So, before I get into the main body of talk,

I'd like to acknowledge quite a few people who I've worked with on the material,

I'm going to talk about today.

I'd like to mention in particular Harriet Mills and Jon Read.

Harriet at Bristol and Jon at Lancaster,

who've done work on the mobility work that I'm going to talk about.

And then Adam Kucharski from the London School,

who's done a lot of the work on the mobility model.

So the talk today is about influenza virus.

It's about how influenza virus infects its human host and it's about

the behavior of the human host such that

it influences the transmission dynamics of influenza.

And I've put a image of mortality report on there.

And that kind of digital data image to remind me talk a

little bit about traditional epidemiology versus digital epidemiology.

So a kind of advance spoiler.

A lot of the results I'm going to talk about,

you would characterize them really as

traditional epidemiology or built on traditional data sets but there are

some topics and questions that are much more being

influenced these days by modern data streams and analytics.

So I want to share them now,

maybe get some feedback and discussion about how these kind

of topics are going to change in the next short little time.

So our conceptual model,

our conceptual epidemic model of influenza is very old and we use the most

traditional of epidemic data to kind of understand how flu goes around.

The chart at the top of this slide is taken from a 2005 paper but the data are

from around the time of the 1918 epidemic

and it's access all-cause mortality for New York.

It's taken by the Olson paper in PNAS,

which gives one of the nicest estimates or the most kind of

robust estimates of influenza mortality in a well-defined population.

And we can track the fact that influenza is an epidemic disease just by looking,

just by counting the extra deaths that occur.

So this is kind of one of our original bases for studying flu as an epidemic.

And then the charts at the bottom show age-specific antibodies against flu.

So we've been able to isolate influenza virus for

a very long period of time certainly in eggs and some other systems.

So if we think that someone's had flu,

we can take a sample from them,

we can grow the virus and store it,

and then we can test the ability of

a person's serum to react against individual strains of flu.

So for a very long time,

we've known that flu changes relatively quickly as time goes by.

So the chart at the bottom of this slide is taken from a paper in the early 50s.

The chart on the left shows that at the time the samples were taken,

young people had high titres to recent strains.

It's all recent strains on the left.

And then around the same time,

a similar study showed that old people had

higher titres to all the strains and young people didn't have high titres.

So we've known that flu acts as an epidemic disease and we've known that it

changes relatively quickly as measured by antibodies for a long time.

And then, the final piece of

the puzzle is best expressed by this data from a paper in 1972 by Hobson.

And this shows how your antibody titre is predictive of your susceptibility for flu.

So, this is from a data from

around a thousand British people in

the northwest where they tried to deliberately infect them with

a few different strains of flu and they've stratified

these data according to the strength of their antibodies against

flu on the X-axis and then

the probability of getting infected on a deliberate challenges on the Y-axis,

and you get these beautiful log-linear relationship.

So, as you get lower and lower,

antibodies against flu, your susceptibility goes up.

So that, with the fact that it's drifting in this antibody space the whole time,

gives us a really nice conceptual model of flu which we can express as an SIRS model.

The thing to remember about flu when you're describing it with an SIRS model

is that the R-to-S transition is capturing a lot of different bits of biology.

So it's certainly catching the drift,

so the virus is changing and not the people,

and it's increasing the proportion of people who are susceptible.

If there is waning immunity,

and this certainly is over short periods of time, if there is waning immunity,

that's also built into the R-to-S.

And then if you've got no other demography and you're running this,

then you're also really getting births counting towards your R-to-S transitions.

And you can run an SIRS model.

This is to try and kind of show pre-pandemic,

pandemic and then endemic.

Note the log scale on the left-hand side but you can get

these periodic epidemics every few years

which is kind of similar to what we see with nothing

more complicated than a three-state SIRS model.

And the promises are not that crazy.

So we have a nice conceptual model of

flu and we have a mathematical representation of it.

And just to flash up some nice data,

this is from Marc Baguelin and Edwin van Leeuwen for a project that we're working on,

showing how real data looks kind of like that as well.

So, we've kind of pretty much got it covered.

And I know that sounds obviously setting up the rest of

the talk and it sounds a little bit silly but to be honest,

up until 2009, that kind was how we modeled flu,

and we thought it was okay.

