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
