"New York" George Bellows. Oil. 1911

Read the Reflection, written 2 September 2021, below the following original Transmission.

It is hardly surprising that the vast majority of COVID-19 cases have occurred in cities; after all, more than 80 percent of the world’s population lives in urban environments, and these are significantly denser than either suburban or rural communities. Consequently, understanding the detailed transmission, spread, and mitigation of the disease — and developing realistic pathways to long-term sustainable biological, social, and economic recovery — is intimately tied to developing a deeper understanding of the principles underlying the structure and dynamics of cities. This is critical at both a coarse-grained global scale as well as at a more fine-grained local level. Indeed, a much-needed conceptual perspective is one in which we view this as a quintessential complex adaptive system, where all components are inevitably interrelated, resulting in a plethora of “unintended consequences.” 

We should not be totally surprised that an accidental mutation of a virus in a city in China, when left unchecked, would potentially lead to huge unemployment in the U.S., the fall of global markets, no football games in Spain, less pollution in India, and a shortage of yeast in the U.K.: the ultimate “butterfly effect,” where the subsequent time development is exponentially sensitive to the initial conditions, making detailed predictions extremely challenging. We are seeing that many dimensions of society are severely less robust than we might have thought. The spread of COVID-19 is a complex chaotic phenomenon in more ways than one! 

The big question is, of course: to what extent, if any, can any of this be quantitatively predictable? It certainly involves considerably more than “just” traditional epidemiology, vaccinology, and health care. In the near term, these obviously play a dominant role, but as we move forward into the recovery phase, and more importantly, into developing a long-term sustainable phase, this needs to be holistically integrated with socioeconomic dynamics — such as finance, inequality, neighborhood structure, and so on — coupled to the physical infrastructural organization of buildings, transport, etc. In a word, we need to develop and integrate our thinking about epidemics and similar “predictable” threats — such as earthquakes, tsunamis and conflicts — across multiple time and spatial scales, with a quantitative “Science of Cities.” It is a daunting challenge. 

Despite this, some baby steps have been made. Urban scaling, the theoretical framework quantifying how urban metrics change with size, reveals that cities are highly nonlinear yet share surprisingly “universal” commonalities.1 For example, socioeconomic quantities (Y) like wages, patents, and wealth scale superlinearly with population size (N) following a classic simple power law whose exponent is ~ 1.15: i.e., as N1.15. In English, this means that their percentage increase is 15 percent larger than that of the population: i.e., dY/Y = 1.15 dN/N. Consequently, the bigger the city, the more wealth, innovation, and social connectivity there is per capita — a major reason why cities are so attractive. This has its origins in the mathematics and dynamics of social networks. Cities are machines we evolved to facilitate, accelerate, amplify, and densify social interactions. The larger the city, the more the average individual interacts with other people in a multiplicative positive feedback process; by engaging in social discourse, exchanging ideas and information, making financial transactions, and, unfortunately, transmitting viruses!2 

Consequently, all of the benefits and attractions of larger cities that result from increased social connectivity have a dark side: more crime, greater inequality, more pollution, and more disease, all following superlinear scaling laws.3 Not only are there systematically more cases but, equally importantly, their growth rate, like all socioeconomic urban phenomena, increases systematically faster. If the number of cases increases exponentially with time (t) as ert, then the rate parameter (r) is predicted to systematically increase with city size as ~ N0.15. Consequently, a city of a million people will double the number of cases in approximately half the time a city of 10,000 (one hundredth of its size) will, since r changes by a factor (100)0.15 ~ 1.99. 

Such superlinear scaling predictions have been confirmed with data from past AIDS epidemics,1,4 so it is not surprising that the growth rate of COVID-19 has likewise followed similar laws, at least in its initial phase before intervention, as recently shown.5 The underlying theory potentially provides a quantitative framework for mitigating the spread of the disease by appropriately pruning the social network (i.e., by decreasing connectivity, or “social distancing”). But, importantly, the city’s social network is coupled with the physical constraints of infrastructural networks like transport and commerce. This necessary component is typically missing from epidemiological models, which are therefore blind to the strong dependence of social distancing on a city’s size. Consequently, they are unable to incorporate or predict the inherently greater risk in larger cities, a fact which needs to be taken into account when formulating policy decisions.

There are a plethora of other problems and risks associated with the pandemic that are being hotly debated, many related to the economy, poverty, and quality of life, and therefore, by implication, to the role of cities. How does an individual’s risk of infection change based on the city, or the particular neighborhood, they live in? Can urban scaling theory help formulate optimal strategies for aiding cities of different sizes? What can we learn from urban scaling theory that might inform us about trajectories of recovery and what cities and urban life might look like post-pandemic? To what extent can humans live by the internet alone? Or is physical three-dimensional social connectivity, the very essence of urban life, like sleep: without it you die, regardless of how much nutrition, entertainment, or money you have? The short, but incomplete, answer to these questions is that cities are not monochromatic, and comprehensive policies for preparing responses to, and recovery from, a variety of crises should begin by at least taking into account the overall size and underlying network structures of cities. 

