The Rules of Contagion

by Adam Kucharski

  As our awareness of contagion increases, many of the ideas honed in the study of infectious diseases are now translating to other types of outbreaks. After the 2008 financial crisis, central banks latched onto the idea that the structure of a network could amplify contagion, a theory pioneered by STI researchers in the 1980s and 1990s. Recent efforts to treat violence as an infection – rather than simply a result of ‘bad people’ – echo the rejection of diseases caused by ‘bad air’ in the 1880s and 1890s. Concepts like the reproduction number are helping researchers quantify the spread of innovations and online content, while methods used to study pathogen sequences are revealing the transmission and evolution of culture. Along the way, we’re finding new ways to speed up beneficial ideas and slow down harmful ones. Just as Ronald Ross hoped in 1916, a modern ‘theory of happenings’ is now helping us analyse everything from diseases and social behaviour to politics and economics.

  In many cases, this has meant overturning popular notions of how outbreaks work. Like the idea that we need to remove every last mosquito to control malaria, or vaccinate every person to prevent epidemics. Or the assumption that banking systems are naturally stable and online content is highly contagious. It has also meant hunting for new explanations: why cases of Guillain-Barré Syndrome were appearing on Pacific Islands, why computer viruses persist for so long, why most ideas struggle to spread as easily as diseases.

  In outbreak analysis, the most significant moments aren’t the ones where we’re right. It’s those moments when we realise we’ve been wrong. When something doesn’t look quite right: a pattern catches our eye, an exception breaks what we thought was the rule. Whether we want an innovation to take off or an infection to decline, these are the moments we need to reach as early as possible. The moments that allow us to unravel chains of transmission, searching for weak links, missing links, and unusual links. The moments that let us look back, to work out how outbreaks really happened in the past. Then look forward, to change how they happen in future.

  Notes

  Introduction

  1. Original tweet, which had 49,090 impressions in total. Unsurprisingly, several users would subsequently ‘unretweet’ it: https://twitter.com/AdamJKucharski/status/885799460206510080 (Of course, a large number of impressions does not necessarily mean that users read the tweet, as we shall see in Chapter 5.)

  2. Background on 1918 pandemic: Barry J.M., ‘The site of origin of the 1918 influenza pandemic and its public health implications’ Journal of Translational Medicine, 2004; Johnson N.P.A.S. and Mueller J., ‘Updating the Accounts: Global Mortality of the 1918–1920 “Spanish” Influenza Pandemic’ Bulletin of the History of Medicine, 2002; World War One casualty and death tables. PBS, Oct 2016. https://www.uwosh.edu/faculty_staff/henson/188/WWI_Casualties%20and%20Deaths%20%20PBS.html. Note that there have recently been other theories about the source of the 1918 flu pandemic, with some arguing that the introduction was much earlier than previously thought e.g. Branswell H., ‘A shot-in-the-dark email leads to a century-old family treasure – and hope of cracking a deadly flu’s secret’, STAT News, 2018.

  3. Examples of quote in media: Gerstel J., ‘Uncertainty over H1N1 warranted, experts say’ Toronto Star, 9 October 2009; Osterholm M.T., ‘Making sense of the H1N1 pandemic: What’s going on?’ Center for Infectious Disease Research and Policy, 2009.

  4. Eames K.T.D. et al., ‘Measured Dynamic Social Contact Patterns Explain the Spread of H1N1v Influenza’, PLOS Computational Biology, 2012; Health Protection Agency, ‘Epidemiological report of pandemic (H1N1) 2009 in the UK’, 2010.

  5. Other groups reached similar conclusions, e.g. WHO Ebola Response Team, ‘Ebola Virus Disease in West Africa – The First 9 Months of the Epidemic and Forward Projections’, The New England Journal of Medicine (NEJM), 2014.

  6. ‘Ransomware cyber-attack: Who has been hardest hit?’, BBC News Online, 15 May 2017; ‘What you need to know about the WannaCry Ransomware’, Symantec Blogs, 23 October 2017. Exploit attempts increased from 2000 to 80000 in 7 hours, implying doubling time = 7/log2(80000/2000) = 1.32 hours.

  7. Media Metrics #6: The Video Revolution. The Progress & Freedom Foundation Blog, 2 March 2008. http://blog.pff.org/archives/2008/03/print/005037.html. Adoption went from 2.2% of homes in 1981 to 18% homes in 1985, implying doubling time = 365 × 4/log2(0.18/0.02) = 481 days.

  8. Etymologia: influenza. Emerging Infectious Diseases 12(1):179, 2006.

  1. A theory of happenings

  1. Dumas A., The Count of Monte Cristo (1844–46), Chapter 117.

  2. Kucharski A.J. et al., ‘Using paired serology and surveillance data to quantify dengue transmission and control during a large outbreak in Fiji’, eLIFE, 2018.

