Acute Infectious Diseases in Space and Time with Bryan Grenfell

and it’s pledged today to introduce Brian Granville who is a professor of ecology and evolutionary biology and public affairs at Princeton University Brian began his research career as a PhD student at the University of York in England where he was trained in population biology and he actually worked on the population biology of whales so in terms of scale of organism he’s changed quite radically over the past few years he then did moved on to his postdoctoral work where he began working on the dynamics of affects diseases again from an ecological perspective he after his postdoc went up to several faculty positions firstly at Imperial then at Sheffield is that right and then Cambridge Penn State and then most recently he moved to Princeton last year Brian holds a number of accolades including he’s a fellow of the American Academy for the Advancement of science he also holds a medal from the Zoological Society London and he’s also I noticed an order of the British Empire my first met Paul when he was an undergraduate in Cambridge and I can tell you all the stories later on thanks very much for the invite it’s always great to come here so what I’m not going to talk about is environmental change in particular but I am going to talk about non-stationarity I’m going to talk about the dynamics of particularly highly immunizing infections like measles and to some extent influenza and measles as a particular case study is is the kind of c.elegans of epidemiological dynamics if you like in terms of its historical data and but I’m also going to talk about measles currently in the Sahel in Asia in particular where it’s still a major killer my texture really is going to be looking at the effect of external forcing shortened season or forcing longer term demographic forcing on the dynamics of these oscillators as a first step and I’m gonna argue that this forcing is quite a quite a handy model if we’re thinking about are there not other kinds of non-stationary effects in populations and ecosystems and so on and then also gonna talk about more complex infections particularly like influenza where an immune escape that is we saw recently with the influenza pandemic immunity isn’t always that strong how did these demographic influences interact with an immune escape and what are the mechanisms that really drive that so I’m gonna I’m gonna go across quite a wide range of things and there’s a large cast of characters Cambridge Penn State our colleagues at NIH who’ve been involved in this and and also a number of funding organizations on both sides of the Atlantic so what I want to do to start with is to talk about the population dynamics of measles and I apologize to some people in the audience who have seen bits and pieces of this several times I suspect though some people won’t have done so measles is is a kind of paradigmatic post natural enemy oscillator in ecological terms we see these lovely biennial epidemics in the UK data these are just notifications of infection they notified about 60% of infections which isn’t really bad for an ecological system slightly more annual dynamics post-world War two and these these epidemics are driven by what we buy by a number of and the first of them is Israeli population immunity and is what one can call the epidemic clockwork by that I mean and we can summarize the dynamics of something like measles and we don’t care in this case how many viral particles you’ve got we care about whether you’re susceptible or infected or recovered after maternal immunity is waned susceptible individuals who’ve

never seen the infection become infected it’s a respiratory virus it’s very infectious and then after a short infection they moved through to a recovered class and their immune then to reinfection for life and the reason for the strength of the immunity is not really well understood and it’s very interesting why it’s so strong most infections aren’t this strong then vaccination with an attenuated virus but this isn’t an immunity that’s that’s also really very very strong and seemingly pretty long-lived so if we think about an infection now spreading through a population then if we think about a pandemic like situation where you introduce one individual into a big population of susceptible individuals one infected individual will infect this kind of magical number in my neck of the woods r0 which is the number of secondary cases that you might cause on average in a a totally susceptible population and this number was kind of bandied about a lot for pandemic flu maybe for pandemic flu it was some of the historic pandemics it was maybe two or three or more for this recent one it’s probably one point not very much not very transmissible for measles it was about twenty so you would you could cause on average maybe twenty secondary cases there are cases of outbreaks in the Faroe Islands where someone went to a dance and had not been infection for 40 years and they infected hundred and twenty people in a night so it’s extremely infectious what happens then though is that in a kind of predator-prey sense this rapid increase in the number of cases depletes the susceptibles really quickly and the births can’t really keep up with that because that’s a kind of linear thing and therefore you get a rapid depletion and this is this in direct effect of herd immunity so the epidemic turns over at a kind of critical proportion of susceptibles and there’s a lot of there’s a lot of mathematics that that can be expressed but essentially that picture captures that so this