SIAM News Blog

When Contagion Rules

By Paul Davis

The Rules of Contagion: Why Things Spread – and Why They Stop. By Adam Kucharski. Basic Books, New York, NY, July 2020. 352 pages, $30.00.

The Rules of Contagion: Why Things Spread – and Why They Stop. By Adam Kucharski. Courtesy of Basic Books.
A book about pandemics that came off the presses just as COVID-19 upended life as we knew it? Precious little about COVID itself? Terrible timing? Completely irrelevant?

Wrong on all counts. Adam Kucharski’s The Rules of Contagion is a deeply informed and widely accessible account of the evolution and breadth of model-based epidemiology. The subtitle proclaims the book’s scope: Why Things Spread – and Why They Stop. All of these “things” are timely; some are humorous, most are frightening. They include misinformation on the internet, gun violence in cities, viral tweets, financial crises, and the spread of genetic variants of diseases, including highly contagious COVID variants.

Kucharski, an associate professor and a Sir Henry Dale Fellow in the Department of Infectious Disease Epidemiology at the London School of Hygiene & Tropical Medicine, writes about—and works in—a data-driven side of applied mathematics that has taken center stage in the last year. The field is a perfect microcosm of the larger world that many SIAM members inhabit: mathematics, modeling, data, and computation, blended in whatever proportions best suit the moment’s challenge.

Kucharski writes with a sense of presence—an awareness of unknown outcomes and possible alternatives—not with biblical certainty. He tells stories with the authority and personal insight of a feet-on-the-ground participant who is balanced by the judgment and perspective of experience.

In the first chapter, Kucharski offers “A Theory of Happenings” — a sketch of the origins of epidemiological models that is free of equations and jargon. He describes mechanistic models that arose naturally to answer questions beyond the reach of experiments, such as “Can malaria be stopped without killing every mosquito?” As they evolved, the models revealed even more insight. The best, perhaps, was the possibility of herd immunity — the first of many points where Kucharski’s story touches today’s ongoing COVID-19 crisis.

These models were ultimately able to answer other questions as well. In 2015, the island of Martinique faced an outbreak of the mosquito-borne Zika virus. With Zika came Guillain-Barré syndrome, a muscle-weakening immune disorder that can gradually paralyze a victim (and had coincidentally threatened Kucharski throughout his childhood). What was the likely shape of the outbreak curve? Would the small island’s supply of eight ventilators suffice for a slow, flat outbreak or be overwhelmed by a rapid, sharp spike? Data-driven modeling predicted a slow, flat outbreak. In the end, no more than five patients at a time ever required the use of ventilators.

Kucharski’s allegiance to data is apparent throughout the book. Some SIAM members might be startled to hear his suggestion that the papers of Alfred Lotka and others led outbreak analysis “away from real-life epidemics.”1 Kucharski goes on to explain that two decades after Lotka, mathematical epidemiologist Klaus Dietz brought “the theory of epidemics out of its mathematical niche and into the wider world of public health” when he introduced the reproduction number \(R\): the average number of new infections that one infected person is expected to generate. Dietz recovered this powerful idea from a paper by malaria researcher George MacDonald.

Of course, \(R\) and its subscripted relatives have been prominently featured in the news since the arrival of COVID-19. SIAM News readers will likely appreciate Kucharski’s subsequent description of the four factors that influence \(R\). He calls these factors “DOTS” — Duration, Opportunity, Transmission probability, and Susceptibility. Here the rubber of mathematical modeling meets the twisting road of real-life data.

The subsequent chapters are filled with Kucharski’s accounts of epidemiological models’ insights into a wide swath of human endeavors and social challenges, particularly those enabled by networks. Social influence, computer viruses, and assaults on privacy are but a few examples. \(R\) and DOTS are only two of many perspectives from which to penetrate the mysteries of these branching, diverging, and intertwining plot lines. The pleasures of reading The Rules of Contagion are the insights that result from artful and informed mathematical modeling; the worries are the threats of the malicious outbreaks under study.