  3. Pastula D.M. et al., ‘Investigation of a Guillain-Barré syndrome cluster in the Republic of Fiji’, Journal of the Neurological Sciences, 2017; Musso D. et al., ‘Rapid spread of emerging Zika virus in the Pacific area’, Clinical Microbiology and Infection, 2014; Sejvar J.J. et al., ‘Population incidence of Guillain-Barré syndrome: a systematic review and meta-analysis’, Neuroepidemiology, 2011.

  4. Willison H.J. et al., ‘Guillain-Barré syndrome’, The Lancet, 2016.

  5. Kron J., ‘In a Remote Ugandan Lab, Encounters With the Zika Virus and Mosquitoes Decades Ago’, New York Times, 5 April 2016.

  6. Amorim M. and Melo A.N., ‘Revisiting head circumference of Brazilian newborns in public and private maternity hospitals’, Arquivos de Neuro-Psiquiatria, 2017.

  7. World Health Organization, ‘WHO statement on the first meeting of the International Health Regulations (2005) (IHR 2005) Emergency Committee on Zika virus and observed increase in neurological disorders and neonatal malformations’, 2016.

  8. Rasmussen S.A. et al., ‘Zika Virus and Birth Defects – Reviewing the Evidence for Causality’, NEJM, 2016.

  9. Rodrigues L.C., ‘Microcephaly and Zika virus infection’, The Lancet, 2016.

  10. Unless otherwise stated, background information is from: Ross R., The Prevention of Malaria (New York, 1910); Ross R., Memoirs, With a Full Account of the Great Malaria Problem and its Solution (London, 1923).

  11. Barnes J., The Beginnings Of The Cinema In England, 1894–1901: Volume 1: 1894–1896 (University of Exeter Press, 2015).

  12. Joy D.A. et al., ‘Early origin and recent expansion of Plasmodium falciparum’, Science, 2003.

  13. Mason-Bahr P., ‘The Jubilee of Sir Patrick Manson: A Tribute to his Work on the Malaria Problem’, Postgraduate Medical Journal, 1938.

  14. To K.W.K. and Yuen K-Y., ‘In memory of Patrick Manson, founding father of tropical medicine and the discovery of vector-borne infections’ Emerging Microbes and Infections, 2012.

  15. Burton R., First Footsteps in East Africa (London, 1856).

  16. Hsu E., ‘Reflections on the “discovery” of the antimalarial qinghao’, British Journal of Clinical Pharmacololgy, 2006.

  17. Sallares R., Malaria and Rome: A History of Malaria in Ancient Italy (Oxford University Press, 2002).

  18. Ross claimed that the participants had been told what was involved, and that risks of the experiments were justified: ‘I think myself justified in making this experiment because of the vast importance a positive result would have and because I have a specific in quinine always at hand.’ (source: Ross, 1923). However, it is not clear how fully the risks were actually explained to participants; quinine is not as effective as the treatments used in modern studies of malaria (source: Achan J. et al., ‘Quinine, an old anti-malarial drug in a modern world: role in the treatment of malaria’ Malaria Journal, 2011.) We will look at the ethics of human experiments in more detail in Chapter 7.

  19. Bhattacharya S. et al., ‘Ronald Ross: Known scientist, unknown man’, Science and Culture, 2010.

  20. Chernin E., ‘Sir Ronald Ross vs. Sir Patrick Manson: A Matter of Libel’, Journal of the History of Medicine and Allied Sciences, 1988.

  21. Manson-Bahr P., History Of The School Of Tropical Medicine In London, 1899–1949, (
London, 1956).

  22. Reiter P., ‘From Shakespeare to Defoe: Malaria in England in the Little Ice Age’, Emerging Infectious Diseases, 2000.

  23. High R., ‘The Panama Canal – the American Canal Construction’, International Construction, October 2008.

  24. Griffing S.M. et al., ‘A historical perspective on malaria control in Brazil’, Memórias do Instituto Oswaldo Cruz, 2015.

  25. Jorland G. et al., Body Counts: Medical Quantification in Historical and Sociological Perspectives (McGill-Queen’s University Press, 2005).

  26. Fine P.E.M., ‘John Brownlee and the Measurement of Infectiousness: An Historical Study in Epidemic Theory’, Journal of the Royal Statistical Society, Series A, 1979.

  27. Fine P.E.M., ‘Ross’s a priori Pathometry – a Perspective’, Proceedings of the Royal Society of Medicine, 1975.

  28. Ross R., ‘The Mathematics of Malaria’, The British Medical Journal, 1911.

  29. Reiter P., ‘From Shakespeare to Defoe: Malaria in England in the Little Ice Age’, Emerging Infectious Diseases, 2000.

  30. McKendrick background from: Gani J., ‘Anderson Gray McKendrick’, StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies.