is the first component of the dynamics which is really the epidemic clockwork but then there’s a bunch of other effects which influence the dynamics of measles and these are the dynamics of measles again in Wales here similar to what we saw before onset of vaccination and we see much more irregular dynamics and a gradual trend downwards as the authorities gradually got their act together and increased rates of vaccination but before telling you what the other components which drive the dynamics of this ecological oscillator are I wanted to just show you some observed data because the other nice thing about these systems is that there are a really great data these are cyst or achill data Finland and Wales the areas of the circles proportion to cases London is in yellow and then smaller places are in shades of orange and yet London’s yellow here and it’s scaled on to zero one year so that we can see it compared to the rest of the country there’s a kind of annual period at the start and then there are these lovely at least to the eyes of the dynamicists biennial oscillations so very very synchronized biennial oscillations and you see that there are big epidemics there’s a big epidemic every other year in terms of our threshold our clockwork it took about two years almost exactly two years for the birth rate to top the susceptibles up to a threshold where there could be another epidemic but then you see in between the big epidemics there are small epidemics as well and I’m going to come back to that seasonality so now and yet the other thing that we see here is the spatial temporal dynamics and we’ve done we and a lot of other people that a bunch of work on this not going to focus on spatial temporal dynamics today but there are strong waves of infection moving away from the big places to the small places and the infection kind of winks out in the small places due to demographic stochasticity small numbers of cases in drops means that you know you might the crucial three people might not go to the supermarket and therefore the affection like the chains of transmission might break and therefore has to be started from big places so that that’s kind of forest fire dynamics that drives those oscillations those observations oscillations in space then when we move through to the vaccine ER things get much more D synchronized and that’s about to get another story and much more irregular in their dynamics but you see that another reason why people have looked at this stuff a lot apart remits public health importance which I’ll come back to later is that the data are really great simple so anyway there’s a bunch of other effects and I’m not gonna and there’s and again and there’s again a lot of work on this but it’s published and I can put you other papers if you’re interested that influence the dynamics so the recurrent epidemics but that I mean the epidemic clockwork that we talked about this topping up of susceptibles and then using them up very quickly by the epidemic and there’s demographic

stochasticity that is the epidemic disappears in small places in the troughs between epidemics doesn’t disappear in big places that threshold was about a quarter of a million in these UK data so in cities above that size the infection always kind of tottered along in the troughs between epidemics the other effect is seasonality and what we’ll come back to this but that’s effectively the seasonal aggregation of kids in schools which acted like two people pushing a swing with feather for the mathematicians in the audience that this is like a damped pendulum in its dynamics and if you push it at either end across the biennial cycle then you’ll force the the oscillations to be sustained and then there are long-term secular changes which are vaccinations obviously but there are also changes in the cyclicity which I’ll come back to and explain in a minute so there’s a bunch of if you think of a kind of a dynamic analysis of variance there’s a bunch of drivers that push the dynamics to different extents and there’s also a big complicated story about those waves and spatial temporal dynamics but that’s not germane here and just to say and I’m not going to go into the details of this because I want to get to the more applied questions we can use time-series analysis to look at the non-stationary dynamics here your the dynamics of measles in London just on just on a log scale to make them a bit more sinusoidal and we can use wavelets spectra so we look at power as a function of time as well as frequency and we can see that by the strong Biennial dynamics there and then a gradual change in period in the vaccination irit so there’s a massive kind of time series analysis that we can do on these sorts of data so that’s kind of frequency domain time series analysis looking for patterns so then you have to do process and to do that you have to fit those SI R models to the data it’s effectively to estimate are not and the seasonality and we can do that with States based models so we can fit two step ahead predictions of the model and the step ahead predictions this is of the the number of cases next generation which is about two weeks is a function of the susceptibles now in the cases now depending on the seasonality of transmission and we can fit we can fit models to capture that seasonality of transmission and to cut a long story short they’re quite successful at capturing this is for London the the the the the biennial bit dynamics through much of the pre vaccination era and the annual dynamics earlier on and the annual dynamics the other ingredient of this model is birth rate so that’s the fuel that’s driving this oscillator that’s pushing it back and forth Annie well in the baby boom post of post-world War two at high birth rates you tend to get annual dynamics so that’s that’s that the non stationarity and this is kind of like reverse vaccination if you like it’s increasing the birth rate which pushes the dynamics and means that the threshold is hit more frequently so that’s how we get it the kind of mechanisms here by fitting these models so what about the dynamic impact of vaccination finally vaccination acts like a reduction in birth rate effectively and this is just to illustrate and I think it’s a great illustration for for Public Health people actually if you and then this is that this is not our work particularly and it’s a bunch of work by a previous people particularly do dash Ensler and Joan Aaron and then we did some work with David earn on it if we just take our our seasonally forced measles model and we vaccinate and these are two different runs and and and this red case is vaccinating in the epidemic trough we get sort of slightly longer period slightly complicated dynamics if we vaccinate in a peak year as the epidemics going down we’ll get will get completely different dynamics so there is the possibility of exotic dynamics you have coexisting attractors for example depending when you vaccinate when you perturb the system you might get well get different behaviors this happens incidentally because if you vaccinate in a high year it’s about to be followed by a deep trough so you’re really exacerbating that trough trough effect and pushing it into a different regime and if we fit the dynamics with our time series versions of those si R models we see that these relatively irregular dynamics so you fit to the pre vaccination era and you kind of project forward it’s still messy and you have to allow for kind of extra vaccinations that happened in 1968 they did some kind of catch-up vaccination when they started vaccinating of older kids and if you were low for that you get a reasonable picture of qualitatively what happened but it’s very hard to predict

the irregularities because of those coexisting attractors because of the effects of stroke hasta city so prediction even in this seemingly very predictable system is actually pretty tough read so really what we’re trying to do is project what the dynamics are going to do so one final ingredient so far I’ve talked about the forcing of the dynamics relatively gently relatively low seasonal amplitude there was tremendous excitement in some parts of the ecological community about 20 years ago particularly bill Shafer which is a tremendously stimulating incursion into this area looking at some of the irregularities in in the dynamics of things like measles and and interpret them in interpreting them in this way so this is a bifurcation diagram and it and what what we essentially do in each column of this figure is we pick a seasonality and we just run into two monistic version of something like the model that I showed you and we look with the number of troughs that is we look at the period of the cycles and the richness of the dynamics so it’s very low seasonality you get annual dynamics there’s only one sort of trough at moderate levels of seasonality there are biennial dynamics so there are deep troughs and shallow troughs and deep troughs and shallow troughs and so on but crank the seasonality up a little bit more this is a forced oscillator and you get chaotic dynamics and very very irregular and a lot of people got very excited about this but a bunch of us and I was one of these miserable people pointed out that this is 50 million people in this simulation and this is rather a deep trough okay you can’t you can’t simp simple chaotic dynamics in this system really won’t explain what we see and it’s much more variations like these limit cycle behaviors and changes in cyclicity because of birth rates and so on so it seemed that these exotic dynamics were irrelevant then is that really true so to explore that I’m going to talk about a collaboration and this is a lot of this work was by Matt Ferrari who’s now on the faculty of Penn State who talked about a piece of this a couple of years ago up the School of Public Health and this is with our great collaborators that adds episode which is the kind of research arm of medicine on frontier who of grit links with Nisha so we wanted to look at dynamics and vaccination and measles in the Sahel measles still kills some hundreds of thousands of children a year a lot of them in this Sahelian region so we’d like to now apply our models from developed countries and try and look at optimal vaccination strategies here because it’s not possible to get the very high levels of vaccination that would allow one just to interrupt transmission for kind of health system reasons first thing we need to do though is we need to understand in general what we might expect from the previous work about epidemiological dynamics at high birth rates so Nisha has very diverse most of the populations along the southern edge of the country northern Nigeria is down here and very very high reported birth rate 50 per thousand like triple the birth rate that we saw in those historical measles data for the UK a relatively low vaccination coverage so what’s our expectation just from taking the simple models that I talked about cranking up the birth rate of this echo is a bunch of work that was done about 20 years ago by Angela McLean and Roy Anderson and what they pointed out was that if you crank down the birth rate you get rather irregular dynamic sidled that is if you vaccinate for example as I discussed but what I want to focus on you is if you crank up the birth rate for the models that we developed and fitted reasonably well for the UK for example or the US you get very very regular annual dynamics and you see the troughs here are very very very very shallow so that you would get strong persistence the population would no persist measles was no persistent in a population of 100,000 not a quarter of a million as I said before so that’s the prediction very irregular dynamics if in fact we look at the seasonal dynamics in in of measles in Asia where there are absolutely magnificent data then the there are indeed annual patterns nationally but of course one needs to disaggregate and if we disaggregate by district and let’s focus on on Nia May the capital then in fact we get nothing like what we expect in the model so the models wrong we get irregular dynamics very very spiky epidemics lots and lots of fade-outs lots and lots of missing epidemics so very very different from what we see very erratic epidemics very variable around the country and the

reason is this is a longer time series for Nia May and Nia May has a population of 700,000 so it should persist easily measles should persist easily it disappears after all these major epidemics in fact and it’s because if we fit those models that I talked about those si are models to the data to the time series we find that this thick line this is transmission rate this thick line is the seasonal swing of transmission rate for those old UK data and this is the seasonal swing for near me and it’s much much more seasonal and and that seasonality is focused that most of the transmission is focused in the dry season and the supposition here is that as far as we can tell so far and I’ll come back to this it’s it’s this isn’t to do with schooling at all because the median infection age is about 2 or 1 it’s to do with families moving in and out of the cities associated with our annual agricultural migrations we’ve not got the seasonal disaggregation of birth rate yet but so it could also be birth rate variations associated without the seasonality and birth rate could also be a driver so it forces very strong local extinction so let’s use the models to look at that a bit more systematically and this is another bifurcation diagram and this is how you read it as before I’m looking at the dynamics as a function of the strength of seasonality but I’m adding an axis of birthrate now and I’m color coding so you run us we run our simulations and we look at the cyclicity that we see in the simulations as a function of birth rate and strength of seasonality so these are the data for the seasonality the low seasonality amplitude for London that we saw and you see that all we see there are annual and biennial epidemics it’s very strongly locked to annual and biennial patterns and that baby boom effect would for example be as you crank up the birthrate you might move from biennial to annual epidemics if you crank the seasonality up to the level of Nia may you in fact get much more in general irregular dynamics and over much of the of the range you get chaotic tone because you get extremely irregular dynamics and that’s because there’s this incredibly strong seasonality now one shouldn’t get excited to your about that about chaos rearing its head here really because these troughs are very deep it’s and this isn’t simple deterministic chaos the the measles would go extinct at near Mays population size in this hatched region so what we’re really talking about this kind of determinist somewhat deterministic instabilities in the dynamics leading to these very very irregular patterns so what are the implications for vaccination and for the uncertainty of the system so yeah so by uncertainty I mean if we now think about cranking up vaccination rates which remembers a bit like dropping birth rates okay cranking up vaccination rates in near me then you’re moving down in this direction and then at some point the infection will wink out because you’ll hit the herd immunity threshold then it’s gonna stay irregular right down to the edge of extinction of infection so what’s gonna happen is the dynamics are currently like this so you might have irregular epidemics every few years with fade-outs what you’ll get what you would have got in the old you in the in the current UK case where vaccination rates are not really fantastic in some some groups you’ve got a low grumbling infection because it’s weakly seasonal what you would get in in in these regions is nothing very much then an extremely violent epidemic and the more violent it is the higher case fatality rates tend to be for example then a long gap and then an extremely violent epidemics so we’re currently interested in at least as a theoretical exercise the way that you the way that you give vaccin the extra vaccinations that’s needed in these regions is by supplementary immunization so you you go in and you as well as routine vaccinations you go in with a supplementary campaign every few years in theory if one could pulse those campaigns of vaccination maybe we can in train these dynamics I think that’s a theoretical exercise because really what one needs to do is grab up the background vaccination and and the key point here in an applied sense actually is you know this is a great vaccine and it’s cheap and we really should be rap keeping the vaccination ramped up in these regions and that’s really the issue but things will be deterministically unpredictable so in fact Lygia population are kind of

