Applied Mathematics for the Life and Social Sciences

Modeling Seminar

AML 612 – Spring 2008

Instructors

Dr. Gerardo Chowell

Email: gchowell@asu.edu

Dr. Carlos Castillo-Chavez

Email: ccchavez@asu.edu

Course Description

Presents and applies concepts and principles of modeling and understanding the tools for representing the structure and operation of complex life and social systems and processes.

Course Goals

By the end of the course, students will

• Be able to identify potential problems in the life and social sciences and corresponding mathematical and statistical tools that can be used for their study.
• Identify major specialized journals of mathematical and statistical applications in the life and social sciences.

Outline of Topics Covered

Seminars will be on recent advances in quantitative applications life and social sciences including applications in epidemiology, ecology, biology and sociology (see below for a list of relevant scientific articles).

Pre-requisites

AML 610 or approval by instructor.

Texts.

The content of this modeling seminar will be based primarily on journal articles (please see below). However some essential texts and papers include the following:

R.M. Anderson and R.M. May. Infectious Diseases of Humans, Oxford University Press, Oxford, 1991.

Brauer, F., Castillo-Chavez, C., 2000. Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York.

J.D. Murray. Mathematical Biology. Springer-Verlag, Heidelberg, 1989 (767 pages) (2nd printing 1990, 3rd corrected printing 1993); Mathematics Book Club (U.S.A.) adoption, 1991, 1996.

Okubo, A. and S.A. Levin, eds. 2001. Diffusion and Ecological Problems: Modern Perspectives, 2nd Edition. Interdisciplinary Applied Mathematics, Vol 14. Springer, New York. Pp. 467.

Coursework and Assessment

Students will write 2-page reaction reports based on scientific publications relevant to the weekly lectures. Reaction reports will count towards 90% of the course grade and class participation will account for the remaining 10%.

Classroom Policies

Attendance.

Weekly and punctual attendance at class is required for this course to function pedagogically as intended. It is therefore compulsory.

Academic Honesty:

Students are responsible for their own academic behavior, and for making themselves fully aware of the University’s policies: http://www.asu.edu/studentaffairs/studentlife/judicial/academic_integrity.htm. Academic dishonesty includes using the un-credited work of others, but also tolerating or assisting dishonesty in others.

Reaction reports will be based on some of the following journal articles

Characterizing the distributions of sojourn times in models from data

Extracting key information from historical data to quantify the

transmission dynamics of smallpox. Nishiura H, Brockmann SO, Eichner M.

Theor Biol Med Model. 2008 Aug 20;5:20. Review.

Transmissibility of 1918 pandemic influenza. Mills CE, Robins JM, Lipsitch M. Nature. 2004 Dec 16;432(7019):904-6.

Statistical models to characterize seasonal processes

Epidemiological evidence of an early wave of the 1918 influenza

pandemic in New York City. Olson DR, Simonsen L, Edelson PJ, Morse SS. Proc Natl Acad Sci U S A. 2005 Aug 2;102(31):11059-63.

Influenza epidemics in the United States, France, and Australia,

1972-1997. Viboud C, Boëlle PY, Pakdaman K, Carrat F, Valleron AJ, Flahault A. Emerg Infect Dis. 2004 Jan;10(1):32-9.

Deterministic versus stochastic compartmental models

Renshaw 1991. Modeling Biological Populations in Space and Time, CUP, Cambridge University Press.

Brauer, F., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Springer-Verlag, New York, (2001).

A final size relation for epidemic models. Arino J, Brauer F, van den Driessche P, Watmough J, Wu J. Math Biosci Eng. 2007 Apr;4(2):159-75.

Allen, L. J. S.: An Introduction to Stochastic Processes with Applications to Biology.

Pearson, Upper Saddle River, (2003).

The Reproductive Number of Ebola and the Effects of Public Health Measures: The cases of Congo and Uganda. G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore, and J. M. Hyman. J. Theor. Biol. 229(1), 119-126 (2004

The effect of public health measures on the 1918 influenza pandemic in

U.S. cities.Bootsma MC, Ferguson NM. Proc Natl Acad Sci U S A. 2007

May 1;104(18):7588-93. Epub 2007 Apr 6.

Estimation of the reproduction number of infectious diseases

The estimation of the basic reproduction number for infectious diseases. Statistical methods in medical research. K. Dietz. 1993; 2:23-41.

Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases. Model building, analysis and interpretation. Wiley Series in Mathematical and Computational Biology. John Wiley \& Sons, Ltd., New York.

Reproduction numbers and sub-threshold endemic equilibria for

compartmental models of disease transmission. van den Driessche P, Watmough J. Math Biosci. 2002 Nov-Dec;180:29-48.

Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. G. Chowell, H. Nishiura, L.M.A. Bettencourt. J R Soc Interface 4, 155-166 (2007)

The Reproductive Number of Ebola and the Effects of Public Health Measures: The cases of Congo and Uganda. G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore, and J. M. Hyman. J. Theor. Biol. 229(1), 119-126 (2004).

Compartmental models with more realistic sojourn times

Destabilization of epidemic models with the inclusion of realistic

distributions of infectious periods. Lloyd AL. Proc Biol Sci. 2001 May 7;268(1470):985-93.

Appropriate models for the management of infectious diseases.

Wearing HJ, Rohani P, Keeling MJ.PLoS Med. 2005 Jul;2(7):e174. Epub 2005 Jul 26. Erratum in: PLoS

Med. 2005 Aug;2(8):e320.

Estimation of the reproduction number of dengue fever from spatial

epidemic data. Chowell G, Diaz-Dueñas P, Miller JC, Alcazar-Velazco A, Hyman JM,

Fenimore PW, Castillo-Chavez C. Math Biosci. 2007 Aug;208(2):571-89. Epub 2006 Dec 13.

Epidemiological models with non-exponentially distributed disease

stages and applications to disease control. Feng Z, Xu D, Zhao H. Bull Math Biol. 2007 Jul;69(5):1511-36. Epub 2007 Jan 20.

Uncertainty and sensitivity analysis

Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. S.M. Blower and H. Dowlatabadi. 1994. International Statistical Review 2: 229-243.

Uncertainty and sensitivity analysis of the basic reproductive rate: Tuberculosis as an Example. M.A. Sanchez and S.M. Blower. 1997. American Journal of Epidemiology 145: 1127-1137

Model Parameters and Outbreak Control for SARS. G. Chowell, C. Castillo-Chavez, P.W. Fenimore, C. Kribs-Zaleta, L. Arriola, J.M. Hyman. Emerg. Inf. Dis. 10 (7) (2004) , Supplementary materials

Preferred mixing

The effects of population structure on the spread of the HIV infection. Sattenspiel L, Koopman J, Simon C, Jacquez JA. Am J Phys Anthropol. 1990 Aug;82(4):421-9.

Networks in nature, society and technology

Collective dynamics of 'small-world' networks. D. J. Watts and S. H. Strogatz. Nature 393: 440-42 (1998).

Navigation in a small world. Kleinberg JM. Nature. 2000 Aug 24;406(6798):845. No abstract available.

Diameter of the World Wide Web. R. Albert, H. Jeong, and A.-L. Barabási

Nature 401, 130-131 (1999).

A.-L. Barabási and R. Albert. Emergence of scaling in random networks

Science 286, 509-512 (1999).

A.-L. Barabási, R. Albert, and H. Jeong. Mean-field theory for scale-free random networks. Physica A 272, 173-187 (1999). [ PDF ] [ cond-mat/9907068 ]

E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabási. Hierarchical organization of modularity in metabolic networks.

Science 297, 1551-1555 (2002).

Scaling laws for the movement of people between locations in a large city. G. Chowell, J. M. Hyman, S. Eubank, C. Castillo-Chavez. Phys. Rev. E 68, 066102 (2003)

Disease and rumor spread on networks

Collective dynamics of 'small-world' networks. D. J. Watts and S. H. Strogatz. Nature 393: 440-42 (1998).

Halting viruses in scale-free networks. Can we stop the AIDS epidemic? Z. Dezso A.-L. Barabási. Physcial Review E 65, 055103(R) (2002).

Epidemic dynamics and endemic states in complex networks.

Pastor-Satorras R, Vespignani A. Phys Rev E Stat Nonlin Soft Matter

Phys. 2001 Jun;63(6 Pt 2):066117.

Infection dynamics on scale-free networks.

May RM, Lloyd AL. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Dec;64(6 Pt

2):066112.

Dynamics of rumor propagation on small-world networks. Zanette DH. Phys Rev E

Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 1):041908.