Kucharski’s ably-told stories ignite such worries around the first computer worms, the Stuxnet worm that took control of Iranian uranium centrifuges, and the household Bluetooth devices that were surreptitiously commandeered to power denial-of-service attacks. Simple bots and deceptive websites notwithstanding, Kucharski warns that “when it comes to online manipulation, it turns out that something much subtler—and far more troubling—has been happening.” False information from fringe websites can be laundered through legitimate news outlets “just as drug cartels might funnel their money through legitimate businesses to hide its origins.”

Kucharski analyzes these network-enabled threats with the same informed perception he brings to contagious diseases and social ills. He demonstrates that understanding the relevant rules of contagion leads to strategies that defend against such threats. For example, some countermeasures to outbreaks of misinformation might “work by targeting different aspects of the reproduction number,” while studies of online contagion have indicated the significance of broadcast events that amplify content. Events that disseminate misinformation are therefore points of attack, much like adult mosquitos are for malaria. After an outbreak of misinformation, mathematical models can estimate the preventive effects of various mitigation efforts. Modeling this kind of contagion builds a framework for both development and assessment of policy options.

Kucharski argues persuasively for making the components of the online information ecosystem—including citizens, media outlets, political organizations, and social media platforms—“more resistant to manipulation.” This complex process begins with a thorough understanding of contagion to avoid the risks that are associated with potentially blaming the wrong source or proposing overly simplistic moderation strategies; e.g., “bad air” was once thought to cause malaria. And some people have blamed masks for causing COVID.

Kucharski’s discussion of “Tracking Outbreaks” in the book’s penultimate chapter directly connects to a present concern: the fear that the COVID-19 virus will evolve to outwit vaccines. Fortunately, publicly-available, anonymous health records help researchers rapidly identify and fight dangerous genetic variants.

But the existence of these well-intentioned public records turns Kucharski’s narrative to a different epidemic: assaults on privacy. Kucharski recounts the classic “outing” of former Massachusetts Governor William Weld’s health records, which were extracted from supposedly anonymous hospital records. This assault utilized a simple “genetic code”—publicly available voter records and Weld’s name, age, and gender—to identify him. The resulting publicity eventually inspired significant changes to the way in which the U.S. stores and shares health-related data.2 Kucharski offers additional disturbing examples about the many cracks in the shields that supposedly protect personal data.

The book’s closing chapter, “A Spot of Trouble,” provides an insider’s prescient closing riff on what most newspaper readers now know about pandemics, misinformation, and other problems. Kucharski specifically warns that “the biggest challenges are often practical rather than computational,” and adds that the messy, complicated nature of datasets reflect the human lives on which they are based.

The Rules of Contagion is relevant to anyone who is interested in the roles of modeling and science in general; mathematical and biological barriers are nearly nonexistent. In fact, early chapters could perfectly frame an upper-level undergraduate or beginning graduate seminar. Participants could pair the text’s descriptions of an epidemiological problem with the corresponding mathematics and modeling in papers from the complete bibliography (as could any reader seeking more technical detail). Readers could also draw on the closing chapter’s daunting ethical dilemmas to approach a more complicated objective of broad scientific education: preparing students to fulfill the social obligations conferred by the gifts of scientific skill.

No one owns the rules of contagion. They are part of the shared grounds of scientific understanding and public good, and they arise in surprising settings. As a practitioner of the arts that he describes, Kucharski is a lively, intelligent, and well-informed guide to the data-heavy side of contagion modeling. His tour is alternately entertaining, gripping, and alarming, especially in this time of pandemic fear, misinformation, and crumbling privacy protections.

The Rules of Contagion provides an intellectual adventure ride and moral challenge; an account of scientific accomplishment; a list of daunting, as yet unanswered questions; and a narrative of battles against diseases won, lost, and in flux. Few books of its type are successful on so many fronts.

And perhaps those readers will recall that “One’s meat is another’s poison.”

Not to mention fruitful research into differential privacy, among other forms of protection. See [1] for more details.

[1] Davis, P. (2016, October 3). A socially useful idea of privacy. SIAM News, 49(8), p. 8.

Paul Davis is professor emeritus of mathematical sciences at Worcester Polytechnic Institute.

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