Andy Dobson on Epidemic Modeling for COVID-19

Episode Notes

Pandemics like the current novel coronavirus disease outbreak provide a powerful incentive to study the dynamics of complex adaptive systems. They also make it obvious, as new information streams in and our forecasts change in real-time, how hard emergent behaviors are to model and predict. For this special mini-series covering the COVID-19 crisis, we will bring you into conversation with scientists in the Santa Fe Institute’s global research network who study epidemics so you can learn their cutting-edge approaches and what sense they make of our evolving global situation.

Due to the pace at which the news is changing, we’ll ignore our normal schedule for the next few weeks and get more, shorter conversations out more frequently.  Please take a moment to subscribe wherever you listen to podcasts, and feel free to suggest questions for upcoming guests on Twitter or in our Facebook group.

This episode’s returning guest is SFI External Professor, Princeton epidemiologist Andy Dobson.  Among the questions we discuss:

What are the benefits and limits of mathematical models in tracking contagious disease? How do epidemiologists make sense of the tradeoffs between a pathogen’s transmissibility and virulence with spatial and evolutionary models? When is it likely that herd immunity will and will not work as a reasonable response to COVID-19?  What happens if COVID-19 becomes an endemic seasonal infection? How are the dynamics of epidemiological and economic systems related, both at the level of disease transmission and for modeling recovery?

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Andy’s Website

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Andy’s first appearance on Complexity Podcast Episode 16

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Episode Transcription

Michael: So, yeah, well, Andy, how are you?

Andy: Doing well. Are you at SFI? Are you also working from home?

Michael: I'm working from home today, yeah.

Andy: Is SFI pretty much cleared out or what's the atmosphere like?

Michael: There are a couple people up there. You know, there's still a residual working group that Laurent and a couple other people are doing this week…but pretty much it was a ghost town.

Andy: Right. That's a such a shame.

Michael: I mean, it's interesting. I've been talking with people about how it's an opportunity at all levels, for us as a society, to sort of back off of these local optima we've gotten stuck on. To reevaluate our behavior and like maybe find a new, better solution, both as individuals and as institutions.

Andy: I think from an environmental perspective, seeing how quickly levels of air pollution and things like that can be reversed is just going to create an opportunity to say, look, this can be done, if we all operate together, and the world will go on lower levels of production, fuel use, etc.

Michael: Yeah, it could. Although, there’s the adjustment period.

Andy: Yes. We will have a significant adjustment period.

Michael: Before we really dig into it, how are how are things for you? What is what is research life look like at Princeton right now?

Andy: Well, I’ve been in Panama for the last three weeks teaching. I teach this course on the ecology and evolution of infectious diseases. And I always joke that most years, we get a disease outbreak that we monitor in the course. It brings realism to what we're doing, but this is certainly the most vivid example we've had. And in Panama, the virus didn't get there until last Tuesday. I was all set to come back Saturday. The students were supposed to stay on. But they all got pulled out by the University. So I had to reorganize them a bit. Everybody came back Saturday, essentially. And Princeton is really quiet. There are people sort of walking around and isolated groups, the road traffic is down. There's a bit of rage when people are trying to cross each other at intersections because they seem there's no traffic, so they’ll just run the light. And so there's people shouting and screaming at each other a bit more than usual, that the campus is now totally deserted.

Michael: So I'd love to hear a little bit about how this real world example is facilitating you teaching epidemiology in your course. I mean, while we're while we're on the subject.

Andy: Well, it works very nicely because everyone on the course is expected to do a research project and also to look at a neglected tropical disease. So we just keep a daily update of where the virus was, what the numbers of cases were in China and what the number of cases were in Italy, then Spain, as an example of this is an epidemic really taking off in real time. And we'd have discussions over dinner about what sort of measures should be brought in to stop this and what epidemiologically can we do and what ethically can we do? I mean, the course is also great in that we're all living together, so I start seeing the students from other 7:30 in the morning, and we're often together till 10:30 at night. So there's lots of opportunities to discuss these things. And this was the situation changes from the morning into the evening. It’s good.

Michael: So we have three of your papers that we can get into here. Let's do that, shall we?

Andy: Sure.

Michael: The first, just in chronological order — as it seems to take seems to make sense to tackle them in that way — is “Mathematical models for emerging disease,” which you wrote for Science Magazine. This is related to a question that people have been bringing up on social media and I want to give some time in this conversation to those questions as well. So it seems right to start with a question you start this article with, which is, “What are the limits of mathematical models in the in tracking, understanding and extracting insights on emerging disease?” Let’s start as you do, with the problem of the problem.