And that's kind of what the rest of the talk is about.

So, I'm going to go through.

So, the SIRS model,

it can just be a starting point, right?

We can refine that in whichever way that we want.

So as I'm sure, you're all familiar with.

We can choose to stratify each of the susceptible,

infectious and recovered by many different dimensions if we want.

We can have risk groups, age groups,

spatial location in the limit of infinitely many compartments,

and I wouldn't recommend this to PhD. students in the room.

We could go down to

an almost individual type representation with compartments if we wanted.

So in terms of purely mathematical sense,

it's a framework from which we can refine

in order to kind of produce more realistic models and try and get some insight.

What I'm going to argue during the rest of the talk is three dimensions for age,

space and immune state.

Then, we've actually made a reasonable amount of progress on those or we've kind of

discovered some interesting stuff in relatively recent times.

The age story might be well known to quite a few people.

Then I'll talk about some specific examples for space and then I'll try and save

as much time as I can for the immune state thing which is

the stuff I'm working on most at the moment.

Okay, so now, thinking a little bit

about how age is important for a kind of disease dynamics of flu.

This is the topic when you search in Google Images for pandemic in 1918.

And I'm sure next year,

we're going to see lots of versions of this on the news and in the Science press.

And it's just to remind me to talk about

a lot of the studies of flu that were done in the early 2000s.

So after the September 11th attacks in the U.S,

there was a very strong horizon

scanning exercise that was conducted in many places across the world

because people in government who were responsible for averting or

dealing with catastrophic events were heavily

criticized for not anticipating this unusual risk.

So, it led to the whole smallpox vaccination question

which was alluded to yesterday during some of the questions.

And then once people realized that bioterrorist

infectious disease was actually quite difficult and unlikely to be a problem,

quite a few people said, "Well, Mother Nature terrorist disease is probably more likely."

And it led to a very concerted wave of pandemic planning during the early 2000s.

And there are a lot of different modeling studies done and Joe and I,

while we're working here in Hong Kong,

we kind of started to get into this.

So, we did a really nice household-based model of

pandemic influenza which turned out to be a model

of moderate or severe influenza pandemics.

We didn't kind of realize that at the time.

And along with many other groups around the world,

we tried to anticipate how effective simple interventions would be.

So we looked at household quarantine with and without antivirals and things like that.

And we came up with estimates of how

the infection attack rate would be affected by interventions.

So here it shows for given different basic reproductive numbers,

what we thought the attack rate would be with

no interventions and then how we thought it would be reduced for quarantine.

This is an example of lots of different projects that were very

influential because they showed it was worth investing in this preparedness,

so that in a moderate or severe pandemic,

you'd make those savings.

But, this is another paper that we did during the pandemic based on discarded serum,

I think some blood transfusion serum in here as well,

where we actually measured the infection attack rates in Hong Kong as

the main wave of the epidemic went through Hong Kong.

And as you can see,

the average infection attack rates were much,

much lower than we anticipated using a kind of standard SIRS type model.

And there was high levels of infection in

children but much lower rates of infection in adults.

I think lots of you'd be familiar with this story.

So, why was that?

Along with lots of other groups,

we figured it out pretty quickly.

So, it was really two effects.

The top left there

is one of the other results apart from Marc's excellent work from the PLoS Med study.

It's one of the other results in the PLoS Med study where they

characterized the way that people make contact with people at different ages.

So the top left chart that shows you that children tend to

make social contact with children much more frequently than they do with adults.

It's generally age-assortative, you tend to mix with people your own age.

And then the bands show that you also mix with parenting age.

There are a lot of parents in relationships in social contacts.

So the age mixing was not uniform.

And then, the chart on the right-hand side is from

a paper Simone led in with the Imperio Group,

showing the susceptibility of individuals was different for the 2009 pandemic,

that children had, on average,

much greater susceptibility than did older adults.

And if you took the very simple SIRS model and you

stratified by age and you introduce

those components of age-specific mixing and differential susceptibility,

you got much better fits.

And you came out with pretty good infection attack rates.

So this is a good example of how we very

quickly refined the existing model and got much better insight.