about 20 million is is probably not at all the regional driver here because measles probably if Nisha was kind of isolated measles will probably go extinct for long periods completely across the country their driver is northern Nigeria where we’re just beginning to collect data and it’s this oscillator that you really need to understand and it’s probably regional coordination of vaccinations that’s going to help us quite a lot there but for measles and for a lot of systems and we’re particularly interested in this and I’m in particular my postdoc Nita Bharti is interested in this it’s the population movements there for trans boundary population movements that we’re really interested in and I think cell phone data as cell phone usage spreads in this region and it’s still not that high and it’s going to be very useful there but another thing that Nita and Annie Tatum that you know at University of Florida is looking at is night lights now night lights are surprisingly effective these days if you correct for less night’s clothes and so on at spotting fires and so on so that we can capture crudely roughly what the population movements into a note of the cities are regionally sorry seasonally and what we tend to see is that there’s there are density changes that are consistent with our population movement things so in the dry season trying to correct for everything else from the images so far then you see stronger night lights in these red regions than in then in the wet season and that seems to indicate an increase in density but what we really need to do now is get more data on the seasonality of birth rates look grown truth more specifically how people move so that we can get it why this seasonal oscillator is so strong and then also transboundary movements and if you talk to the people who work on malaria or many many other infections movement patterns are really key and I think you know it’s very interesting and a cross-disciplinary problem and then finally you know for many regions won’t have good data as good as there are Phoenicia so it’s interesting to wonder if one can then take patterns of movements and patterns of seasonal aggregation of people across Africa for example across this belt and think about how you know measles Co varies with the with the agricultural season and try and make larger metapopulation models and that’s you know that’s an aspiration for the future but you’ve really got to get at the movements first big interest currently and again this is a mostly map Ferraris work is that the local dynamics of access to care in an applied sense is absolutely key by that I mean it’s all very well improving the supply chain or even getting better vaccines and getting the vaccines to clinics for example but you’ve also got a you’ve also got to think about how easy it is for people to access those clinics so a bunch of work that we’ve been interested in recently is how in rural areas vaccination rates are much lower and how because people just can’t get at the vaccine and thinking of in future about how one might optimize that access in these regions is going to be very important because again it’s a way of fighting this seasonality so just to summarize the measles part then we’ve seen the epidemic oscillator we can we’re going to played in that Sun sandpit of nonlinear dynamics in ecology there are seasonal and demographic forcing these nonlinear these are non-stationary effects particularly demographic changes and vaccination changes I wonder if the main impact of environmental change if we want to think of that in terms of cholera or we want to think about it in terms of malaria then there might be direct sea drivers environmentally and there may be climatic drivers of measles dynamics seasonally but it doesn’t seem that that’s the case currently and but I wonder if the major effect on these directly transmitted infections is going to be by things like trends of urbanization trends of population movement as environmental drivers change and I think I think trends of nutrition perhaps and I think that’s going to be an interesting area for future work and growth in this area so what I want to do now is confess that measles is it’s up is in fact the exception a fear of these childhood infections have extraordinarily strong immunity and most infections are in quotes much smarter than that immunity is much more imperfect TB is a classic example HIV is in a different sense much more chronic infections but even acute infections like influenza there’s considerable patterns of immune escape I just want to illustrate roughly what I mean by that

so if we compare measles and flu they’re both RNA viruses they both have quite a large error rate in the polymerase so there’s a lot of variability generated there’s a lot of basis for immune evasion in terms of variation but if we think about the susceptible to infected to recovered class for measles then each of these is supposed to be a strain of the virus but so far it seems that cross immunity is incredibly strong any straight vaccinating or having natural infection and any strain of measles will protect you against any other there are even quite strong cross-species effects for the other vaccines for other more below viruses in the Middle’s group like canine distemper for example very strong very strong cross immunity that means that all these within host intricacies that would produce variations in the virus don’t matter because you can check them away because it’s the same recovered flus okay so that means you get a simple oscillator you get these multi-annual