Andy: I mean, that is the key question. And we're actually seeing that being really tested, as we follow the news at the moment. I think there's sort of two sides to the answer. One is that the models provide the most powerful macroscope we have of trying to understand disease patterns at large scales. And to make any form of projection of cases and any response to possible treatments, you need those models. Now, the other end of that is how much detail do you need before you can make valid projections or provide useful policy insights? And what quality of data have we got to parameterize those more? In a way, the projections are strange. And so the Chinese have been very good about providing access to the information they're collecting. The Italians are also being very good about that. Though getting this information out when people are literally trying to stop people dying is very, very hard. You don't want people wandering around with a clipboard trying to write everything down. Plainly, the good thing is we have mathematical frameworks that we've used before for Ebola, and that we use all the time for the measles and influenza. So the key parts of the model structure are there. It’s also applied to humans so lots of the human demography is there for different types of countries. But it's like saying, “What is different about this virus?” That means that the structure of those models have to be modified to take that into consideration. And then the second sort of unknown is, “How do we model social interactions between people of different ages? And how much detail of that do we have to capture before it's radically changed by different interventions?”

Michael: When we had you on the podcast for the first time, you talked about the way that different interactions, different network structures, can create these sort of reservoirs. Something that's been on my mind that I brought up with Laurent [Hébert-Dufresne] yesterday is that we've been looking at this in terms of just the number of sizes of congregations, but there's also different network structures, different degrees of clustering within congregations of different sizes. So I'm curious how you understand that, not just different sizes of groups of people, but different kinds of groups.

Andy: Again, like you said, just different contact network architectures might play into the spread of this. That gets to the crux of what we just taught: that lots of the models we have are parameterized assuming normal behavior. Children go into school, grown ups go into work, some sick people being in hospitals, people mixing at home and occasionally seeing their grandparents, and very much forced by the opening and closing of the school semesters where the mixing patterns change. And that is constantly kicking a system that's inherently nonlinear, but giving it a kick two or three times a year depending on how the school system works. That all disappears as we move into the thing that now everybody is to stay at home in much smaller clusters, which will have the age of whatever the family is or whether people decide to go home with their parents or whether to isolate in different age classes, like the elderly people by themselves, perhaps in bigger aggregations in senior homes, older couples and middle-aged couples, and then children isolating themselves from their parents. We need to know how to capture that. And what proportion of people that are in each of those categories, and how do they mix? One big advantage we have now that we haven't had before, is the people who've been looking at social mixing based on cellphone data can provide really rapid ways of parameterizing. And it's a question of, well, “What proportion of people are on Facebook? What proportion are on WhatsApp? What proportion are on the next latest thing? And can you aggregate that data in a way that tells you something meaningful about social interactions?”

Michael: I'm afraid as you say in your your email signature, PJ Plauger: “My definition of an expert in any field is a person who knows enough about what's really going on to be scared.” While I think it's important that, speaking for SFI, we don't seem as certain about anything but there, it's good to point out where the gaps are in our understanding. One of the things that you say towards the end of this paper, which I think broadly applies to complex phenomena, is that emergence and prediction have this asymmetrical, complex relationship to each other. And that we're often in a position where it seems like we expect people to be able to bring to bear electronic surveillance and complex mathematical models into some kind of control room scenario. But we're dealing with something that we don't understand and in many respects the emergent behaviors of this are only going to be clear in retrospect, right?

Andy: That's totally true. I mean, most of the time, we are looking at epidemic data after the epidemics happen, and building up a knowledge of that. One of the things that makes me optimistic is there's been a huge expansion in this area. Back in the late 80s, early 90s, the whole area took off when HIV appeared. And lots of the methods and incentive to do this work came from people desperately trying to understand HIV as it was happening live as an epidemic. HIV operates on a slower timescale. Although transmission can occur fast, a couple of days, people are alive for up to a decade while still infectious. Here, everything is happening much faster. But as I say, lots of the tools we've developed them for social mixing and understanding age structured or socially structured epidemics come from all that work. It also attracted lots of bright young people in the field to study it. So there are a significant number of people out there all interacting with each other, to try and find ways to deal with this. That makes me optimistic.

Michael: You mentioned here in the in the gap between understanding what a particular genome does in well-studied lab models, and then what it might do in the wild. One of the approaches that might help us understand this is actually drawn from ecology, predicting sudden changes of state in lakes and other ecosystems, like looking at how times series data give us an understanding into phase transitions. I'd love to hear you expand on that.

