Optional Texbook: Modelling Disease Ecology with Mathematics by Robert Smith?
This is a light and friendly introduction to disease modelling, especially suited to the nonmathematician.
Course Content: The objective of this course is to present a detailed introduction to modelling infectious diseases. We will discuss modelling at the population level, as these models represent some of the most classical results. We will then focus on host-pathogen interactions within the host.
We will cover a variety of topics on the mathematical modelling of infectious diseases (HIV, malaria, human papillomavirus, West Nile virus, measles, anthrax and smallpox). Topics will include vaccines, drug resistance, the basic reproductive ratio, bioterrorism and networks.
Theoretical tools will include differential equation models, game theory, uncertainty/sensitivity analysis, Latin Hypercube Sampling and impulsive differential equations. Current literature will be assigned and discussed in class throughout the course.
Course Objectives: Our specific goals for the course as outlined as follows:
1. Illustrate the broad range of infectious disease problems which can be modelled mathematically.
2. Learn the skill of gleaning and synthesising the literature to study a particular question.
3. Create mathematical models from non-mathematical descriptions of problems.
4. Interpret the results of models and evaluate their biological implications.
5. Show the necessity of simplification and approximation in models and identify their effects.
Prerequisites: This course is accessible to students with a background in both mathematics and biology/epidemiology. No pre-knowledge in biology is assumed, but students must have basic calculus and ordinary differential equations. Other topics will be reviewed in class as we go.
Assessment:
| Assignments | 25% |
| Essay | 25% |
| Project presentation | 10% |
| Project | 40% |
Readings will be assigned each week here on this website. Each week, someone will formally present the readings to the class in a 20 minute presentation. (You may do this in pairs if you wish.) You are expected to keep up to date with the readings and discuss them in class, whether or not you are formally presenting them that week. As a result, class attendance is mandatory.
Assignments will be posted here, or given in class.
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 readings:
Week 1
Simple epidemic models (class notes)
Partial Fractions (class notes)
Week 1
R0 (class notes)
Eigenvalues (class notes)
The R0 sleight of hand (class notes)
Week 2
A Light Introduction to Modelling Recurrent Epidemics
Modeling an outbreak of an emerging pathogen
Infection Control in Jails and Prisons
Illicit drug addiction, infectious disease spread, and the need for an evidence-based response
Week 2
HIV Vaccination (class notes)
HIV Vaccination Handout (class notes)
HPV Vaccination (class notes)
HPV Vaccination Handout (class notes)
Week 3
An epidemiological model for West Nile virus: invasion analysis and control applications
Stage-Structured Infection Transmission and a Spatial Epidemic: A Model for Lyme Disease
A postmodern Pandora's box: Anti-vaccination misinformation on the Internet
A Broken Trust: Lessons from the Vaccine-Autism Wars
Week 3
A model for the eradication of Guinea Worm Disease (class notes)
Neglected Tropical Diseases (class notes)
Week 4
On the Delayed Ross-MacDonald Model for Malaria Transmission
Health-related stigma: Rethinking concepts and interventions
Week 4
Microbicides for HIV prevention (class notes)
Week 5
Mailborne transmission of anthrax: Modeling and implications
The Looming Threat of Bioterrorism
A Multidisciplinary Approach to an Ethic of Biodefense and Bioterrorism
Week 5
Malaria Spraying (class notes)
Malaria Spraying Notes (handout)
Week 6
Group interest versus self-interest in smallpox vaccination policy
Human papillomavirus, vaccines and women's health: questions and cautions
Week 6
The impact of media on an influenza pandemic (class notes)
Week 7
An Epidemiological Model of Rift Valley Fever
HIV/AIDS in Africa: Gender Inequality is Fatal
Health Care Utilization: The Experiences of Rural HIV-positive African American Women
Week 7
Impulsive differential equations (class notes)
Week 8
Highly Active Antiretroviral therapy and the Epidemic of HIV+ End-Stage Renal Disease
Week 8
Modelling imperfect adherence to HIV induction therapy (class notes)
Can we spend our way out of the HIV epidemic?
Week 9
Optimal drug treatment regimens for HIV depend on adherence
Recurrent epidemics in small world networks
Public Health Strategies for Pandemic Influenza: Ethics and the Law
Quarantine Matters: quotidian relationships around quarantine in Australia's northern borderlands
Week 10
The reinfection threshold does not exist
Week 11
Modeling Tick-Borne Disease: A Metapopulation Model
Malaria Vaccination (class notes)
Malaria Vaccination Handout (class notes)
An in-host model of acute infection: Measles as a case study
Assignments:
Assignment 1 will be emailed.
Essay: The choice of topic is up to you. However, it must discuss the scientific, ethical and sociological implications of your topic. 2000-3000 words. (Draft due July 5. Final version due July 23. You must hand in your draft with your final essay.)
Examples of essays from previous classes:
For the essay, I expect it to be well written. When you get out into the real world (or even if you stay in academia), writing reports is going to be the bread and butter of what you do. There's no getting away from it: writing is the backbone of almost every professional industry. So the more practice you get, the better. This is a good chance to hone your skills. So you should have an introduction, a coherent argument and a conclusion. I cannot emphasise how important this is - or how much it will help you in the long run.
References: Both your essay and your project should have between 15 and 50 ACADEMIC references, cited in full. You can additionally include websites if needed (Wikipedia is not acceptable), but you must have at least twice as many academic references as non-academic ones.
Project: The final assessment will be a project. This can be done in groups. Your project must be related to mathematical models of infectious disease, but is otherwise open.
A one-page project proposal must be submitted by May 31.
A one-page outline of the model (with the equations) and the assumptions is due by June 15. (Basically, this should be everything preceding the analysis.)
Projects are due by July 30.
Example of projects from previous classes: