Notes on Complex Systems

As ever, still trying to process everything. Last week, Zeynep Tufekci laid out an argument ("It Wasn’t Just Trump Who Got It Wrong," The Atlantic, March 24,  2020) that the current crisis is less the result of federal incompetence [although she doesn't excuse the government] and more linked to a broad public inability to engage in 'systemic thinking.' As she points out, had media outlets and government officials been better able to do so, they would have understand that the initial outbreak of cases in Hubei Province (with a population of 50 million people) was distinct - and far more dangerous - from previous outbreaks of SARS and MERS. She writes:

Many pieces with these flu comparisons usually included discussions of R0 and case-fatality rate, but numbers alone do not make science or sensible risk calculation in complex systems. We needed instead to think about these numbers and measurements in the context of the global system, including how epidemics and the health-care infrastructure work, and consider the trade-offs between resilience, efficiency, and redundancy within the system, and how the second- and third-order impacts can reverberate.

Let’s then go back to what we knew as of January 29 and think about it from a complex-systems perspective. A novel coronavirus (the same family as SARS and MERS) had been observed in Wuhan in early December 2019. The NEJM paper informed us that unlike SARS, this coronavirus included hard-to-detect cases. With SARS, the infectious phase reliably came with a high fever, allowing airports and health authorities to use temperature checks to quickly find and isolate affected individuals. And despite being easily detected, SARS still threatened to become a terrible pandemic in the much-less-interconnected world of 2003. In 2020, Wuhan may seem remote to Western audiences, but it’s a bustling, giant city with more than 500 direct international flights a day, situated in a country that has made great strides in domestic transportation since 2003, with more flights and high-speed train lines. Plus, in 2020, China is practically the manufacturing base of the world economy—something that had started in 2003, of course, but on a smaller scale.

She continues by arguing that engaging with Covid-19 required (and still requires) a better understanding of how complex systems work:

In complex systems, one can think about linear interactions and complex or nonlinear interactions. In linear interactions, we can add numbers to guess at combined impact. If the flu kills about 40,000 people annually in the U.S., and car accidents kill another 40,000 people annually, their combined impact is pretty much just that. They are both predictable events for which we have built infrastructure and expectations; our system anticipates both. But adding one more flu-like illness (as COVID-19 was presented) isn’t a linear event. Tipping points, phase transitions (water boiling or freezing), and cascades and avalanches (when a few small changes end up triggering massive shifts) are all examples of nonlinear dynamics in which the event doesn’t follow simple addition in its impacts—that’s why this coronavirus was never just about its R0 or CFR.

In many complex systems, efficiency, redundancy, and resiliency pull in different directions: More efficient systems, which are cheaper, eliminate redundancies, which provide resilience but cost more. For example, commercial airplanes always have two or more engines and have a co-pilot, even though one pilot and one engine is sufficient to fly the plane safely. The redundancy adds to expenses, but increases safety and resiliency in case something happens to one pilot or engine. In fact, commercial aviation is so safe because redundancy is mandated by regulation and built into every level, but our commercial-flying experience is so miserable because airlines have made it as efficient as possible to save money. (If one plane doesn’t arrive on time, there is no backup waiting to fly instead, for example.)

This syncs up with a podcast I listened to the other day with Andy Dobson, an epidemiologist affiliated with the Santa Fe Institute. That conversation referenced once of Dobson's papers about mathematical modeling ("Mathematical Models for Emerging Disease," Science, vol. 346, issue no. 6215). Dobson writes:

By contrast, in the absence of a time series of data for prior outbreaks, predicting outbreaks for novel or emerging pathogens has been marked by lack of accuracy (10). The problem is directly analogous to predicting hostile cyber-attacks on computer systems; in both situations, the quality of useful information in the early stages of an outbreak is limited and swamped by a diversity of other signals leading to too many false-positive predictions. By extension, this problem is hugely compounded with maps that seek to illustrate epidemic hot-spots for emergent disease (11). These are at best misleading (10).  

It seems like his critique is directed at others who seek to focus less on the mechanisms of transmission (modeling R0) and instead to use a variety of other proxies (socio-economic, environmental, ecological) to model hot-spots.

But one of the things that struck me in Dobson's short article is his stress that without an accurate time series for a disease, any sort of modeling is filled with huge uncertainties. What are the sources of data upon which one is able to build a model?

Dobson's interview also raises the issue of how we model social interactions (which are necessarily spatial ones as well):

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.

Networks, non-linear systems, models - I suppose one of the things I'm working at right now is trying to develop a vocabulary to make sense of where I am (where we are). And from there - hopefully - trying to figure out some way to communicate those stories to others.