Mathematical Biology and Applications
Instructor
Lev V. Idels
Vancouver Island University
Spring 2008
An introduction to classical mathematical models from Population Biology
and Ecology. Topics chosen from harvesting and competition models,
epidemic models for HIV, SARS,
tion outbreaks, marine protected areas models, metapopulation and patch
models, chemostat models, and nonlinear hostparasitoid 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
The goal of this course is to give students an
understanding of the biologicalmathematical 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 email: 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).
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:
outbreaks analysis e.g. SARS,
Grading:
% 
9010 
8589 
8084 
7679 
7275 
6871 
6467 
6063 
5559 
5054 
049 
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 (
Important Dates:
Ø Submit 12 page Research Proposal (Letter
of Intent): Due 4^{th} week (worth/penalty 6%)
Ø Submit Final Report on Group Project: Due
7^{th} week
Ø Final date for submitting draft for
feedback: Due 9^{th} week
(worth/penalty 6%)
Ø Final 810 page report: Due 11^{th}
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 selfevaluation 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 610 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. Ricker’s
Fisheries Model* 8. Measles Models with Vaccination 9. NicholsonBailey Model*
10. Chaos in Biological Populations. 11. Optimal Design of Marine Reserves* 12.
Cholera Outbreak in
13. SARS Outbreak in
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:
#2 
QH 352 R46 1993 
1993 
Modelling biological populations in space and time 



#3 
QH 323.5 E34 2005 
2005 
Mathematical models in biology 



#4 
QH 323.5 M88 2002 V.1 
2002 
Mathematical biology 3rd ed. 



#5 
QH 352 K66 2001 
2001 
Elements of mathematical ecology 



#6 
QH 352 B73 2001 
2001 
Mathematical models in population biology and epidemiology 



#7 
QH 323.5 F37 2001 
2001 
Dynamical models in mathematical biology 



#8 
QH 541.15 S72 M64 2001 
2001 
Modeling in natural resource management : development,
interpretation, and application 



#9 
QH 352 G67 1998 
1998 
A primer of ecology 2nd ed. 



#10 
QH 541.15 M3 C37 1997 
1997 
Case studies in mathematical modeling : ecology, physiology, and
cell biology 



#11 
QH 323.5 M88 1993 
1993 
Mathematical biology 2nd,
corr. ed.  



#12 
QH 352 G47 1989 
1989 
Population harvesting : demographic models of fish, forest, and
animal resources 


http://www.math.rutgers.edu/~sontag/mathbiolinks.html
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/dissLM/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/biopattern.html