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Jim: This is another in our extra COVID-19 related mini podcasts. Today’s guest is Michelle Girvan, a physics professor at the University of Maryland College Park Campus and external faculty at the Santa Fe Institute, and she’s also one of the strongest researchers in the area of network science that I know of. And I’ve asked her to come on today to talk a little bit about networks and network propagation of epidemiology and what we have to think about on the back side of the curve in terms of dynamic responses to manage this disease on the network. Michelle, take it away. Why don’t you talk to us a little bit about the very basics of network science, how diseases propagate on a network, and how changes in the nature of the network, such as through social distancing, can change the dynamics of network propagation of a disease.
Michelle: Thanks, Jim, for having me here. I am delighted to be here to talk about applying network science to this pandemic that we’re experiencing. What’s interesting for me from a modeling perspective is how much the general public is starting to learn about mathematical modeling. So, that’s really exciting to me to see news articles in the Washington Post and the New York Times talking about these SIR models, susceptible, infected, recovered, and talking about modeling parameters and quantities like R naught. That’s probably what some of you have seen a bunch in the news. R naught is the average number of people infected when one person gets infected, and this is at the start of the disease before you have any herd immunity.
Michelle: And herd immunity, another term you’ve probably heard, is something where a lot of people who have contracted the disease, that can slow down the spread because there aren’t so many susceptibles.
Michelle: So, let’s go back. That’s some of the basics of epidemics 101, but epidemics 101 really thinks about a fully mixed population so every person is equally likely to interact with every other person. They have a certain number of connections on average, and everyone has about the same number of connections. What’s important from a network science perspective is to think about heterogeneities in the connection patterns between people.
Michelle: One of the most important heterogeneities is degree distribution. Some people have huge numbers of connections, while most people have lower, more average numbers of … more typical numbers of connections, just a few strong connections. And that really changes the spreading pattern. If you consider a network where everybody has the same number of connections compared to a network where there are the same total number of connections in the system but some people have a much bigger share of those connection. Consider those two networks, the first a homogeneous network and the second a heterogeneous network.
Michelle: It turns out if you do the math spreading on the heterogeneous network is much more rapid and you end up with a much greater fraction of the population infected. The reason being is that those people who have a high number of connections, they’re likely to get the disease, and then, because they have a high number of connections, they’re also likely to spread the disease really quickly.
Michelle: This is one of the parts that’s not mentioned so much in this great news coverage about mathematical modeling, but not only do we have to think about R naught and the average properties of the network, but we have to think about the heterogeneous properties of the network. And that’s where closing schools comes in and is important, because schools are a big source of heterogeneity, because school children interact really strongly with one another. It’s kind of a source of giving people a lot of connections, and so closing these large things, shutting down big conferences, part of that intervention strategy is not to really change the average properties, but to cut off that high end, that tail end of the distribution which is so responsible for spreading.
Jim: So for instance, at a conference with 1000 people who are jammed into a room and are shoulder to shoulder in the hospitality suite afterwards, man, that’s a mixing bowl for viruses big time that’s very different than the average interactions that we might have on the street. Is that what you’re getting at?
Michelle: Absolutely. Absolutely. There can be two ways that this happens because we have these highly clustered interactions like conferences, or because we might have individuals that we would call super spreaders who just go around and are connected to so many people. It’s that tail end that we really want to control in our network type interventions.
Michelle: One way to think about the network science part of this is to realize that on average your friends have way more friends than you do. This is the friendship paradox in network science, and I think it’s the first thing that you should learn if you’re trying to wrap your mind around network science.
Jim: Say more about that. I remember reading about that early on when I started digging into network science back in the early double aughts when I was, “What? How could that possibly be true?” And then I worked through the math and I go, “Yup, for the average person, it’s true.” Could you run through a simple example or illuminate that for us a little bit?
Michelle: Sure. We all think of ourselves as average, and we probably think of our friends as average, and so our friends are just like us, right? But consider Facebook, for example. If you go and you’re on Facebook and you look at what your number of friends are and you look through all your friends and find out their average number of friends, probably that average is going to be a lot higher than your own number of friends. And the reason is because an average person in the network, you take the whole network, you pick a person at random, you look at that person’s number of friends. That’s different than following a random link. So, picking a random one of your own friends by following a link from you to them, that link is followed preferentially by their number of connections. Because there are some people who have so many more connections, you’re way more likely to be connected to somebody who has lots of connections.