predator-prey type dynamics and you get rather a boring phylogeny for the service molecules with just some spatial variations on this and thanks to any homes for these for these viral phylogenies for flu as we know then just to cartoon eyes it there’s a progressive change every year or in many years at least so therefore we get a kind of ladder like phylogeny rather uncertain population patterns complicated population patterns whole immunities our other slippery things of flu because the virus is changing all the time but but all the patterning is really in the in the in the phylogeny so very very different patterns and now I’m going to think about how and another and there’s a and there’s a bunch of theoretical work trying to explain how patterns of influenza changed through time and how the dynamics and the evolution are related and maybe the h1n1 pandemic will tell us more about that but what I want to do is step back from that and think about how our analysis of demographic drivers and how they push measles dynamics are affected if we think about the dynamics of these imperfectly immunizing infections now we can think of influenza as really an S IRS infection so very crudely you’re now susceptible you’re infected you’re recovered from infection you remain but then you go back into the susceptible class very crudely ok so how is that going to affect our coupling of birth rate to dynamics that we saw for measles well we know that the dynamics of these very strongly immunizing infections like measles and promptly track the the dynamics of the infection so if you change the birth rate you will change the dynamics and we saw that very clearly in practice and in theory if we think about this snow as a kind of environmental oscillator and we think about this big flow so there’s a small birthrate they’re relatively there’s a big big Fleur if immunity only lasted a year or two for example there’s a huge flow of individuals back into the susceptible class so that’s like a big averaged birth rate okay so if we think of this as a kind of oscillator of some sort driving the system then this is a much more powerful oscillator kind of swamping it so if I simulate that here’s a here’s a simulated baby boom here’s the effect on measles dynamics and we see that there’s a a nice tracking of the dynamics in terms of the epidemics if I now assume and this is just an analytical interpretation of this which I won’t go into here if I just assume that same model but the immunity only lasts a few years then the same baby boom has no effect so this is a kind of demographic buffering effectively if infections don’t track birth rate then it’s an implication that there’s very strong imperfectness in the immunity and I’m not gonna go into details you but if we look at the dynamics of the simple models here then this is really very much like if we look at the the susceptibles that is the prey against the the cases that is the the Predators this is very much like the lockable terror model for predator prey dynamics this is for the population dynamics folks in the audience and vaccination and the tracking of birth rate and a vaccination is very much like the paradox of enrichment so if you vaccinate or you reduce birth rate then

you’ll reduce the number of cases of equilibrium but you won’t reduce the proportion of susceptibles and that tracking of birth rate of popular of the dynamics as you change the recruitment rid of susceptibles is very much like the paradox of enrichment in predator prey dynamics talk about that in more detail if people are interested later on but if we look at si RS infections then at different birth rates or vaccination rates there’s no change so the equilibrium which is the intersection of these narc lines really really sits there because effectively if you you vaccinate or you reduce the birth rate you’d still get a lot of people coming back into the susceptible class so there’s much much more buffering of the dynamics so if we’re thinking about now demographic change or environmental change the same thing applies and we’re thinking about perfectly immunizing infection should track that really strongly imperfectly immunizing infections shouldn’t track it and here’s a possible instance which is respiratory syncytial virus in the US and against plotted on the same axis serous as another imperfectly immunizing infection parainfluenza virus and there’s a trend associated with birth rate in this case but not in this case so this may be an instance of that but we’ve not got a conclusive example and one possible example a very immunizing infection is rotavirus here which is a major human diarrhea virus and jinney pizza who’s used to be in harvard and is now in my group and give a talk a couple of weeks ago about this indeed this does track the birth rate very strongly route of iris so but for example influenza does so I think much more rather more weakly so imperfectly immunizing infections should really track birth rate changes and environmental influences much more gently than than imperfectly immunizing infections the theory tells us so corollary of this demographic TRUCKING is that if we look at the theory transmission must be at least partly density dependent if you increase the density of susceptibles which effectively what you’re doing by increasing birth rates that translates through via this kind of paradox of enrichment thing into it it translates through into more predators that into others into more cases very very promptly very strongly immunizing infection so there must be a density effect so but therefore that r0 the transmission rate must kind of track host density to some extent now certainly true in in a in a complicated way which I can come back to if you want to discuss it the childhood infections certainly to have smallpox towards the end of the smallpox eradication high-density countries they had to reach higher levels of vaccination uptake but it’s not always the case and this is just to give an advert for a piece of work with our collaborators at the Marine Mammal Center so this is an animal disease example and this is our wonderful collaborator francis garland this collected data from these glamorous beasts Californian sea lions of leptospirosis which is a major human zoonotic infection over since the 1980s and the laser art these are whole outs of infected animals and you’ll see that there are these fluctuations and it seems to be that it seems that it’s an endemic infection but all I’m all I’m going to say about this is this is that this is a different example because in this case there are massive changes in the population this is pup recruitment which is shot up the population had recovered since the 1970s it been have been threatened then and and population size has changed similarly an El Nino particularly this El Nino had a very very strong effect on pup recruitment but if we look at our naught as a function of population size then there’s no trend this is frequency dependent transmission it looks as though densities of populations local density stay pretty constant across a wide range of recruitments and population dynamics and therefore in this case that the dynamics kind of carry on regardless of the disease as a function of population size now that doesn’t matter in any applied sense here because this is a very healthy population but I don’t know if you know but a wonderful example of a very exotic infectious disease recently which is a transmissible cancer in Tasmanian devils wonderful work by Hamish McCallum that’s a frequency dependent transmission it turns out probably because it’s somewhat sexually transmitted aggressive contacts an associated sexual transmission and in that case the populates that can reverse

of this the population the transmission rate and the death of these animals from the cancer will stay high even as densities decline so it’s a doomed population unless they take they take major effects so this this this effect of frequency versus density dependent transmission is a very important modulator of all that I’ve talked about and I should say that’s a paper just about to be submitted by Jamie Lloyd Smith and Kim Pepin and a bunch of other people and one of these folks would be great to come and talk about this it’s a lovely story so finally I just want to drill down into some detail just to explore just that a bunch of people have got in this audience and and and I’m interested in it as well ultimately if we’re going to understand these infectious diseases we despite what I say for infections like flu certainly we’ve got a drill down and look at mechanism or we’ve got to get down to to some extent that within hosts dynamics and look much more mechanistically at the evolution of immune escape no that’s a complicated business here’s the flu virus with the hemagglutinin and neuraminidase which are the other are the ant are the antigenic surface proteins and in particular that the hemagglutinin gets you into cells roughly speaking neuraminidase gets you out of cells if you’re a virus and both of them vary and the hemagglutinin is the one that varies over time as i described and that’s that’s the thing that drives the pandemic changes and and the seasonal influenza changes in particular but if we think about how if we really wanted to understand this what data would we need data or the key thing here we need data across scales of the dynamics that the the dynamics of mutation of viral shedding and in immunity and individual animals transmission the epidemic dynamics and in particular Thunder effects in epidemic troughs regional dynamics and kind of global phylogenies now this is a key night audience and you’ll have spotted that these are not humans you can’t do this in human systems you have to have animal systems and the horse is by no means an ideal it until animal but it’s useful and in this case because it does have a global phylogeny because it’s it’s it’s harbors an endemic infection of h3n8 influenza in fact recently jumped to dogs in the US and the UK interesting Lee and and because horses thoroughbred horses are much more looked after than humans they’re extremely valuable there’s a lot of work testing vaccines and looking at this level so I want to look at the the the the calibration between immune escape and determinants of transmission just to give an illustration of the sorts of data that we need at these different scales and this is me standing next to this pony it wouldn’t let me get any closer than that actually so these are welsh mountain ponies at the Animal Health Trust in Newmarket in the UK these are our these are my collaborators this is a model horse and these animals the nice thing is they could definitely guarantee from sort of isolated farms and they would see illogically test them before the experiments you could get naive animals so you could actually have controls to some extent when you did infection experiments and the infection experiments were actually testing vaccines so the way that they tested the vaccines was to immunize naive animals with a with a with a vaccine and then challenge the horse with the same vaccine or a different vaccine added at a given distance in terms of