Andy: We’re certainly seeing that with the money markets at the moment. The the prediction that a huge increase in variance is suggesting something is changing to a different state…we’ve seen that on an hourly basis.

Michael: How do you see epidemiologists using that kind of an insight to model thresholds in the pandemic?

Andy: Well, most pandemics, there's one critical threshold and that's that basic reproductive number of the pathogen, or R0. When does an infected individual infect more than one person? Then you've got the epidemic taking off. Control is working out how do we change behavior, intervene to prevent, to get that number below one. So there's really only one main threshold. You can then look at that at different scales. How does it move from house to house? Or how does it move from village to village, town to town, country to country? And we've seen a sort of series of R0s of this thing taking off. So that's the main threshold, that we're concerned about with epidemic behavior. The interesting thing we want to know now about that is, is there any geographical signal to that? It looks to some of us that as you move away from the equator, that number of people that an infected person is transmitting to seems to be getting bigger. We're also seeing that the time course of the epidemic, the trajectory seems slower in some warmer countries than in colder countries. Now, we don't know if that's purely because if you're up in Scandinavia, you're still spending a lot of time indoors in close contact with people, whereas if you're in parts of Africa or Southeast Asia, you're outside and not as close proximity and not breathing the same air. The other coronaviruses do seem to have a very strong seasonal signal, in that they disappear over the warmer months or longer days, and then come back again in the fall. So will you see that sort of pattern as this epidemic develops, offset against the fact that nearly everybody is susceptible? You're gonna have less of a chance of seeing that in a population when nearly everybody is susceptible than you will in a population where there's levels of immunity that buffer the epidemic, and so it's looking for opportunities to spread.

Michael: So this seems like it dovetails into the next paper that you sent me to discuss here, which is “The evolution of pathogen virulence across space during an epidemic.” We'll link to this in the show notes. This was for American Naturalist and it’s really interesting, in that it regards different waves of the same pathogen as it evolves and as the virulence changes over time. Can you unpack this a little bit, please?

Andy: Yeah. I mean, I'm sure it's only a matter of weeks before we get people wildly speculating about, “Is the pathogen going to evolve to get more aggressive, or will it evolve to become benign?” Lots of people have been interested in the evolution of virulence, going right back to the sort of classic studies of Frank Fenner who was one of the people responsible for helping eradicate smallpox. Frank was also interested in the myxoma virus, myxomatosis in rabbits, because myxoma was used to control rabbits in Australia. When they first introduced it, they introduced the most virulent strain they could find. It killed like 99.8% of the rabbits. But quite quickly through time, it evolved to much lower levels of virulence. And then people—particularly Roy Anderson, and a bunch of other people, looked at ways of modeling that and found that that's the type of evolution of virulence you would see if there's a strong tradeoff between transmission efficiency and expression of virulence. Essentially, if you kill the host faster, it's not going to be around for long enough to transmit the disease. So the more virulent you get, the more the ability to transmit goes down because you're not infectious for so long. And what seemed to be selected for with myxoma in rabbits was a reduction in variance because it made more hosts get infected. The number of hosts you infect is the sort of evolutionary fitness of the virus. Now, what's different about coronavirus and this bacteria we've been studying in the finches—and those finches are in nearly everybody's backyard across the US—is the evolution of virulence in a system where transmission occurs before virulence is expressed. So that reduces the potential for there to be a tradeoff between virulence and transmission. And if you think back to the early days of this coronavirus, one of the big things we were worried about is, “How long are people infectious before they show symptoms?” And people that were still very focused on that and how different that might be from location to location. This is a system we've been able to monitor since it emerged in 1983 and jumped from domestic poultry into wild birds, mainly how finches and spread up and down the East Coast of the US, and then right across the Great Plains into California down into the southeast and deserts. And then it's become endemic everywhere. Now, again, it's similar to coronavirus in that transmission occurs for about a week before symptoms appear and when symptoms appear, the efficiency of transmission goes down. And when we make mathematical medical models of that, it creates the potential for virulence to increase as it becomes more endemic because there's no tradeoff between transmission and virulence, or a much weaker trade off between those two. And there’s an additional twist there, which is the thing that sort of disconcerted me about say UK’s initial policy of “Let's just let herd immunity build up, let's get everybody infected, and then we'll have herd immunity but we'll bring it down.” But if it operates in a similar way to this bacterial thing, that having everybody immune selects strains that will produce greater immunity. And if that greater immunity is associated with more virulence, then you'll start selecting for more virulent strains. It’s potentially equally possible that strains that are more immunogenic produce less virulent strains, though the mechanism of that will be more torturous to derive than for them to be more.

