MAT 3395 (Winter 2023)

Professor: Dr. Stacey Smith?

Professor	Dr. Stacey Smith? (the question mark is part of my name)
Email	stacey (dot) smith (at) uottawa (dot) ca

Texbook: Modelling Disease Ecology with Mathematics, second edition, by Stacey Smith? (American Institute of Mathematical Sciences, 2017). Available free here.

Syllabus: A formal syllabus can be downloaded from here, although it's almost identical to the first part of this webpage.

Course Content: The objective of this course is to present a detailed introduction to modelling, using infectious diseases as the primary motivation and Matlab as the software.

We will cover a variety of topics on the mathematical modelling of infectious diseases (HIV, malaria, yellow fever, measles). Topics will include fitting curves to data, bifurcations, chaos and the basic reproductive ratio.

Assessment:

Weekly assignments	20%
Midterm	40%
Project Presentation	15%
Final Project	25%

Assignments: Assignments will be taken from the textbook and are due each week. You may work in pairs or groups.

Project: The project will consist of four parts:

1. A one-page proposal (due Jan 30)
2. The mathematical model (due Feb 13)
3. A 20 minute individual presentation (before the end of semester)
4. The final project (due at the end of semester)

For the final project, you must include both mathematical analysis and numerical simulations. Your projects must be done in groups of at least three, but your project presentations will be individual.

Click here for the Presentation Marking Scheme and some general tips.

Some project ideas for diseases can be found here:

Disease projects

Your project should be of the same order as the more complex examples found here. If you wish to use one of these as a starting point, that's great, but you are encouraged to think beyond the parameters of the suggested project.

Here are some examples of past projects:

1. Modelling a Ponzi Scheme
2. Simulations of Optical Thin Films
3. Traffic Problems On The Quebec Bridges
4. The Effect of Vaccination against Tuberculosis (TB)
5. African trypanosomiasis or "Sleeping sickness" (This later became a published paper)
6. Avian Flu Model
7. Predator-Prey Dynamics
8. Deformed Wing Virus in Honey Bee Colonies Vectored by Varroa Destructors

Plagiarism: The university takes plagiarism very seriously. This includes copying other assignments or reproducing any work from another source without citation.

Note: Any changes or announcements will appear on the course website. You should check the website regularly for updates. Note that I will not answer math questions by email.

Class notes:

Course intro

Week 1

Curve Fitting (Chapter 3)

Matlab Overview 1

Splines (Chapter 4)

Week 2

Simple epidemic models (Chapter 5)

Matlab Overview 2

Week 3

R0 (Chapter 6)

Fun extra reading: The Joys of the Jacobian

Week 4

A disease with lifelong immunity (Chapter 7)

The spread of Measles (Chapter 8)

Week 5

Partial Differential Equations (Chapter 9)

Extra PDE notes

Week 6

Case study: HIV vaccination

Extra HIV vaccination notes

Case study: HPV vaccination

Extra HPV vaccination notes

Week 7

Application: Guinea-worm disease (Chapter 18)

Matlab code for impulsive differential equations for the Guinea Worm model:
GWD.m
GWDf.m

Week 8

The Discrete logistic equation (Chapter 10)

Bifurcations (Chapter 11)

Week 9

Application: AIDS and End-stage renal disease (Chapter 16)

Week 10

More advanced epidemic models (Chapter 12)

Measles with vaccination (Chapter 13)

Week 11

A disease with an asymptomatic class (Chapter 14)

Impulsive differential equations (Chapter 15)

Week 12

Respiratory Syncytial Virus

COVID-19

Week 13

Application: Zombies (Chapter 19)

The viral spread of a zombie media story

Project presentation