  31. Letter GB 0809 Ross/106/28/60. Courtesy, Library & Archives Service, London School of Hygiene & Tropical Medicine. © Ross Family.

  32. Letter GB 0809 Ross/106/28/112. Courtesy, Library & Archives Service, London School of Hygiene & Tropical Medicine. © Ross Family.

  33. Heesterbeek J.A., ‘A Brief History of R0 and a Recipe for its Calculation’, Acta Biotheoretica, 2002.

  34. Kermack background from: Davidson J.N., ‘William Ogilvy Kermack’, Biographical Memoirs of Fellows of the Royal Society, 1971; Coutinho S.C., ‘A lost chapter in the pre-history of algebraic analysis: Whittaker on contact transformations’, Archive for History of Exact Sciences, 2010.

  35. Kermack W.O. and McKendrick A.G., ‘A Contribution to the Mathematical Theory of Epidemics’, Proceedings of the Royal Society A, 1927.

  36. Fine P.E.M., ‘Herd Immunity: History, Theory, Practice’, Epidemiologic Reviews, 1993; Farewell V. and Johnson T., ‘Major Greenwood (1880–1949): a biographical and bibliographical study’, Statistics in Medicine, 2015.

  37. Dudley S.F., ‘Herds and Individuals’, Public Health, 1928.

  38. Hendrix K.S. et al., ‘Ethics and Childhood Vaccination Policy in the United States’, American Journal of Public Health, 2016.

  39. Fine P.E.M., ‘Herd Immunity: History, Theory, Practice’, Epidemiologic Reviews, 1993.

  40. Mallet H-P. et al., ‘Bilan de l’épidémie à virus Zika survenue en Polynésie française, 2013–14’, Bulletin d’information sanitaires, épidémiologiques et statistiques, 2015.

  41. Duffy M.R. et al., ‘Zika Virus Outbreak on Yap Island, Federated States of Micronesia’ NEJM, 2009.

  42. Cao-Lormeau V.M. et al., ‘Guillain-Barré Syndrome outbreak associated with Zika virus infection in French Polynesia: a case-control study’, The Lancet, 2016.

  43. Stoddard S.T. et al., ‘House-to-house human movement drives dengue virus transmission’, PNAS, 2012.

  44. Kucharski A.J. et al., ‘Transmission Dynamics of Zika Virus in Island Populations: A Modelling Analysis of the 2013–14 French Polynesia Outbreak’, PLOS Neglected Tropical Diseases, 2016.

  45. Faria N.R. et al., ‘Zika virus in the Americas: Early epidemiological and genetic findings’, Science, 2016.

  46. Andronico A. et al., ‘Real-Time Assessment of Health-Care Requirements During the Zika Virus Epidemic in Martinique’, American Journal of Epidemiology, 2017.

  47. Rozé B. et al., ‘Guillain-Barré Syndrome Associated With Zika Virus Infection in Martinique in 2016: A Prospective Study’, Clinical Infectious Diseases, 2017.

  48. Fine P.E.M., ‘Ross’s a priori Pathometry – a Perspective’, Proceedings of the Royal Society of Medicine, 1975.

  49. Ross R., ‘An Application of the Theory of Probabilities to the Study of a priori Pathometry – Part I’, Proceedings of the Royal Society A, 1916.

  50. Clarke B., ‘The challenge facing first-time buyers’, Council of Mortgage Lenders, 2015.

  51. Rogers E.M., Diffusion of Innovations, 3rd Edition, (New York, 1983).

  52. Background from: Bass F.M., ‘A new product growth for model consumer durables’, Management Science, 1969.

  53. Bass F.M. Comments on ‘A New Product Growth for Model Consumer Durables’, Management Science, 2004.

  54. Ross’ simple ‘susceptible-infected’ model can be written as:

  dS/dt = -bSI, dI/dt = bSI, where b is the infection rate. The peak rate of new infections occurs when dI/dt is increasing fastest, i.e. the second derivative of dI/dt is equal to zero. Using the product rule, we obtain: I = (3 – sqrt(3))/6 = 0.21.

  55. Jackson A.C., ‘Diabolical effects of rabies encephalitis’, Journal of NeuroVirology, 2016.

  56. Robinson A. et al., ‘Plasmodium-associated changes in human odor attract mosquitoes’, PNAS, 2018.

  57. Van Kerckhove K. et al., ‘The Impact of Illness on Social Networks: Implications for Transmission and Control of Influenza’, American Journal of Epidemiology, 2013.

  58. Hudson background from: O’Connor J.J. et al., ‘Hilda Phoebe Hudson’, JOC/EFR, 2002; Warwick A., Masters of Theory: Cambridge and the Rise of Mathematical Physics (University of Chicago Press, 2003).

