Mathematical Biology and Applications

Instructor Lev V. Idels

Vancouver Island University

 

Spring 2008

 

http://nsf.gov/news/speeches/colwell/rc03norwaycsis/img011.jpg

 

 

 

 

 

 

 

 

 

 

 

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An introduction to classical mathematical models from Population Biology

and Ecology. Topics chosen from harvesting and competition models,

epidemic models for HIV, SARS, West Nile, and Bird Flu, models of popula-

tion outbreaks, marine protected areas models, metapopulation and patch

models, chemostat models, and nonlinear host-parasitoid models.

Credit will only be granted for one of MATH 345 or MATH 346. (3:0:0)

Prequisite: Min. "B" in both MATH 121or 100 and MATH 122 or 101

Aims: This course targets undergraduate students majoring in both computing and biological sciences, broadly defined to include mathematical, computer science, biology minors, and also included fisheries & aquaculture, and natural resource protection students.

The goal of this course is to give students an understanding of the biological-mathematical interface, and how mathematics contributes to the study of biological phenomena. In this course, students will learn how to fashion and use these tools to explore questions ranging across the biological sciences.

 

Office: 360/304 Ph: 7533245 Local 2429 e-mail: idelsl@mala.ca

Webpage: http://web.mala.ca/math/lev.html

 

To help me manage my email inbox, please include "MATH 346 in the subject line of any email message you send to me (without it, your message runs the risk of being deleted without being read).

Appointments: If you need to see me outside of the announced office hours ( Monday and Wednesday 12:00-2:00pm), please set up an appointment with me, either by speaking to me before or after class, or by sending me an email message (include "MATH 346" in the subject line, please).

Syllabus

We use text: G. de Vries, T. Hillen, M. Lewis et al Course in Mathematical Biology Qualitative Modelling with Mathematical and Computational Methods SIAM, 2006, and this course is designed around some essential topics such as:

 

  • Dynamics in interacting multiple species populations and applications in Ecology.
  • Nonlinear host-parasitoid models. Metapopulation and patch models.
  • Models for the spread of infectious diseases: modelling the spread of the HIV virus,

outbreaks analysis e.g. SARS, West Nile and Bird Flu Viruses

  • Fitting models to data graphically and analytically.
  • Harvesting strategies. Basic fishery and forest models. Managing renewable resources, including marine protected areas models.

Grading:

%

90-10

85-89

80-84

76-79

72-75

68-71

64-67

60-63

55-59

50-54

0-49

Letter Grade

A+

A

A-

B+

B

B-

C+

C

C-

D

F

Grade Point

4.33

4.00

3.67

3.33

3.00

2.67

2.33

2.00

1.67

1.00

0.00

         40% Final Exam

         30% Individual Project

         10% Group Projects

         20% Four Assignments (TBA) Assignments # 1 & 2

Assignment # 3 Assignment # 4

Important Dates:

  Submit 1-2 page Research Proposal (Letter of Intent): Due 4th week (worth/penalty 6%)

  Submit Final Report on Group Project: Due 7th week

  Final date for submitting draft for feedback: Due 9th week (worth/penalty 6%)

  Final 8-10 page report: Due 11th week

Individual Project

 

Each of you will find a problem from your own field, construct a mathematical model for the problem, analyze the model using the material from the course, and solve the problem based on your mathematical analysis. There are no good or bad models; I expect you do a self-evaluation on the performance of your model, and suggest future development. You are allowed and expected to find help from your major professors, me, or/and library, and internet. Discussions among group members are encouraged. You are expected to start thinking about the problem now.

Give me a clean version of your work, without all the dead end scratchwork. Where you fill in by hand make it legible. It would be surprising if you could do all this in less than 5 pages; but I don't want to read 20 either. Probably 6-10 would be good, depending on your layout, font size, number of graphs, figures, and tables.

Note: You may do the project on any topic with the following restriction: you should use a modelling approach that is different from the one you used for the group project.

