.

Is that an image taken from an actual number five for actual noble fell brown people.

Yeah.

I mean, spared no expense here.

So I'm gonna try and build you a mathematical file in this program called Joe Dobro, which anyone can try and follow along with the programs.

Free to grab it if you want to try it.

The three very was.

I'm gonna use a written on the screen already.

Just second.

You could see that right s for susceptible.

Meaning a bunch of people that are possibly able to get Aziz I for infected people who have got the disease are for recovered by which I mean are not infected anymore.

To be honest, that doesn't necessarily mean recovered right that they may be dead, which means they're not gonna be infectious anymore.

And that's the sad truth of modeling diseases like this is that there were two ways out.

You recover or you don't.

But either way, you stop infecting people.

I'm gonna I'm gonna use our for recover.

Some people call it removed.

But I will forget to say that word.

So I'm gonna just He's recovered, as long as you know what I mean.

We're gonna build up like organ mathematical models, some sort of simple, almost naive assumptions of how diseases spread and follow the mathematical consequences of those simple things.

Just to make a prediction on DATs the judge, we will do our butt lifting the heavy lifting for us.

So happy for me to start chatting mass.

Okay, I'm gonna set up a population of size one.

This sounds a little bit confusing, and I'm typing into the top of the thing here and equals one, which is mean I'm using, like, my entire population to me, like 100% 0 to 1 measures some fraction of the population on the whole population.

Size one.

You can do these models with a large number, but it everything to scale.

So I'm just gonna go with between zero and one.

Which is why my graph is zero and one about here on the screen.

I'm also going to set up some initial set up.

So presumably, there are some infected people in my population of the ways you gotta be asking why we're doing the model.

So I'm gonna start some values off infected and susceptible and recovered in the infected.

I'm gonna call.

I start No meaning me starting.

I mean, the number of infected people have the star of this.

I'm gonna call 1% which is 0.1 on get there.

Ever announces, therefore susceptible.

So they're susceptible, people start is gonna be end.

The total number people take away.

I start because that's not 9% susceptible.

That's because no one of this stage has recovered.

So our started zero on those, like my initial conditions for a model here looks a bit cryptic.

Basically programming in maths.

I'm gonna set up 23 more variables, in fact, which were used in a minute.

And you'll feel a bit arcane until you realize why.

But use sliders for this.

There's a slider tool here.

It's gonna put it here.

This slider is gonna represent How quickly does this disease gets transmitted?

Like you?

The infection rate s so I'm making a slider.

Won't do anything yet, being c I can change this number.

It's gonna be something to do with how quickly infects people and then another slider for how quickly people recover from this disease, which is gonna be smaller because it takes a while to recover from diseases other ways they usually don't really register anymore.

What are the units of time here back that it doesn't actually matter.

Were so we could pick a unit and run with it.

Let's say days, but I'm not necessarily gonna have the numbers right to model this in days.

But then if you change the union time, you just have to change these parameters to reflect that we can do some because they're on sliders.

We can do the playground later on to see if we can change the units.

Okay.

And at the moment they're called A and bay A and B.

Yeah, T I give them different names.

If you like to really help me, help me remember what they are.

Well, yeah, Let's rename it.

Let's call.

This transmission was quite trans or coding has to have a horrible names, right?

but I still typing really long names all the time.

Let's call it recover.

So I've got transmission rate and a recovery rate, and I'm gonna use them to build some night.

What's one more parameter I need, Which is how long I'm gonna let the model run for.

You'll see why this is useful.

Later.

I'm gonna call.

It's the max time.

I'm gonna get up to about 24.

Okay, Good.

Now we're into the real master.

What I'm gonna do is set up three what they call differential equations, which sounds scarier than it should.

But these are equations which tell us the sort of naive assumptions were gonna make about these three numbers.

What I want to know in the end, is what these numbers are over time.

How many susceptible, How many are infected and how many have recovered.

But what I can tell you is straight away what those numbers are.

I can guess that how quickly they're gonna change depending on various things.

So I'm gonna write down three equations would tell me about the rate of change of these things.

The 1st 1 is called s Dash.

I'm gonna call it s dash on.

That is sort of mathematical code for if you're gonna write it longhand, maybe D S d T If you know any calculus that's the derivative off s with respect to time.

But in everyday language is the rate of change of the number of susceptible people, how quickly it's changing and it's gonna depend on time.

So this bit looks technical, But I'm typing in a bunch of variables.

The rate of change of susceptible depends on time on the number of susceptible.

Lt's on the number of effective on the number of coverage.

One of these things might affect that, but in practice and here, this is the first time we actually gets a matter it on the screen.

