THE ROLE OF MATHEMATICS IN MEDICINE
Tentative Schedule and Readings
Starred readings are the topics for the one-page papers, due on the Tuesday of that week. Hand in
journals on Jan 22, Feb 12, March 5, April 9 and April 23. They will be returned on the Thursday
of that week (except for the last one, of course).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Date
Jan 8
Jan 15
Jan 22
Jan 29
Feb 5
Feb 12
Feb 19
Feb 26
March 5
March 19
March 26
April 2
April 9
April 16
April 23
Topic
Introduction
Testing for rare diseases
Length-biased sampling
Competing risks
Timing of screening for diseases
Virus dynamics of HIV
Quarantine for disease control
Damon Toth
Acute liver damage from tylenol
The timing of transplantation
Antibiotic resistance evolution
Mutation in cancer progression
Gleevec and CML
Contact tracing and STDs
Wrap-up
The math
Algebra (we hope)
Conditional probability
Probability distributions
Survivorship analysis
Optimization
Differential equations
Dynamic optimization
ANTHRAX!
Enzyme kinetics
Queuing theory
Stochastic models
Population genetics
Age structured models
Bioinformatic methods
Expect the unexpected
Main Reading
[1, 2]
[3]∗
[5]
[7]
[9, 10]∗
[13]
[15]
[16]
[17]
[19]∗
[22, 23]
[26, 27]∗
[30, 31]
[32]
Extra
[4]
[6]
[8]
[11, 12]
[14]
[18]
[20, 21]
[24, 25]
[28, 29]
[33]
References
[1] A. R. A. Anderson and V. Quaranta, “Integrative mathematical oncology,” Nature Reviews
Cancer, vol. 8, pp. 227–234, 2008.
[2] C. Castillo-Solórzano, P. Carrasco, G. Tambini, S. Reef, M. Brana, and C. A. de Quadros,
“New horizons in the control of rubella and prevention of congenital rubella syndrome in the
Americas,” J. Infect. Dis., vol. 187, pp. S146–S152, 2003.
[3] R. I. Kopelman, J. B. Wong, and S. G. Pauker, “A little math helps the medicine go down,”
New Eng. J. Med., vol. 341, pp. 435–9, 1999.
[4] S. Wacholder, S. Chanock, M. Garcia-Closas, N. Rothman, et al., “Assessing the probability
that a positive report is false: an approach for molecular epidemiology studies,” Journal of
the National Cancer Institute, vol. 96, pp. 434–442, 2004.
[5] M. Wolkewitz, A. Allignol, S. Harbarth, G. de Angelis, M. Schumacher, and J. Beyersmann,
“Time-dependent study entries and exposures in cohort studies can easily be sources of different and avoidable types of bias,” Journal of Clinical Epidemiology, vol. 65, pp. 1171–1180,
2012.
[6] S. W. Duffy, I. D. Nagtegaal, M. Wallis, F. H. Cafferty, N. Houssami, J. Warwick, P. C.
Allgood, O. Kearins, N. Tappenden, E. O’Sullivan, et al., “Correcting for lead time and
length bias in estimating the effect of screen detection on cancer survival,” Am. J. Epidemiol.,
vol. 168, p. 98, 2008.
[7] H. Welch, P. Albertsen, R. Nease, T. Bubolz, J. Wasson, et al., “Estimating treatment benefits
for the elderly: the effect of competing risks,” Annals of Internal Medicine, vol. 124, pp. 577–
584, 1996.
[8] Y. K. Tu, R. West, G. T. H. Ellison, and M. S. Gilthorpe, “Why evidence for the fetal origins
of adult disease might be a statistical artifact: The “reversal paradox” for the relation between
birth weight and blood pressure in later life,” Am. J. Epidemiol., vol. 161, p. 27, 2005.
[9] A. L. Barratt, “Cancer screening: benefits, harms and making an informed choice,” Australian
Family Physician, vol. 35, pp. 39–42, 2008.
[10] A. Bleyer and H. Welch, “Effect of three decades of screening mammography on breast-cancer
incidence,” New Eng. J. Med., vol. 367, pp. 1998–2005, 2012.
[11] Independent UK Panel on Breast Cancer Screeing, “The benefits and harms of breast cancer
screening: an independent review.,” Lancet, vol. 380, pp. 1778–1786, 2012.
[12] N. T. van Ravesteyn, D. L. Miglioretii, N. K. Stout, et al., “What level of risk tips the
balance of benefits and harms to favor screening mammography starting at age 40?,” Annals
of Internal Medicine, vol. 156, pp. 609–617, 2012.
[13] A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D. Ho, “HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time,” Science,
vol. 271, p. 1582, 1996.
[14] S. Philpott, B. Weiser, K. Anastos, C. M. R. Kitchen, E. Robison, W. A. Meyer III, H. S.