List of Topics for Individual Project:

1. Optimal Harvesting* 2. The effects of Dynamic Environments* 3. Models for Parasitism

4. Metalife and Metapopulation 5. Logistic Models in Population Dynamics* 6. Fox Production Models*

7. Rickers Fisheries Model* 8. Measles Models with Vaccination 9. Nicholson-Bailey Model*

10. Chaos in Biological Populations. 11. Optimal Design of Marine Reserves* 12. Cholera Outbreak in South Africa: Data and Parameter Estimation(textbook)

13. SARS Outbreak in Canada: Data and Models(textbook) 14. Pharmacokinetics Models. 15. Bacterial Growth in a Chemostat

16. Cellular Dynamics of HIV. 17 Marine Protected Area Models. To be continued.

 

Individual Project Report

 

The project report should consist of the following components:

  1. Introduction (background and problem description).
  2. Formulation of the mathematical model (assumptions, restrictions, equations).
  3. Approach to solve model and/or learn about the model.
  4. Results, conclusions and list of references.
  5. Self-assessment (Which parts of the model worked and which didn't?  What roadblocks did you encounter?  What would you do differently if you could start over?  Etc.).
  6. Supporting materials (copy of code, tables, details of calculations, etc).

Reading List:

#2Print/Email

QH 352 R46 1993

1993

Modelling biological populations in space and time
  Renshaw, Eric

 

#3Print/Email

QH 323.5 E34 2005

2005

Mathematical models in biology
  Edelstein-Keshet, Leah

 

#4 Print/Email

QH 323.5 M88 2002 V.1

2002

Mathematical biology  3rd ed.
  Murray, J. D. (James Dickson) 2 Available at Nanaimo Campus Library

 

#5Print/Email

 

QH 352 K66 2001

2001

Elements of mathematical ecology
  Kot, Mark, 1956- 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#6Print/Email

QH 352 B73 2001

2001

Mathematical models in population biology and epidemiology
  Brauer, Fred. 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#7Print/Email

QH 323.5 F37 2001

2001

Dynamical models in mathematical biology
  Farkas, Mikls, 1932- 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#8Print/Email

QH 541.15 S72 M64 2001

2001

Modeling in natural resource management : development, interpretation, and application
  Shenk, Tanya M. 2 Available at Nanaimo Campus Library and Cowichan Campus Library

 

#9Print/Email

QH 352 G67 1998

1998

A primer of ecology  2nd ed.
  Gotelli, Nicholas J., 1959- 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#10Print/Email

QH 541.15 M3 C37 1997

1997

Case studies in mathematical modeling : ecology, physiology, and cell biology
  Othmer, H. G. (Hans G.), 1943- 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#11Print/Email

QH 323.5 M88 1993

1993

Mathematical biology  2nd, corr. ed. --
  Murray, J. D. (James Dickson). 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

#12Print/Email

QH 352 G47 1989

1989

Population harvesting : demographic models of fish, forest, and animal resources
  Getz, Wayne Marcus. 1 Available at Nanaimo Campus Library in Stacks (main book collection)

 

 

Interesting Weblinks:

http://www.math.rutgers.edu/~sontag/mathbio-links.html

Jianhong Wu's homepage!

Gerda de Vries @ Work

nsf.gov/news/speeches/colwell/rc03norwaycsis/sld007.htm

Avoiding Mistakes in Population Modeling

nlds.sdsu.edu/index.html#vortex

www.arcytech.org/java/population/facts_math.html www.biomatematica.it/urbino2002/pages/course_on_line.htm

www.vrvis.at/vis/resources/diss-LM/node75.html

www.sci.wsu.edu/idea/Logistic/ecology.html

http://www.math.ualberta.ca/~thillen/

www.math.lsa.umich.edu/~tjacks/Math463_05.html

faculty.oxy.edu/angela/mathbio.html

www.resnet.wm.edu/~jxshix/math490/bio-pattern.html

www.math.ualberta.ca/~mlewis/

 



[1] From Speech Archives by Former NSF Director Rita R. Colwell