The rate of change of susceptible Sze is negative because the number of successful people will go down because they're getting infected.

Does that bit makes it?

And we're working on this assumption that once you've been infected, if you've recovered or died, you can't get again.

Yeah, we are assuming in this particular mortal of disease that won't see you've infected and recovered, you are now sort of immune.

In some sense, you don't become susceptible again.

The thing is, the if you got loads of susceptible people on a few infected people first, anyway, the susceptible we will go down.

So what I'm expecting here is a negative rate of change, which is arriving and negative Sign of the top of the screen there, and it's gonna depend on three things.

One is the parameter a, which I've called trends now, trying the transmission rate on DDE that will also depend on how many people are susceptible.

So if there's lots of susceptible people you can imagine, we're gonna lose them to the infection's quite quickly and also depend on how many infected people are.

So this is a relatively simple There's a number, the transmission rate multiplied by the central people multiplied by the infected people on its negative because the susceptible people going down, they're gonna turn into infected people.

So that is my first equation.

It's a differential equation is a rate equation.

That's what it means it by different situation we need to do to MME.

Or for the other two variables, and it's not too bad.

So I'm gonna go with my next I dash is gonna depend on the same four possibilities here.

But this time the first was obvious because if people were susceptible and that's what this first equation we typed in was capturing, they're gonna become infected next.

So anything that's gone away from susceptible has become infected.

So it's exactly the same as what I just wrote down.

But this time, positive.

So you see, it's the same thing.

Transmission rate, times s times I.

But this time it's not gonna negative, son, because the infected people going up, presumably if they're moving from susceptible to infected.

However, I hope we're all aware that some people can recover, and so that will cause the number infected to go down.

So I need a negative bit, and this is where the recovery becomes in liquid.

It recovered for that right, and that would depend on how many people are infected.

The more people infected, the more people that can recover.

Obviously I had a certain rate, so that's got my number in there as well.

I noticed you're not attaching any, like waiting's or anything to these.

To these numbers, it all seems like a really what one.

There are two waiting's, the two waiting's of these precise numbers trans transmission right and recovery rate.

So there are waiting's.

But I'm trying to keep the model simple.

So there's at this moment it's 3.2, and that'll affect how many people are gonna move from susceptible to infected and the recovery right?

He's gonna affect how many people move from infected to recover it.

So those are the waiting's if you like, but they're the only parameters, and this is the thing with models.

You you start simple, and you realize that even simple mortals can capture behavior.

And then you upgrade the models, which will be a whole week's course instead of a single word.

Let's do one more equation, which is the R Dash, the rate of change of recovered people.

So the same four variables in here.

And this time it's a simple and again because anyone who's infected and now recovered is gonna move into this category.

So it's precisely the term I just had a the end of the infected rate, but this time positive.

So the recovery most plied by the number of infected.

So actually there are only two terms in this.

There's the negative version in the susceptible to infected one, then agains up negative there in positive there and then the effective.

When you got in the negative people that's recovering from infected to recover it.

So again, some turned up negative there and positive that.

So that was That was the hard man.

That's that's the modeling.

But that's what mathematicians get paid for to come up with these models.

To be honest, they're not rocket science there.

Sensible guesses of how things might behave.

Solving these equations is a different matter.

Before we do that, I'm just gonna change the color soon.

Keep track of this so susceptible.

We made blue infected.

We had a sort of brownie read on recovered.

Let's go with curry.

Is that all right?

Can you see those colors?

Okay.

Ben's color blonde, by the way, people.

Which is why he's asking me all the time.

You got no idea I had a long chat with Brady about Is that actually read?

Anyway, we're gonna go with this.

We got a brownie red infected color, which is.

So if you want to solve differential equations, then you two go and study some serious math.

And I'm not here to teach you to solve different equations.

What's nice about mathematicians is that they have programmed computers to do numerical solution, just like a calculate IQ and solve equations for you.

Judge over here can solve differential equations s o I got type in here.

Come on called end sold, in fact, that his insulin OD the O.

D.

Stands for ordinary differential equation.

Mathematicians are as bad as everyone else coming up with the acronyms that no one recognizes but ordinary differential equation.

In this case, it's a system of three differential equations on dhe.

This command is just gonna spit out the solution.

So this is the exciting.

But you just get to type it in on a well, should duel the work for us.

First of all, I need a list of derivatives, and that's the three things I just typed in these air rate equations or derivatives injured.

We need curly brackets for a list.

So it s dash.

I called it and then by dust and then our dust close that list.

They asked the initial X coordinate and on our scale, X axis is time.