AMH6 Populations and disease

General Information

This page relates to the Applied Mathematics Honours course "Populations and disease".

The lecturer for this course is Mary Myerscough.

For general information on honours in the School of Mathematics and Statistics, refer to the relevant honours handbook.

The exam will be held starting at 9.15 on Tuesday June 10, in Carslaw room 453. This is a copy of the first page of the exam.

Lecturer:
Dr Mary Myerscough, room 626 Carslaw, email M.Myerscough@maths.usyd.edu.au, phone 9351 3724. An information sheet is available as well as information on the reading assignment that is an integral part of the course.
Timetable:
Lectures in 2008 are on Tuesday at 2pm in Carslaw room 352 and on Thursday at 10am in Carslaw 361.
Lecture Notes:
These will be handed out in class. They will not cover the whole of the course but may be available for some sections. Copies of the Lecture notes listed here may lack some diagrams.

Introduction to continuous models for age-structured populations.

Stage-structured populations.

Handout on Perron-Frobenius Theorem for Leslie matrices.

Examples and other class work:

1. Thinking about structured population models.

2. Birth and death in the termite mound.

3. A population with stable age distribution.

4. Modelling Chemotherapy in Leukaemia.

5. Modelling discrete age-structured populations using Leslie matrices.

6. Examining Caswell's teasel model. Here is some information about teasel and which has some pictures.

7. Travelling waves in the spruce budworm model.

Short Assignments:

Assignment 1 with solutions

Assignment 2. Since most people received close to full marks, I do not plan to circulate solutions. Please come and see me if you have any questions.

Assignment 3 with solutions.

References:
These references are referred to in the course or on course handouts. I anticipate that this section will develop over the semester. I will add links to articles that can be downloaded and links to catalogue pages in the library catalogue for the books.

Cameron, D.A., Iver, D.J., Evans, T.A and Myerscough, M.R. 2008 Optimal reproduction strategies in two species of mound-building termites. Bulletin of Mathematical Biology, 70:189-209.

Caswell, H. 2001 Matrix Population Models. Construction, Analysis and Interpretation. Second edition. Sinauer Associates, Massachusetts.

Diekmann, O. and Heesterbeek, J.A.P. 2000 Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, Chichester.

Hastings, A., Hall, R.J. and Taylor, C.M. 2006 A simple approach to optimal control of invasive species. Theoretical Population Biology, 70:431-435.

Hethcote, H.W. 2000 The mathematics of infectious diseases. SIAM Review, 42:599-653.

Kot M. 2001 Elements of Mathematical Ecology. Cambridge University Press.

Murray, J.D. 2003 Mathematical Biology. Third edition. Springer, New York.

Tuljapurkar, S. and Caswell, H. 1997 Structured-population Models in Marine, Terrestrial and Freshwater Systems, Chapman and Hall, New York.

Wilson, D.P., Kahn, J. and Blower, S.M. 2006 Predicting the epidemiological impact of antiretroviral allocation strategies in KwaZulu-Natal: the effect of the urban-rural divide. 2000 Proceedings of the National Academy of Science 103:14228-14233.