number of number of amino acids in the viral hemagglutinin so you a challenge to you let the antibodies drop off a bit which islands with the same virus or with a slightly different or a very different virus and then you see how determinants of transmission very weak or at least we did that when we reanalyze these data and no animals were hurt in this course of this experiment these are two of the animals usually experiment experimental animals are killed but these were given to small children I think it’s it’s it was a kind of unusual exception of the usual rules and what we see if we look at amino acid changes between the challenged virus and the immunization so this is the same virus more or less and this is the control which this would be like a pandemic virus this would be at a kind of infinite distance so this is if you if you if you just have a naive animal at the start then these are various correlates of r0 so the probability that you get infected that you cero convert the probability that if you cero convert you excrete the virus and the period for which you excrete it and you see they all increase so that if that so that are that these components of transmission rate are increasing however it’s

important to stress here that they didn’t directly measure transmission you didn’t take the horse and put it with six other horses and see how many it infected okay that would have been the kind of Holy Grail experiment and I think people are doing this now with guinea pig models and so on in ferret models to get at this a little bit more explicitly so if you put that into a population model you see that it takes about four amino acids in the app in the active sites of the of the hemagglutinin to allo the effective reproduction ratio to go both one and that means each case course is more than one case and then you would get a big epidemic so um these are qualitative results and and it’s it’s a it’s an animal model or not the human infection so you wouldn’t make specific extrapolations here but it’s it’s a point that to move to the next generation of epidemic models and to think about you know the long-term effects and control of epidemics we’re going to need to drill down into these kind of immunological depths and to think about women on dig’ microbiology virology so overall conclusion I’ve looked at demographic drivers human movements thought about measles there’s a there’s a whole other spatial temporal story that I’ve not talked about and the big challenge is combining evolutionary and epidemiological dynamics so rotavirus which Ginni talked about a few weeks ago to some of you and flu should probably show similar individual level dynamics of immune escape kind of this immune escape this heterologous and homologous immunity but incredibly different epidemic patterns and understanding the kind of zoo of patterns and of viruses at the population level and how those relate to the kind of within the kind of cross scale dynamics is a kind of really interesting I think okay thanks thanks Brian so we have some time for questions Scott oh sorry it’s got huge man actually stepping up so like there you want to record for posterity i I was just wandering in the flute in the flu example at the end whether you saw any interacts any evidence for interactions among mutations in other words you sort of had a count of genetic distance between the vaccine but is there any synergistic effects of mutations it’s a great question we looked and we couldn’t this is mainly I should say might work by my colleague University of Georgia now we looked and the design wasn’t kind of balanced you know so we didn’t really see those effects this is just this was just published in science and the next paper in the in this in the issue was a wonderful paper by Hinsley at I’ll by folks from NIH where they looked at immune escape in making a mouse model for flu in night in chains of naive and and partially immune animals and looked at how that Co varied with a vidit e of the hemagglutinin for the cell and you know that’s exactly what you’re talking about but there’s probably all kinds of compensator imitations and all kinds of stuff going on you’re right it’s a good question I have a question sort of fungal on a little bit from scotts which is to what extent do you think there is ability if we you know you talked about probing into the depths of mechanism that in some sense by doing that you will ultimately be able to say something about the either the predictability or the unpredictability of there being an outbreak sometime in the for example you know in terms of the evolutionary process how much is it gradual evolution versus punctuated equilibrium tight dynamics what I was supposed to give a pessimistic answer until he came to the last sentence there actually because I think predictability is really hard to you but I mean and if you know if you could if you could in seasonal flu case a lot of people are working on this if you did know enough to predict where it was going to evolve next year or in the next few years and could tailor the vaccines this is not a transmissible virus so that would be a very powerful to literally but in terms of punctuated versus gradual wicked flu is kind of the classic example where we do know that right so gradual is seasonal flu we don’t quite understand it works but we have a rough idea punctuate it is is is recombination is reassortment and is something jumping out of birds or pigs and so on you know so we have a qualitative idea of that understanding when you’re predicting when pandemics are going to happen you know good luck