Chris Kempes
Santa Fe Institute

Geoffrey West
Santa Fe Institute



  1. L. M. A. Bettencourt, J. Lobo, D. Helbing, C. Kühnert, and G.B. West, (2007) Proc of the Nat Acad of Sciences (USA) 104, 7301–7306. 
  2. M. Schlapfer, L. M. A. Bettencourt, S. Grauwin, M. Raschke, R. Claxton, Z. Smoreda, G.B. West, C. Ratti. Journal of the Royal Society Interface 11, 20130789 (2014). 
  3. L. M. A. Bettencourt and G.B. West, Nature 467, 912 (2010). 
  4. F. Antonio, S. de Picoli, Jr., J.J.V. Teixeira, 2 and R dos Santos Mendes, PLoS One. 2014; 9(10): e111015. 
  5. A.J. Stier, and M.G. Berman, and L. M. A.. Bettencourt https://arxiv.org/pdf/2003.10376.pdf (2020) 


T-025 (Kempes & West) PDF

Read more posts in the Transmission series, dedicated to sharing SFI insights on the coronavirus pandemic.

Listen to SFI President David Krakauer discuss this Transmission in episode 32 of our Complexity Podcast.


September 2, 2021


The 1918 flu pandemic took roughly two years to complete its three-wave progression of global infections. Since then, much has changed: we have come to understand the fundamentals of molecular biology, including how RNA viruses hijack cells for replication, developed a huge variety of sophisticated models of viral evolution and epidemiology, designed vaccines for a large number of diseases, and created the infrastructure for producing any mRNA or DNA sequence on demand and at low cost. There has been almost unimaginable progress in the biological and medical sciences in the intervening century. At the same time we have developed sophisticated methodologies for understanding social behavior, including the dynamics of social networks. And, with the advent of the IT revolution, we now have rapid communication across the globe and the ability to gather enormous amounts of data. None of these extraordinary advances was part of our toolkit a hundred years ago. Yet, despite all of this, and rather surprisingly, the first major pandemic to hit since then will take approximately the same length of time, namely about two years, to work through a similarly three-wave structure. Somehow all of the marvelous scientific advances of the last hundred years do not seem to have changed the timescale or temporal pattern of the pandemic.

How can this be? At first glance it is one of the more unexpected aspects of the present pandemic, but on closer inspection it is something that perhaps we might have anticipated.

In our original Transmission we described the need to understand how scale fundamentally affects the dynamical evolution of systems. For example, as cities grow and become more densely connected, with higher interaction rates between people, the transmission rate of any virus—or, for that matter, any idea—systematically increases. Consequently, larger cities are generally more creative than smaller ones as manifested, for instance, in the systematic increase in the number of patents they produce per capita. However, the dark side of this increasing connectivity is that cities are fundamentally more susceptible to the rapid spread of disease between people.

The answer to why the COVID-19 pandemic is taking roughly the same amount of time to play itself out as did the 1918 flu pandemic, despite all of the marvelous scientific advances, could be that the same societal infrastructure that has produced these innovations has also caused numerous commensurate shifts in human society. The same features and dynamics that increased the rate of innovation have also demanded a faster overall pace of life, resulting in increased global interactions through travel, upticks in human population and density, and radical surges in the rates at which information and misinformation spread. There is inherent feedback and interconnectivity between scientific innovations and social rates because, ultimately, they both originate in the dynamics of social networks, and so the two grow together. Thus, as our advanced technological response and information-gathering and reporting abilities increased, they were effectively compensated for, or counteracted by, faster infection rates that reached all corners of the globe.

Strikingly, when all of this is put together, an approximately invariant (that is, unchanging) timescale may have emerged. This mirrors many aspects of biological and social scaling theory, where certain invariants apply to diverse organisms of radically different size and evolutionary history. For example, the cost of repairing a unit of biomass is an invariant, as is the lifetime energy use per unit mass; this results in the number of heartbeats in a mammal’s lifetime being approximately the same, whether a mouse, a giraffe, or an elephant. These are the results of severe evolutionary pressures that define a strict set of trade-offs that lead to invariants. The question for human society is whether we can escape such invariants. Are all future pandemics destined to take approximately two years, or are there fundamental shifts that can be made to allow innovations to outpace the processes that cause risk to propagate more quickly? We need more fundamental theories of trade-offs to answer these questions, but at present it would seem that the emergent dynamic compensates for the increasing rate of innovation with increased risks in certain dimensions.

However, it is important to note that other well-known characteristics of viruses affect the temporal dynamics of an epidemic, such as transmissibility, mortality rate, and percentage of asymptomatic and vaccinated individuals. After all, many smaller epidemics have ended faster than the two years that we have been discussing, such as the 2009 H1N1 flu or various Ebola outbreaks. Our suggestion here is that for viruses with similar properties, the timescales of risk and timescales of response may offset one another because of similar upstream generative mechanisms. Finally, it is worth emphasizing that though the length of the pandemic may be difficult to control, the huge biomedical scientific advances of the last hundred years have potentially mitigated many infections and deaths relative to an unchecked outbreak or longer timescale to produce a vaccine.

Read more thoughts on the COVID-19 pandemic from complex-systems researchers in The Complex Alternative, published by SFI Press.