MATH 485/585  Spring 2006  Modeling Projects
Math 485 modeling projects should be on one of the topics listed below. The articles or web sites given as references must make the basis of each project and be used as the starting point for bibliographical searches.

Modeling the formation of sand dunes
The first paper discusses a discrete model describing the time evolution of the height of the sand bed. The second and third papers discuss a continuous model and stress the solitarywave behavior of barchan dunes. Computer simulation of aeolian sand ripples and dunes by T.D. Miao, Q.S. Mu and S.Z. Wu
 A model of Barchan dunes including lateral shear stress by V. Schwämmle and H.J. Hermann
 Solitary behavior of sand dunes by V. Schwämmle and H.J. Hermann

Modeling diseases and epidemics
 Resistance to antibiotics
 A model of antibioticresistant bacterial epidemics in hospitals by G.F. Webb, E.M.C. D'Agata, P. Magal and S. Ruan
 Modeling the Hong Kong SARS epidemics using a small world network
The first link points to the main article. The second link is a general discussion on the use of multiscale models to describe epidemics. Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment by M. Small and C.K. Tse
 Multiscale, resurgent epidemics in a hierarchical metapopulation model by D.J. Watts, R. Muhamad, D.C. Medina and P.S. Dodds
 Modeling leukaemia chemotherapy
The first link points to a news article in Nature. The second link points to the article describing the model. Cancer biology: Summing up cancer stem cells by J.P. Huntly and D.G. Gilliland
 Dynamics of chronic myeloid leukaemia by F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L. Sawyers and M.A. Nowak
 Resistance to antibiotics

Modeling the dream team
The first link points to a perspective article published in Science. The second link points to the article describing the model of team formation. Network Theory  the emergence of the creative enterprise by A.L. Barabási
 Team assembly mechanisms determine collaboration network structure and team performance by R. Guimerà, B. Uzzi, J. Spiro and L.A. Amaral

Modeling in Economics
 Modeling price variability (project proposed by Tommy Occhipinti)
 Project description:
How is it that two gas stations that are right next to each other can charge different prices for gasoline? A simple search on www.tucsongasprices.com reveals a spread in price from $2.09 to $2.39 in prices per gallon of unleaded gasoline in Tucson gas stations. Students are no doubt aware of the amazing discrepancy in textbook prices. A quick search into new copies of a popular biology book shows a spread from $95.00 to $180.00. Though most economic models tend to assume that each good has a single price, every day observations show this is not the case. This is because some merchants can charge more than others knowing that not everyone will invest the effort to find the seller with the lowest price. This project would seek to examine the factors that cause price dispersion, and to model these effects mathematically. Questions to consider might include: Why are the prices of some goods spread more than others? What should the actual distribution of prices look like? What will happen to the distribution of prices over time? For instance, might it happen that all sellers eventually converge to a single price? If so, under what circumstances? No preliminary knowledge of economics will be necessary.  Reading material:
The economics of information by G.J. Stigler
 Project description:
 Modeling the distribution of retail stores in a city
 Aggregation of retail stores by P. Jensen, J. Boisson and H. Larralde
 Modeling price variability (project proposed by Tommy Occhipinti)

Modeling collective behaviors of living organisms
The first link points to a general discussion of schooling behaviors and the second to the main article for the project. The third link describes Boids, which are simulated creatures that can collectively reproduce flocking behaviors. Complexity, Pattern, and Evolutionary TradeOff in Animal Aggregation by J.K. Parrish & L. EdelsteinKeshet
 Effective leadership and decisionmaking in animal groups on the move by I.D. Couzin, J. Krause, N.R. Franks and S.A. Levin
 C. Reynolds Boids page.

Modeling gas exchange in the lungs
This project is proposed by Marco Herrera and is based on Chapter 2 of the book Modeling and Simulation in Medicine and the Life Sciences by F.C. Hoppensteadt and C.S. Peskin.
Math 585 modeling projects may either be on one of the topics listed above or be based on the student's graduate thesis work.