And so, most models used those two components and had some measure of kind

of northern hemisphere models that had some measure of

the cumulative infection up to the start of the northern hemisphere autumn.

We were able to do pretty accurate predictions of

influenza through the main wave in the northern hemisphere.

So, then we said, okay.

So, how might that work at the individual level?

So, we also, as well as a discarded serum study,

we also set up a longitudinal serological survey.

So, the chart on the left,

it shows the viral isolation data phone calls in the bottom of the chart,

and then the top of the chart shows about 700 lines for each

of the individuals that we recruited and to a longitudinal serum study.

So, we got the infection status of each

individual and we were

able to infer the infection attack rate which agreed with the discarded serum,

but it also gave us individual level data,

with which we could then kind of look for factors

that might affect an individual's risk of being infected.

When we set up the study,

we also had access to the questionnaire that had been used in the polymod's so,

we run that same questionnaire on the people for whom we got the infection status.

So, we were able to actually ask people how many contacts did you

have three days before we took this survey,

and then that was done around the time that we did the follow up sample,

so we had a serological infection outcome and a response to the contact survey.

So, we thought if age mediates infection through the contact process,

then we could try and explain away age in

our data by measuring the contacts of individuals.

So, just trying to push the rationale further down to the individual level.

The chart on the right,

for the purposes of an overview top,

just says that that didn't work.

So, what we did is we constructed

many many different variants of a logistic regression model,

using all different combinations of how your contacts may contribute to your exposure.

So, thinking about different durations of contacts,

different weightings of contacts,

and we came up with many plausible hypotheses,

and we did all of those models with age included as well and without age,

as a test to see whether we could explain away age in any way at the individual level.

So does your contact pattern predict your infectiousness?

So, this is an AIC scale on the bottom.

There's about a 40 point difference on the AIC scale between those two distributions.

All of the ones over there have got the age term in

and all the ones over there have not got the age term in.

So, you cannot explain away someone's risk age,

specific risk of infection,

by asking them about their social contacts,

which is kind of a negative result,

but that's what we found.

So, we kind of pushed on a little bit more thinking about well,

how can we refine this system to test this a little bit better,

and this is work that was led by Adam Kucharski as a follow up.

So, what we did is we thought again about the kind of the stratified as our model and

we stratified it by age and arbitrarily highly resolved kind of groups,

and then for each of those age groups,

we stratify people by their reported social contacts as well, okay.

So, we've got a model space now where we can have arbitrarily high resolution in

age and arbitrarily high resolution in the contact groups within each age,

and then we didn't just fit the values of the transmissibility for the contact groups,

we assumed they were proportional to the reported number of contacts.

So, the data here is giving you how transmissible you are in a contact group,

because it's averaging people who your age with about the same number of contacts.

That gives us a model space and then we could use a nice kind of,

we used the final size approach to do it efficiently and we could search through that.

I think this is close contacts on the right and all contacts on

the left and we only need half of that space because it's symmetric,

and then the light color on here is a model that was better supported,

the dark color is a poorly supported model,

and we found there's

no justification for having those contact classes within the age groups.

If you just have age groups and you parameterized them using the reported contacts,

then you start to get good explanations for the data.

Okay, so, what it does look like in terms of charts?

Here, we've got the,

observe the attack rate for different risk groups stratified by age,

and we've got kind of the best fitting model shown at

the top for reported close contacts and then all contacts.

So, what you basically see here is that the average behavior of

your age group determines your risk of infection according to these data.

We're only using one parameters of it.

It's basically are nots.

And we get these fairly nice fist,

to the fine detail of that risk of infection by age group.

So, it's your individual behavior doesn't determine your risk,

but the average the distribution of behaviors with in

your age group in terms of contacts contributes to your risk.

So, just to kind of quickly summarize on the context data,

that Polymod-like data has been gathered for many communities.

So, it's almost become

a kind of truth in itself as contact survey stuff,

there's lots and lots of examples being gathered around the world.

There's even efforts to model the contact data based on other data,

so that we don't have to gather it.

The observation I'd make is that there's,

at the moment we've not done a prospective study where we say,

we think these two populations behave differently according to

their contact characteristics and we should be able to predict

a different level of infection based on one say,

Italy having very many contacts and the UK having very few contacts.