  59. Hudson H., ‘Simple Proof of Euclid II. 9 and 10’, Nature, 1891.

  60. Chambers S., ‘At last, a degree of honour for 900 Cambridge women’, The Independent, 30 May 1998.

  61. Ross R. and Hudson H., ‘An Application of the Theory of Probabilities to the Study of a priori Pathometry. Part II and Part III’, Proceedings of the Royal Society A, 1917.

  62. Letter GB 0809 Ross/161/11/01. Courtesy, Library & Archives Service, London School of Hygiene & Tropical Medicine. © Ross Family; Aubin D. et al., ‘The War of Guns and Mathematics: Mathematical Practices and Communities in France and Its Western Allies around World War I’, American Mathematical Society, 2014.

  63. Ross R., ‘An Application of the Theory of Probabilities to the Study of a priori Pathometry. Part I’, Proceedings of the Royal Society A,, 1916.

  2. Panics and pandemics

  1. Mathematician Andrew Odlyzko points out that the final loss could plausibly have been even higher than £20,000. What’s more, he suggests a multiple of 1,000 is reasonable for converting monetary value in 1720 to a present day amount; Newton’s Professorial salary at Cambridge during this time was around £100 per year. Source: Odlyzko A., ‘Newton’s financial misadventures in the South Sea Bubble’, Notes and Records, The Royal Society, 2018.

  2. Background on Thorp and Simons from: Patterson S., The Quants (Crown Business New York, 2010). Background on LTCM from: Lowenstein R., When Genius Failed: The Rise and Fall of Long Term Capital Management (Random House, 2000).

  3. Allen F. et al., ‘The Asian Crisis and the Process of Financial Contagion’, Journal of Financial Regulation and Compliance, 1999. Data on rise in popularity of the term ‘financial contagion’ from Google Ngram.

  4. Background on CDOs from: MacKenzie D. et al., ‘“The Formula That Killed Wall Street”? The Gaussian Copula and the Cultures of Modelling’, 2012.

  5. ‘Deutsche Bank appoints Sajid Javid Head of Global Credit Trading, Asia’, Deutsche Bank Media Release, 11 October 2006; Roy S., ‘Credit derivatives: Squeeze is over for EM CDOs’, Euromoney, 27 July 2006; Herrmann J., ‘What Thatcherite union buster Sajid Javid learned on Wall Street’, The Guardian, 15 July 2015.

  6. Derman E., ‘Model Risk’ Goldman Sachs Quantitative Strategies Research Notes, April 1996.

  7. CNBC interview, 1 July 2005.

  8. According to MacKenzie et al (2012): ‘The crisis was caused not by “model dopes”, but by creative, resourceful, well-informed and reflexive actors quite consciously exploiting the role of models in governance.’ They quote several examples of people gaming the calculations to ensure that CDO
s appeared both profitable and low-risk.

  9. Tavakoli J., ‘Comments on SEC Proposed Rules and Oversight of NRSROs’, Letter to Securities and Exchange Commission, 13 February 2007.

  10. MacKenzie D. et al., ‘“The Formula That Killed Wall Street”? The Gaussian Copula and the Cultures of Modelling’, 2012.

  11. New Directions for Understanding Systemic Risk (National Academies Press, Washington DC, 2007).

  12. Chapple S., ‘Math expert finds order in disorder, including stock market’, San Diego Union-Tribune, 28 August 2011.

  13. May R., ’Epidemiology of financial networks. Presentation at LSHTM John Snow bicentenary event, April 2013. Available on YouTube.

  14. For background on May’s involvement see previous note.

  15. ‘Was tulipmania irrational?’ The Economist, 4 October 2013.

  16. Goldgar A., ‘Tulip mania: the classic story of a Dutch financial bubble is mostly wrong’, The Conversation, 12 February 2018.

  17. Online Etymology Dictionary. Origin and meaning of bubble. https://www.etymonline.com/word/bubble.

  18. Reproduced with authors’ permission. Source: Frehen R.G.P. et al., ‘New Evidence on the First Financial Bubble’, Journal of Financial Economics, 2013.

  19. Frehen R.G.P. et al., ‘New Evidence on the First Financial Bubble’, Journal of Financial Economics, 2013.

  20. Odlyzko A., ‘Newton’s financial misadventures in the South Sea Bubble’, Notes and Records, The Royal Society, 2018.

  21. Odlyzko A., ‘Collective hallucinations and inefficient markets: The British Railway Mania of the 1840s’, 2010.

  22. Kindleberger C.P. et al., Manias, Panics and Crashes: A History of Financial Crises (Palgrave Macmillan, New York, 1978).

  23. Chow E.K., ‘Why China Keeps Falling for Pyramid Schemes’, The Diplomat, 5 March 2018; ‘Pyramid schemes cause huge social harm in China’, The Economist, 3 February 2018.