Michelle: So then when you take a step back and look at it, the average number of connections of your friends, you really expect that to be a lot higher than the average number of connections of an individual, or the number of connections that you have.
Jim: That absolutely makes perfect sense when you think about it from that way, and that’s one of the things why network science was such a huge contribution to the intellectual working capital of the human race is that it produces very actionable insights such as that that are not intuitive.
Michelle: Yeah, absolutely, and I think that that’s a first way for people to understand network science and to realize, oh, when we’re thinking about these epidemiological models, we just do everything at the population average level, we’re missing a lot of important elements that really change the behavior of the whole system and the course of disease spread.
Jim: And I’m really glad that we have a number of people, particularly in our Santa Fe Institute community, who are bringing advanced epidemiological modeling with a network understanding on top of it, because that provides a very different view rather than using these population averages. Could you now address a little bit how things like social distancing, either low end social distancing like staying six feet apart, and more radical, such as stay at home orders, how they change the literal nature of the network and what impact they are likely to have on the spread of the disease?
Michelle: That’s a really good question, and there are a couple ways in which they change the nature of the spreading patters. In these network models of disease spread, you have a lot of different parameters. Not only do you have the network structure, who’s connected to whom, but you also have parameters of the dynamics of the disease, the probability of transmission along an edge. The staying six feet apart from one another, if you still are going about and interacting with the same people, like you’re going to work but you’re staying far apart from one another, that’s really changing the probability of spreading between people. Now, it’s also in part changing the network because it’s giving you fewer opportunities to interact casually with people you might interact with in a normal situation.
Michelle: But what really changes the network is these lockdown situations where you’re staying at home, you’re completely reducing the number of connections you have. So not only have you changed the probability of transmission, but you’ve changed the network topology.
Jim: Yup. So for instance, we think about our relationships with everybody we know, it’s a link between, let’s say, you and me, and if the nature of the link right now was you and I going out to have dinner at a restaurant where we’re sitting 18 inches apart, the dynamics of how the disease spreads probabilistically is one thing. If you and I are talking over Zoom, it’s entirely different. So, if instead of doing this by Zoom we did it face to face, we would be changing the nature of propagation on the network.
Jim: Okay. And so each one of these essentially is changing the property of the link. We don’t stop knowing people, so our social graph in some sense is still unchanged, but the properties of the graph, the properties of each link, change as we social distance.
Michelle: Right. And I like to think about it as we have our underlying social interaction network, and then we have a subset of that network, the network along which the transmission can spread. If we’re … we have a social connection, but that connection is only being realized virtually, that’s not a potential link for spreading.
Jim: Right. And as people switch from physical presence to virtual presence, I’m thinking in my head of nodes of links, the nature of the links changes, it now becomes impossible for Jim to give Michelle COVID-19 because we’ve switched from a face to face meeting to a Zoom meeting. And the more of those that change, literally the propensity to propagate on the network changes very considerably.
Michelle: And another thing that we really have to think about is that the networks adapt in response to the spreading patterns. One thing I think that we as a community have been doing pretty well is cutting down the number of visits to doctors’ offices where you have questionable symptoms and you might … then healthy people might get the disease at a doctor’s office. So there have been various policies, suggestions, call your doctor from home, a move to telemedicine instead of in person visits because what happens is when people are sick, they go to the doctor. And maybe they’re sick with coronavirus, but maybe they’re sick with a common cold, and then if they’re all meeting, especially this is a high density of people who have COVID-19 in a small space, that really increases the transmission.
Michelle: So I think that’s one thing we’ve actually been doing right is keeping people from going directly to the doctor’s office and trying to cut off some of the spread that happens in that way.
Jim: Yup. I-
Michelle: And this is, of course, just for people who have just mild symptoms.
Jim: Yeah, I’ll give you a perfect example. We talked about pre-roll on the show. My daughter is 25 weeks pregnant, and fingers crossed, it’s been a very healthy, non-problematic pregnancy and her and her doctor negotiated changing many of her normal check in visits from in office to telemedicine for exactly that reason. The benefit of a routine office visit for a healthy pregnancy is not zero, but it’s not huge compared to a telemedicine, and the risk is significant, so the math works out, do telemedicine. On the other hand, if she were to have a complication, she would of course go to the doctor or the hospital, because at that point the risk reward works the other way.
Jim: Humans are smart. We’re smart, adaptive agents, and we are making those changes. Again, as we talked about in the pre-roll, most of us are now using order in advance, pick up at the grocery store, quarantine the food in a cooler for a day, et cetera, and that bottom up self organizing modifying the network. My relationship to my grocery store is now a much less powerful vector for viral spread.
Michelle: Right. Absolutely. But I do wonder about some of these changes. Have they gone far enough? Certainly we need our healthcare workers to keep going. We need our grocery workers to keep going, but are we putting enough measures in to protect those people? Because they are interacting with so many people every day, and what else can we do to change their transmission parameters to help protect them?
Michelle: Also, I luckily remove from manufacturing processes and things like that, but are the plants that are manufacturing these goods, what are the network properties of the individuals who are doing this important work during this time? And how can we protect them better?
Jim: And of course a lot of that .. a different topic but something near and dear to a complexity science perspective is, unfortunately, our hyper-capitalist, short term money on money return society has engineered everything for efficiency and not for robustness. For instance, we know these plagues are coming. Look at the data on respiratory illnesses and the number of cases, and if you assume a fat tail distribution, which certainly seems reasonable, something like this is very predictable to have happened. Someone who was thinking in terms of robustness and complexity would have stockpiled billions of face masks, tens of thousands of ventilators, body suits, and so these issues of our poor healthcare workers having to expose themselves, and a lot of them are heroes. My sister in law is a nurse practitioner, and a heroic medical person who is putting her life on the day, literally, every day to help her patients. I would have felt a hell of a lot better, and we’ve actually sent her masks and things like that. My brother has sent her some masks. And if we had been a smart, robust, and resilience thinking society, we would have prepared for this.
Michelle: Right. Absolutely. And right now, that could be a big weakness that we have in our system, because that’s a point … while everything else is closed down, it’s these mega centers like hospitals where there is a big possibility for continued spread of the disease. And if we’re not … if we don’t have enough equipment to make those precautions, we’re not cutting off that tail like we need to.
Jim: Yeah, and as you would say from a network perspective, those are high mixing nodes with a high propensity of sick people. So, just what you don’t want.
Michelle: Absolutely. And another thing that I’ve seen recently, and this is not related to my expertise in network science but I think it’s an interesting feature that’s not been included in a lot of the modeling, is the level of exposure that people have. Healthcare workers, they can be exposed to much higher doses of the virus as compared to somebody who gets it from a surface. And as I’ve read, again, I’m not an expert in this, that how sick you get for many types of viruses is strongly correlated with that level of exposure. So it’s also something we should be taking into account.
Jim: In fact, a mini podcast we are publishing today from Robin Hanson, we discuss in considerable detail dose response and what might seem paradoxical guidance that comes from that. For instance, he’s a famous iconoclast and he talks about maybe young people should voluntarily get the illness, be paid a small premium for doing so, and be given a card that shows they are immune, and maybe people shouldn’t shelter in place at home because if one person in the house gets it, the dosage level in the house is going to be very high. That’s an area that I’d like to see some of our modelers hop on, thinking about this dose response possibility, and maybe it produces some non-intuitive ways of responding.
Michelle: Yes, and you also mentioned something that’s really important and part of the next step out of this quarantine situation, which is knowing who had the infection. A lot of these different strategies like getting the virus, which I’m not sure is good strategy, I’m not condoning that at the moment, but a lot of these different strategies are predicated on knowing who was infected and who wasn’t, so I think that that’s going to be a really important part in designing our way out of this after. If we’re successful in flattening the peak, which it seems like there’s good effort in this area, that these quarantining efforts are making a difference, but then what’s next? And how can we plan for what’s next without the ability to test who’s had the disease or not.
Jim: That’s exactly right. This is a good time to transition to the second topic, which is managing the back side of the curve. That’s now where all my attention is in terms of actual work, trying to figure out what guidance to give to government, not for profits, et cetera, and I feel like we’re way behind the curve on managing the back side of the curve. And it’s going to be more difficult, require a more aggressive, intellectually deep mindset, than managing the front side, which has been essentially fairly straightforward. Break the network, smash the curve. Doing the dance on the back side is going to be very, very tricky if we’re going to avoid the historical second peak in the famous influenza of 1918, which this is probably closest to in magnitude. The second peak four, five, six months later killed more people than the first peak, and there are ideas about how we be much more dynamic in our social distancing so we can take it off in some places and bring it on in others, but that’s going to require data and dynamic decision making. Could you talk a little bit about the network science and any thoughts you have on managing the back side of the curve until we have a vaccine?