Michael: That touches on the other piece, “Incomplete host immunity favors the evolution of virulence of an emergent pathogen.”

Andy: Right. And as far as we know, the little data we have on immunity to coronaviruses is that it's not like measles. It’s not immunity for life—maybe two or three years. But then, interestingly, if you get re-exposed it could be that you don't transmit, and you don't show as bad but you top your immunity up. Which would be good on one hand, and that would keep levels of herd immunity up and protect other people and the transmission efficiency would go down. But that potentially creates that scenario that once it's endemic, you start selecting for the virulence or the transmissibility to evolve in different ways.

Michael: So, this piece, looking at the short term dynamics of emergence of more virulent strains. You talk about less virulent strains dominating the periphery of an epidemic, and more virulent strains emerging and and catching up to them. What does that look like with an outbreak pattern, like the outbreak patterns that we see now? International air travel is very nonlinear, it's not like the Western Front in World War One. It's this mess, just all over the planet. So what are we really talking about in light of that kind of complex transmission pattern?

Andy: Well, you know that that's an interesting question. Certainly it's important to differentiate between what's going on in the early stages of an epidemic when everybody is susceptible and the disease is jumping from groups of infected to new groups of susceptibles. That is suddenly massively facilitated by airline travel, which seems to be hugely reduced in the course of this week. By definition, the finches have their own form of airline travel: they fly around. So when we first saw it emerge, it goes up and down for the flight waves on the East Coast, and then spreads just like birds, drifting into new territories. So it spreads at a much slower rate. As all airline travel is reduced in the US and around the world, and people start using other forms of transportation, people driving out west to get to their homes out there, then they may be spreading it but a much lower rate than the airline. Plus, you know, the slowness of travel operates in some ways as a barrier. We go back to the discussion we had [in Episode 16] about rinderpest. Rinderpest couldn't get into Sub-Saharan Africa until after the invention of steam ships, because then you could move cattle in less than the incubation time of the pathogen to get them into Sub-Saharan Africa. If you put them on sailing ships, they would die on board, you kill the rest of the cattle and the disease wouldn't be introduced.

Michael: One of the questions from social media is, what other kind of spatial models do you think are are useful in understanding this kind of thing?

Andy: Well, that's an interesting question. I mean, everybody thinks their model is the most important. And there will be vociferous proponents of each, people who work in the different areas. The network people will say, “This is the most important part.” But as we said earlier, all these networks are going to have to change dramatically. So that will create the stimulus for people to develop models through a network whose framework is changing incredibly rapidly. That will be important to understand. Again, I think we are going to revert to a situation where we are thinking about sort of meta-population models at different scales: what happens in each individual household, and how strongly and weakly are those households connected, and how are collections of households in one area connected to other towns, and what is the meta-population structure of New York City? Is it is each tower block is a particular sub-population like cruise ships turned up vertically, and they will jump from “cruise ship” to “cruise ship” or tower block to tower block? It’s crucial to know locations where transmission is occurring that couples different points in the network together. Now, is it delivery drivers? Is it people sneaking out for anonymous assignations? We noticed with foot-and-mouth in the UK, the trend was to isolate all the farms and perhaps the plots surrounding them. But often it was things like the beds moving between farms, or a pair of boots, that would move it around. And sometimes it was farmers meeting other farmers’ wives or even other farmers that was moving the disease around. It was embarrassing outbreaks that could only be explained in one or two different ways.

Michael: I was speaking with Laurent, about this. He and Sam Scarpino and a couple others have been working on the way that this stacks and interacts with contagions of information. There's a reasonable argument for mapping this in terms of populations that abide by different kinds of behavior. Like there's a sort of virtual layer to this. That it's it's not just about spatial coordination, but also about memetic transfer and the way that people's behaviors are governed by their beliefs about what kind of practices to adopt.

Andy: That is always going to be an interesting signature, that people's different cultural behaviors will have a huge effect on the way that these pathogens move. Particularly with something that requires quite a physical proximity to move them around, how people's social systems are structured by age, coupled on top of that spatial distribution, and whether they all meet once a week to aggregate in a church or something…that’s a very powerful mechanism for speeding up an epidemic. Solitary hermits are usually pretty healthy because they're not interacting with each other.

Michael: A question on a lot of people's minds is related to the statement you made in that first paper about not being able to understand these things except in hindsight. When we had you on the podcast the first time, we spent a lot of time on the issue of the interplay between epidemics and economics, and the way that susceptibility to disease can help lock people into poverty,  create these these stable patterns within the global economic system that makes it difficult for us to lift people into a state of economic health. I'd be curious to know how you're thinking about this, in light of the anxiety a lot of people are understandably feeling about the economic impacts of the social isolation and not knowing where the line is…especially with our testing being as incomplete as it is. Maybe that’s two questions.

Andy: Well, I mean, this is a sort of an alternate form of virulence in in some ways, that having to suddenly close, all sort of social sites where people meet socially—bars, restaurants, hotels—closing all that down has a huge knock-on effect. It should slow down transmission, but suddenly all those people don't have jobs. They're relying on money coming in week to week. How can you supply funds so they can feed themselves and convince them to stay isolated for the relatively—I don't want to use the word “prolonged”—but the length of time they're going to have to be isolated. That money will eventually allow them to go back to some sort of jobs and probably the ones they had before. But the stress they're going to get, well, that is going to be deeply disturbing for lots of people. It's a thing we talked about two months ago [on the podcast], that there are lots of people who live in Africa in the US, South America, in poverty, and that increases their susceptibility to disease. But here we have the situation that people who thought they had stable jobs, that were bringing in a weekly wage, suddenly become much more susceptible to this because once that wage disappears, that puts all sorts of additional stresses on their life, which might increase their contact people and increase their susceptibility to this. So it's not gonna be an easy problem to deal with.

Michael: It seems like epidemiological thinking might help us model better market forecasts and maybe better strategies for recovering from this situation when things start to die down. If they start to die down.

Andy: Well, certainly, you've got to integrate epidemiological thinking into how you're going to get the economy started again. What are ways to start up so people can fly, on attested non-infectious airlines that have a certificate showing they're not infected, that's a valid certificate. Or having people getting the sort of banking economy and the wreck that is the whole service industry of restaurants, bars, hotels…getting that going again, because it's on the order of 5% to 8% of the US workforce. So you've got to get those people going again. The good thing is that there's an industry of people working on models for this disease, so tons of those insights will be available. There will be heated discussions about which models are right, but there are enough mechanisms to test them and try them out without actually having to do the experiment of mixing people together to see which one worked and which one doesn't. And then to pull back if anything starts to go wrong. Again, this is going to be interesting, as China now mentally thinks it’s through the worst of this and starts putting its workforce back, the levels of herd immunity…even though somewhere between 80,000 and 100,000 people have been infected in China, you really have to get about 50% of the population infected and recovered before you're going to have any herd immunity that's going to slow down future outbreaks. And 100,000 out of a billion is a tiny percentage.

Michael: So what do you suppose the odds are that this is going to remain endemic? What happens if this just becomes a seasonal illness?

Andy: If you take that portion of people who have been infected in China and subtract it from one, that that's the probability that this is going to become endemic. We’re going to have to find a way to deal with it as an additional form of seasonal flu and hope that we do it in a way that doesn't select for it to become more virulent. I think the first vaccine trials were started in Seattle yesterday, and I think in China today. We need to switch around quite a lot of manufacturing ability for vaccines to get a vaccine broadly available. Even if we had one tomorrow, to have it broadly available would still take about a year. Once it's endemic, it's likely you'll only have to vaccinate people after a certain age, as well as sensibly just vaccinating them when they're at high school or junior school to get herd immunity.

Michael: What are some of the most potent and useful resources that you might suggest to people right now if they want to learn more about this, or just want to stay on on top of things?

Andy: There are a very good online courses on infectious disease. Penn State has an excellent one that's got a very good group of people explaining that the biology and mathematics of epidemic diseases. And there's a whole host of literature out there, like the Anderson & May book I mentioned on The Infectious Diseases of Humans. It came out in 1990 and is still the Old and New Testament on this, if you like, and it leads you down the right structure for a whole variety of different types of diseases. And there are some very good people to follow on Twitter, and it’s well worth doing that. Jeremy Fox From the Wellcome Trust, good advice. Marc Lipsitch for the Harvard School of Public Health has been providing excellent advice. So the people that they seem to be Eddie Holmes from University of Sydney has been provided great stuff on the genetics of this and how that's all happening. Following them and the people they seem most connected to is going to provide us with what I think is really solid scientific input on a day-to-day basis.

Michael: Excellent. Andy, thanks again for taking some time to talk with us.

Andy: Hopefully we can get a beer together once this is over.

Michael: That would be great.

Andy: Good! Say hi to everybody for me.

Michael: I will. Stay safe out there.