Sacks, U. Mathur-Wagh, C. Brunner, and H. Burger, “Preferential suppression of CXCR4specific strains of HIV-1 by antiviral therapy,” J. Clin. Invest., vol. 107, p. 431, 2001.
[15] T. Day, A. Park, N. Madras, A. Gumel, and J. Wu, “When is quarantine a useful control
strategy for emerging infectious diseases?,” Am. J. Epidemiol., vol. 163, pp. 479–485, 2006.
[16] R. Brookmeyer, E. Johnson, S. Barry, et al., “Modelling the incubation period of anthrax,”
Statistics in Medicine, vol. 24, p. 531, 2005.
[17] C. H. Remien, F. R. Adler, L. Waddoups, T. D. Box, and N. L. Sussman, “Mathematical
modeling of liver injury and dysfunction after acetaminophen overdose: Early discrimination
between survival and death,” Hepatology, vol. 56, pp. 727–734, 2012.
[18] J. G. O’Grady, G. J. Alexander, K. M. Hayllar, and R. Williams, “Early indicators of prognosis
in fulminant hepatic failure.,” Gastroenterology, vol. 97, p. 439, 1989.
[19] T. G. Liou, F. R. Adler, D. R. Cox, and B. C. Cahill, “Lung transplantation and survival in
children with cystic fibrosis,” New Eng. J. Med., vol. 357, pp. 2143–2152, 2007.
[20] E. Foster, M. Hosking, and S. Ziya, “A spoonful of math helps the medicine go down: an
illustration of how healthcare can benefit from mathematical modeling and analysis,” BMC
Medical Research Methodology, vol. 10, p. 60, 2010.
[21] R. B. Freeman Jr, R. H. Wiesner, J. P. Roberts, S. McDiarmid, D. M. Dykstra, and R. M.
Merion, “Improving liver allocation: MELD and PELD.,” American Journal of Transplantation Supplement, vol. 4, p. 114, 2004.
[22] A. W. McCormick, C. G. Whitney, M. M. Farley, R. Lynfield, L. H. Harrison, N. M. Bennett,
W. Schaffner, A. Reingold, J. Hadler, P. Cieslak, et al., “Geographic diversity and temporal
trends of antimicrobial resistance in Streptococcus pneumoniae in the United States,” Nat.
Med., vol. 9, pp. 424–430, 2003.
[23] A. McGeer and D. E. Low, “Is resistance futile?,” Nat. Med., vol. 9, pp. 424–30, 2003.
[24] S. M. Blower and T. Chou, “Modeling the emergence of the ‘hot zones’: tuberculosis and the
amplification dynamics of drug resistance,” Nat. Med., vol. 10, pp. 1111–1116, 2004.
[25] N. Jumbe, A. Louie, R. Leary, W. Liu, M. R. Deziel, V. H. Tam, R. Bachhawat, C. Freeman,
J. B. Kahn, K. Bush, et al., “Application of a mathematical model to prevent in vivo amplification of antibiotic-resistant bacterial populations during therapy,” J. Clin. Invest., vol. 112,
p. 275, 2003.
[26] N. L. Komarova, “Mathematical modeling of tumorigenesis: mission possible,” Current Opinion in Oncology, vol. 17, pp. 39–43, 2005.
[27] F. Michor, Y. Iwasa, and M. A. Nowak, “The age incidence of chronic myeloid leukemia can
be explained by a one-mutation model,” Proc. Nat. Acad. Sci., vol. 103, pp. 14931–14934,
2006.
[28] S. A. Frank, “Age-specific incidence of inherited versus sporadic cancers: A test of the multistage theory of carcinogenesis,” Proc. Nat. Acad. Sci., vol. 102, pp. 1071–1075, 2005.
[29] D. Hanahan and R. A. Weinberg, “The hallmarks of cancer,” Cell, vol. 100, pp. 57–70, 2000.
[30] F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah, C. L. Sawyers, and M. A. Nowak,
“Dynamics of chronic myeloid leukaemia,” Nature, vol. 435, pp. 1267–1270, 2005.
[31] I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C. Mueller, and M. Loeffler, “Dynamic
modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications,” Nat Med, vol. 12, pp. 1181–1184, 2006.
[32] M. R. Golden, W. L. H. Whittington, H. H. Handsfield, J. P. Hughes, W. E. Stamm, M. Hogben, A. Clark, C. Malinski, J. R. L. Helmers, K. K. Thomas, et al., “Effect of expedited
treatment of sex partners on recurrent or persistent gonorrhea or Chlamydial infection,” New
Eng. J. Med., vol. 352, p. 676, 2005.
[33] J. D. Ross, A. Sukthankar, K. W. Radcliffe, and J. Andre, “Do the factors associated with
successful contact tracing of patients with gonorrhoea and Chlamydia differ?,” British Medical
Journal, vol. 75, p. 112, 1999.