Michelle: That is such an important question, and as you mentioned, so much harder to answer. From a mathematical modeling perspective, whether we’re doing this fully mixed population assumption or whether we’re adding in some of the details of the network structure and the heterogeneities where some people have lots of connections but most people have a lower number. So, regardless of what approach you take, in the beginning, it’s much easier to capture this because you can make an assumption that almost everybody is susceptible, and then as a significant fraction of your population gets infected with this and then recovers, modeling that side of things is much harder. And it’s much harder in this scenario when you have the hidden variables, that you don’t know the states of individuals, whether they’ve recovered or not, or whether they were never infected. And so, the mathematical modeling is more complicated because … for two reasons. You can’t just consider everybody to be susceptible, but the main really harder part of connecting mathematical modeling with intervention strategies is you need to know what class each of your … the individuals are in. Are they still susceptible, or are they recovered and now hopefully, as we’ve heard enough of, there is evidence that they should be immune, at least for a while.
Jim: Yup. And again, this is multi-dimensional analysis, which unfortunately our society isn’t great at, and we need to have disease testing to catch people with symptoms to crack down on them quickly after the fact, and as you point out, the immunity testing would be huge to certify people to work in dangerous … virologically dangerous front line positions. Wouldn’t it be great if there were an ID certificate that said, I am immune, and let those people go back to work as Uber drivers and working as the store clerks, et cetera. And the other thing is this monitoring so that we can bring our resources to bear.
Jim: And I will say there’s one hopeful part of this, as I’ve been thinking about the network dynamics. Let’s say the smashing the curve works, we see a crash in the number of new cases so it gets down to a very low number in late June and early July, but we ramp up testing. Then, when the inevitable hot spots re-flare up, they’re going to be small at first, and yet we’ve built up this big reserve of ventilators and 15 minute test equipment, we should be able to mobilize them very rapidly. If necessary, have the Marine Corps fly them in on helicopters and swarm these new hot spots with 15 minute tests, with antibody testing, et cetera, and if we need to, shut them back down again. Maybe it’s just a county, a little county in West Virginia that somehow never had any disease at all, so it has no immunity, somehow somebody visits from someplace, it gets started and flares up. But if we do a high enough level of testing, we’ll be able to detect it early, and because we’ve already mobilized all the equipment and stuff we can fly it in and squash it.
Jim: But to do that requires a war fighting, data-driven, model-driven mentality, which so far is only slowly spinning up.
Michelle: Absolutely. It really has to be an organized effort. So, two things that you touched on which really, I think, are worth emphasizing and thinking about more. I love this idea of doing antibody testing. There is a little bit of a concern that people who want to go back to work will intentionally get the virus so that they can now be card-carrying certified recovered. That’s something to worry about. And then, another thing is to think about the timing and to use some of these mathematical network-based models to really time the intervention strategies and the social distancing requirements at various times. Because what I suspect on the back side of the curve, also as it was on the front side of the curve, you need to start changing people’s behavior before it looks bad.
Michelle: Before the hospital system is overwhelmed. It’s kind of hard to convince people to change their behavior when things aren’t looking too bad, so the timing of those strategies is something that we really need this combination of data analysis and mathematical modeling to get right.
Jim: In fact, Jessica Flack told me in an interview I did the other day … I can’t find it on the internet, but she said that Paul Romer was suggesting that it was economically worthwhile to do … what was it? 20 million tests a day so that we had essentially instant information on any flare up, so we’re not waiting for hospitals to be overrun, but we find in this county in West Virginia three cases where there had been none for six months, and then we immediately marshal the resources to squash it. So, it’s a … you have modeling and you have data and you have the ability to instantly respond, and you don’t wait for weeks to go by for these high-volume signals to occur. That’s an interesting idea. And I think he said it would cost $350 billion or something, but it would be money well spent.
Jim: I think this kind of thinking is what managing the back side of the curve is going to be all about.