We should be able to predict some differential infection

based on those studies, we've not really done that yet,

and I think that would be something that be nice to do,

and then there's an awful,

this is that we kind of overlap into the digital epidemiology space,

we should be able to get

much better information about the way people form social contacts by

cross referencing geographical and digital data with social digital data.

So, that would be, I think,

maybe linking up those last two bullet points might be a fun thing to do.

Okay, so, I think the age flu,

and age mixing is kind of

a well-understood case study for how

model refinement can really help improve our understanding of the system.

I think we've kind of got quite a bit further to go on how space works.

So, I just want to talk about you know,

a couple of specific examples that I've been involved in.

So, top left,

isolation data for pandemic flu I think for the U.S.

We know that flu's epidemic,

we know it spreads rapidly when it comes,

if there's not enough immunity.

We kind of know how it spreads.

It has to reproduce within

one human host and it's either

through contacts or aerosol or some combination of the two,

but the virus itself reproduces in one of us and then transfers

through the environment somehow to get into

another one of us in order to start reproducing again.

So, we know how that works.

We know how it travels long distances, okay.

Flu has to get on a plane to travel transcontinental or you know, long distances,

and if we build models based on

airline travel about how flu strains are going to get exported,

either in a pandemic or during seasonal flu, they do pretty well.

So, if we actually know the volume of people traveling,

we can predict long distance patterns of flu.

What I'd argue is that in between those,

for shorter distances, we don't

really have a good understanding of exactly how flu is transmitted.

So, that if you look back at the simulation models that were done prior to the pandemic,

the local spread that we predicted with those was really rapid and very homogeneous,

and what we actually saw was relatively slow spatial spread

locally and very asynchronous peaks.

There's not great data on this,

it's difficult to get a kind of bond or example,

but I think most people who follow

the epidemiology in different places would kind of agree with that.

So, the question really is,

can we start to characterize the relative probability of infecting

people at kind of different social distances?

So, if I sneezed now,

there'd be a chance I could infect you,

but then if I shook your hand afterwards,

it would be a bit lower than that,

that's a difficult thing to quantify.

And then, if I were to sneeze or if I were to travel from here,

where is it likely to go next,

within the next one kilometer,

10, kilometers, or 100 kilometers?

So, that's the kind of problem space that we're in for this study,

and this is what a contact questionnaire looks like.

This is our version from a study in China of the of

the Polymod study and it's just basically you have

this long table where you ask people kind of how many contacts did you have?

Was it a group contact? What kind of contact was it?

And you know we've done lots of these studies.

The thing that we did in the study in China,

that was a little bit different, is we geolocated each contact.

So, we didn't do that with an electronic,

it was still traditional epidemiology,

but we negotiated a list of locations with each community as we arrived.

So, we had a pick list that we constantly add to within the community,

and then when someone says that they make a contact at the market in the town over there,

down at the sports field,

we make sure we negotiate it off

the pick list and then we've got accurate Geo locations for the pick list.

So, we get finally resolve special occasion.

And this is a description of the study.

So it's the Fluscape study

running Guangzhou which is just a couple of hours on the train north of here.

And we selected around 50 communities at

random in a kind of transect spreading out from Guangzhou.

In each community, we go once a year.

We do the social contact survey.

We take blood and we do some other questionnaires as well.

And the data in this bit of the talk is about where they report the social contacts.

So you can just see, we've published some preliminary work,

looking at how the distance of social contacts

drops off according to child or adult, urban and rural.

And this is just an example of how most of the contacts are quite

local and they tend to go in the same direction from each place.

They're not kind of randomly spread in space,

but it's just kind of an illustration of the study area.

So then, what we're interested in is

if you like better parameterization of the simulation models, okay?

So, if you want to run a simulation model at very high resolution,

you can't go and do questionnaires on every single person in the population space.

If you're doing more aggregated models,

you might have census data that tells you how people go from place-to-place.

It may be that mobile phone data could give you

actual flows between very high resolution deems in these spaces.

But the way that we've kind of tackle that is by trying to build

a statistical model of how people move

in order to then parameterize the spatial transmission model.

And these mobility models are not new.

They've been around in geography for a very long time,

and they get used for all kinds of things like

deciding whether you want to put a new routes on an airline network and things like that.

These types of analysis have been done all the time.

So, the thing that we might like to suggest is there's

a conceptual difference in whether you think of these models as a flux model.

I should stop trying to look at the screen.

A flux model or a mobility model.

So, a flux model is kind of,

a more typical way to think about this,

you can divide your space up into

500 different locations and you measure the flow of people between those locations,

or you try to have a statistical model of the flow between those locations.

So you're dealing in this flow as your units of mobility, or of your unit of travel.

Then the other way thinking about it is each individual has a propensity to travel.

So you want to go and achieve some task which is make a social contact and that

individual is more likely to do that social contact nearby than they are far away.

And we build a statistical model of

your relative propensity to make a contact over different distances.

And then obviously, if there's nobody in a particular location,

you're not going to go there.

So the propensity model will be mediated by the surrounding population density, okay?

They're not fundamentally different.

You can always build.

You can estimate the mobility from

the flux and you can make the flux model from the mobility.

But if you're thinking of high resolution transmission models

or individual-based transmission models,

then you need a model for how individuals choose to make their social contacts.

So it's useful to think of this kind of fundamental mobility version,

if that's what you want to do.

And the thing that's motivated a lot of interest,

and it's not going away in terms of the topic,

the radiation model papers,

which a lot of you will be familiar with was published in Science in 2013 by Simone,

and that was a parameter free model of flux for the U.S.

I think it was county level in the U.S.

And so, what that basically says is that if you

want to know how much flow there is between two locations,

say R and J, then you look at the total number of people living

within the ring that just covers the ring with R at the center and J at the outside.

You look at the total number of people inside that ring and you call that S.

And then use this kind of absorption term at

the bottom which doesn't have any parameters in it at all.

It's just based on the number of people in each location,

the number of people in the ring and then the S,

the total outbound flow from R. So you apportion

the outbound flow from any little square according to this absorption type _term.

And I'm not familiar with the physical literature but apparently,

it comes from radiation absorption through different media.

And then, this was presented as an alternative to

the gravity model which in this work, I've not going a slide in it.

We implemented with an offset and a power term.

So, it basically described your probability of traveling between

two locations would be driven by the kind of decay rate for the distance,

a little kind of offset term to say that that

your probability of travel didn't go down for a while if the offset was high,

because it doesn't make that much difference traveling one kilometer to a few kilometers.

And then we also consider putting having a term for the destination population,

so essentially, the J term here.

Do you count that population as

everyone counts the same or would you scale the impacts of the population?

So the destination per our term.

And then we estimated the most likely version of these models.

We also tried to be fair.

We used a more recent version of radiation that does include some kind of offset term,

and we fit our data and we fit the model to the data and then saw which ones did best.

So this is the self-reported social contacts

in and around Guangzhou between a distance of one kilometer and a 100 kilometers.

When you fit all the data,

the offset gravity gives you the best fit,

but it's only a little bit better than the kind of pure gravity,

and then the radiation and offset radiation do very equally at this scale in the data.

You can stratify the data.

So the way that these charts are working is,

the gray lines are the data and the colored lines are the model and the confidence bounds

or the kind of binomial type confidence bound on the observations.

You can stratify by rural and urban and then the cool thing

that came out of this is the offset gravity generally does better.

So you need this little tweak to make short journeys so that you don't start

discriminating between short journeys generally when you fit this to the data.

But in the urban-only data,

the need for the offset went away and you get this just beautiful fit.

That's not very scientific and I'm not sure the best ways to characterize output.

The fine features of the probability of making journeys of

a different distance are reproduced with great fidelity by this very simple model.

So, the interaction of this power term on

the particular distribution of population density is getting just about the right shape,

which we think is really neat for these data and encouraging that

simple models can maybe explain these overall complex flows.

And then, just to kind of bring you back,

we were aiming to do better to understand the transmission dynamics of these flu.

So we checked that it did make a difference when you

simulated flu transmission across this space.

If you chose one kernel over the other then you did

get different epidemic curves coming out of that.

So that's it for the main part of that study.