Michelle: Absolutely. I hadn’t thought about how that investment might be really sensible from an economic payoff. Certainly, from an ability to change the back side of the curve, absolutely it’s going to change things, and so I think it is a good investment because by waiting and having to quarantine and shut so many industries down, it’s a huge economic impact. But if we could have really large-scale testing, it would be very costly, but it’s great to really see that analysis done, to see the economic benefits of that.
Jim: And I’ve … look at the stock market alone, how much has it lost? $6 trillion, something like that, and that’s … a $200 billion a year investment in absolutely ubiquitous testing, shit, it would be damn cheap to get our economy back to work. This kind of thinking, informed by modeling and exactly the kind of network analysis combined with epidemiology that we’ve been talking about, is what we need to be driving whoever is in charge of thinking through the strategy on the back side of the curve.
Michelle: I wonder if we could get companies involved, big companies involved in this somehow, to say, well, you guys could send your full workforce back to work if you agree to pay for the testing.
Jim: Frankly, I’ve been writing down business ideas that this epidemic produces, and one of the ones near the top of the list is a business that does nothing but certify people for their immunity. So, a company could hire this company, Ruttco, for $100 per employee to certify them as immune. And of course we’d have to have some caveats, tests aren’t always accurate, but if you want them to be more accurate, have them tested twice and we’ll charge you $200, and that will take basically the product of the error rates, so the error rate goes way down.
Michelle: And you also want to certify … you also want the company to monitor people who are susceptible and continually monitor them, so it would be nice for them to be able to go back to work, too, but we’re trying to guarantee a pretty safe environment, and to do this we keep testing the susceptibles all the time.
Jim: Yeah, that’s the Paul Romer argument. 20 million tests a week … a day, I think. Some crazy number, but basically constant surveillance everywhere, so it’s relatively safe to go back to your office as long as you know that if Sally at the other end of your floor got the disease, even though she’s pre-symptomatic and has been told she has to go quarantine for 15 days, your risks go way, way down. And if you’re young and healthy, it probably makes sense to go back to work. So again, thinking holistically about networks, propagations, interventions, testing, mobilization. I believe that if we did this right, we could manage the back side of the curve so that we did not get a second peak until the vaccine gets here, but it will require a very fancy dance to do it, and I sure the hell hope the powers that be are able to organize a set of talent, skills, analysis, and action taking sufficient to do this. It’s doable, and it will allow our economy to restart. It will save probably as least as many deaths and disabilities as have happened from the first wave, but it’s going to require smarter footwork than we’ve seen on the front side.
Michelle: I totally agree. The back side is the challenge that we all need to put our minds to now.
Jim: Okay. Well, thank you, Michelle. This has been a wonderful episode, exactly what I was hoping, but before we sign off, I’d like you to tell our audience about a Zoom-based course that you guys are offering on network epidemiology.
Michelle: I direct the COMBINE program at the University of Maryland. COMBINE stands for computation and mathematics in biological networks. Network epidemiology is an important focus within the field of biological networks, and when we shifted to an online environment I thought, okay, well, I want my COMBINE fellows to stay in touch, so let’s do a little series on network epidemiology. But then I thought, well, if we’re going to do an online series, there are a lot of people who might want to learn about this, so why not have a bigger reach? So then we partnered with the Vermont Complex Systems Center, Santa Fe Institute sent out a bunch of announcements for us, and we got a whole bunch of people involved in this online series on understanding and exploring network epidemiology in the time of coronavirus. So, this is a four-week series meeting once a week. We have tutorials and seminars, but then we have discussion sessions and we have people sign up to participate in group projects. And so, they’re all self-organizing on a Slack site, so the live online sessions are already over-subscribed. We had many more excellent, dedicated applicants than we could accommodate, but we want these resources to reach anyone who is interested, so we’re putting everything on our YouTube channel.
Michelle: You can get to our YouTube channel from the main COMBINE website. COMBINE is Combine.umd.edu. You can also Google combine UMD and find those videos. We had an excellent tutorial yesterday introducing us to network epidemiology by Laurent Hebert-Dufresne from the University of Vermont, who’s done some really excellent work on network epidemiology in general, and also on coronavirus or COVID-19. So, check it out.
Jim: Very good. And as always, we will have these links on the episode page for Michelle’s podcast. Thank you, Michelle. This has been absolutely wonderful.
Michelle: Thank you.
Production services and audio editing by Jared Janes Consulting. Music by Tom Muller at ModernSpaceMusic.com.