I just want to flag,

because of a comment that someone made yesterday,

we've looked at that general space of spatial matter population models and looked at

the resolution with which you simulate your spatial model.

And to try and show that basically,

depending on the width of your kernel,

you do need to simulate a quite high resolution in order that part of

your pattern is not being

determined by the fact that you're aggregating your populations.

So I just to flag up another paper on this topic.

And also, David Halls talk tomorrow,

which will be another kind of follow on.

So once you have those parameter values from that,

how do you structure the model to investigate heterogeneity and attack rates?

David is going to talk about that tomorrow. So, I think I've covered most of those.

For these data, gravity-like models are much better.

Okay. And then finally, immune state.

So, this is the thing that's kind of occupying most of my attention at the moment.

How can we refine these models to make better use of

the available data on immune states of individuals.

So, in the full scale study for each of

those households we gather

at least 20 households for whom we get at least one blood sample.

And we designed this, this was really

designed to look at the transmission dynamics of flu.

It wasn't designed to do immuno-dynamics and there was

no way we could afford to go and catch virus in this population.

The study design that would let you get out there

and swab people frequently enough and isolate flu in order to parameterize the model.

That was a 20 million dollar study

because you'd need so many people running around swabbing and testing.

So, we thought well, if we just got the blood sample at

regular intervals then we'll infer whether they've

been infected from having this longitudinal serum and it would be fine.

And then, we can fill all of our models and we go down the road a little bit,

And the difference if you're used to doing secondary data analysis as

a model or someone gives you the data and you get to test your hypothesis on the data,

someone else has already done

all the exploratory descriptive statistics, you don't have to.

But when you're gathering the data yourself the first thing you've got to

do is test the obvious hypotheses with the obvious model.

So, we didn't anticipate this that much but we got to this stage and

this is our pilot data on the left hand side showing

the antibody titres against the current strains and

historical strains for individuals in the study ordered by age.

So, the youngest people are at the bottom and the older people are at the top.

And we did lots of historical strains because we want to

infer all the infections because it

seemed crazy to just look at

the most recent infection when we've got people of all different ages.

And, what we saw in these data was obvious patterns.

There's more antibodies in younger people.

Younger people don't have antibodies against strains they couldn't have seen.

There's some strain pattern and there's some individual patterns.

So, that's the the kind of heat chart version there.

The left hand, kind of like this one,

is the same data just put on an on a scatter plot.

So, the antibody titres on the y-axis with a little bit of scatter,

ages on the x-axis and there's some patterns there but it's kind of noisy.

And, we've plotted that one by age.

And then, the key thing that we did,

it was just in Roesler leading on this,

is we re-plotted the data by the age of the individual when that strain first circulated.

Okay. So, if this was done in 2010 and it it was a 20 year old individual

then they would have been 10 years old or

eight years old when the 2002 strain first circulated.

The age of first year circulation is relative,

is different for each of the strains.

And if you do that, the pattern that you get of

antibody titres becomes much more consistent.

You get this rise for people in the strain they would have seen first,

gradual decay, and then maybe an uptake at the end.

And, we could fit a really nice regression model to

that and we said the shape of the term in the middle,

which is the contribution,

to your expected titre from your age at time of isolation,

we said that shape doesn't just drop off a cliff it kind of goes down the plateau.

So, let's call it seniority.

So, rather from the original antigenic strain,

which is just the first strain,

is important, it appears to kind of go down in this gradual way.

So, as in the descriptive sense,

let's call it seniority.

And, if you ever try and publish an original antigenic strain,

it's really difficult because nobody agrees what it actually is,

which makes reviewing really tricky.

So, if you try and suggest something

that's a little bit different from original antigenic strain,

it's almost impossible and we must have had a really nice editor whoever that is.

And I'm not sure whether I know but whoever it is, thank you.

But that's a little bit unsatisfactory because there's no mechanism there.

That's just a descriptive model of someone's antibody titres that you would

expect if you went and tested there flu against historical strains.

So, using some really nice schematic,

just been published in a commentary in science,

what we really want is a model of how you build up infections over the course of

your life and then you will titres against each of

these different strains that builds up over life.

And, you'll get these antibody landscapes where the x-axis here is

the strain history and the y-axis is your expected antibody titre against that strain.

So, this was a commentary that went with a paper by Fonville,

from Derek Smith group, where they had kind of another look at that.

I'll put a paper on that in a minute.

I put a chart for that in a minute.

So, what we wanted to do was basically have,

for all of those same individuals,

have the computer represent their infection history,

have it search through the space of them being

infected or not infected with any particular strain of flu.

And then, also have it search through the space

of immune dynamics that might result from an infection.

So, look at different ways,

different levels of simple boost that you might get or look at some kind of

back boost where if you get any infection with strain three

then it increases your titre to strain one.

Or, look at differential patterns arising by suppression.

So, your boost to

the second infection isn't as high as your boost to the first infection.

There's some kind of suppression going on and cross-reactivity as well.

So, it can be to do,

where there is a red label then assumed are infected,

if it's a black label it's assumed you were not.

And we let the computer loose to look for the best model of

immuno-dynamics and infer infection histories

for each of these individuals as it went along.

And getting the short answer,

it did seem to be able to do a reasonable job.

So, these are not cherry picks.

We looked at the marginals for all of the individuals and these are

uniformly taken from the plot of the modules.

So, it can reproduce that kind of

observed variation antibody titres with

different patterns of infection and the same overall pattern of immuno-dynamics.

By looking at the parameter estimates for the model,

it also suggested mechanisms for how the patterns were arising.

So, it didn't favor antigenic seniority,

which is arising from a back boosting type action.

It suggests the seniority arose from suppression.

So, you get lower responses as you go forward in time.

So, that's up to the end of the paper that was published in 2015 in PLOS bio.

And then, as I was coming out the Fonville paper was coming out the same time

and what we kind of realized is we built a model of your persistent antibody response.

So, and, there's a lot of transient responses as well and we knew that

because the Fonville paper has longitudinal data.

So, you can look at these antibody profiles as they change over

time and they published the,

PCR confirmed individuals, they published

the antibody landscapes recorded different partments in time.

And, you can see how all of the antibodies go up and then decay away.

And, it looks like you get left with most of these people,

the persistent response to the newer strains.

Okay. So, it suggests there's two arms to the response.

I'm conscious of time but I'm near the end.

So, what we've done in follow up work is

we've added in another arm to the immune response.

So, you have this process that's building a persistent response that doesn't wane

over time and then we have a fast waning transient response.

And, they're essentially is the same mechanisms just working side by side.

And we can get really nice fits and we fit it to

the data that's published in the Fonville paper from the Vietnam study.

And, it gives kind of a really nice, it appears to give really nice fits.

We can still estimate the probability in individual infected in

any year and we can reproduce kind of

the boosting patterns and when we fit it to subsequent years we get consistent fit stuff.

From different samples in subsequent years,

we still get really nice consistent fits.

And what that does is it kind of suggests that

the antigenic seniority arises from this kind of

two-armed process in the kind of B-cell population.

So, the chart or the top shows kind of what

our conceptual model is for how this might be working.

So, you imagine virus A that's only got three epitopes

and then you get infected with virus B,

where one of those epitopes has changed.

Okay. So, what we think is happening,

I don't think it's that controversial,

is let's say you get an initial response,

if we look at the antibodies generated

against individual epitopes as you go through time,

the first time the three that are on the first virus will get

a nice big boost at the beginning from the initial infection

but they'll all be present when you get infected with the second virus.

So, your envelope is pretty strong to those.

And then, when you get infected with the next virus,

you'll get a temporary boost to all of those epitopes that were on the earlier virus and

then you're only new persistent response is to

that new epitope four that's coming on the next virus.

So, through that kind of sequential stimulation of B cell populations,

different epitopes that we think you build this repertoire.

So, moving this forward,

we want to test on higher volume data sets as they become available.

Suggests some very testable hypotheses

about convalescent B-cell populations and given modern essays,

we can actually look at those and try and

look at the kind of individual clonal populations.

It can generate augmented infection data for just the rest of

the standard epi by inferring who got infected when.

And then, we're really excited to try and kind of look at vaccines as an alternate,

kind of, exposure history.

So, I will leave those up if we have time for a few questions,

but I will stop there and thank you for your attention.