Registration Deadline: TBA

Instructor: Professor Jane Heffernan, York University

Course Date: TBA
Mid-Semester Break: TBA
Lecture Time: TBA
Office Hours: TBA

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: TBA

Format: TBA

Course Description

The mathematical modeling of infectious diseases is studied on two different scales: between individuals in a population (epidemiology) and within an infected individual (immunology). The objective of this course is to present a detailed introduction to the mathematical modeling of the infectious disease in both epidemiological and immunological contexts. Students will be introduced to the biology (i.e., immune system components (i.e. T-cell activation, clearance of infection, etc), pathogen characteristics (i.e. HIV, influenza, etc), intervention strategies (i.e. drug therapy and vaccination), behaviour) and will gain experience in developing and applying continuous and discrete time stochastic and deterministic models, and computer simulations to tackle real work problems in health and public health. The fundamental predictors of infection, the basic reproductive ratio and initial growth rate will be introduced. Relationships between immunological characteristics and epidemiological effects, such as disease transmission and acquirement of immunity, are also discussed.

Course Objectives:

• Illustrate the broad range of infectious disease problems which can be modelled mathematically.
• Create mathematical models from non-mathematical descriptions of problems.
• Interpret the results of models and evaluate their biological implications.
• Show the necessity of simplification and approximation in models and identify their effects.
• Derive mathematical models from first principles
• Complete a research project in disease modelling that tackles a real-world problem and health or public health

Syllabus:

• What is epidemiology?
• The history of mathematical epidemiology
• The SIR model and Extensions
• What is immunology?
• The history of mathematical immunology
• The basic in-host model and Extensions
• The Basic Reproduction Number
• Stochastic Models
• Sensitivity Analysis
• Disease models with additional structure (i.e., spatial, networks, heterogeneity)
• Disease Case Studies (will be informed by news reports and recent disease outbreaks in Canada)

Software: Students are encouraged to use mathematical software programs and programming languages (i.e., MATLAB, R, Maple python) to aid in their modelling activities. MATLAB code will be shared and discussed related to the syllabus topics and case studies.

References: There is no assigned textbook. The material will be based on the reference texts below as well as papers from the literature. Course material will be subject to revision and/or extension as the course progresses.

• R.M. Anderson and R.M. May, Infectious diseases of humans, Oxford University Press, 1991.
• O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model building, analysis and interpretation, Wiley series in mathematical and computational biology, 2000.
• M.A. Nowak and R.M. May, Viral Dynamics: Mathematical principles of immunology and virology, Oxford University Press, 2000.
• D. Wodarz, Killer Cell Dynamics: Mathematical and computational approaches to immunology, Springer, 2007.
• Brauer, F., van den Driessche, P. and Wu, J., Mathematical Epidemiology, Springer, 2008.
• Keeling, M.J. and Rohani, P., Modelling Infectious Diseases in Human and Animals, Princeton University Press, 2007.
• Access to journals: Science, PNAS, Theoretical Population Biology, Journal of Theoretical Biology, Proceedings of the Royal Society B, Nature.

Evaluation: The final grade for the course will include the following components:

• 40% - Assignments (2 @ 20%)
• 25% - Final Exam
• 10% - Participation, in class presentations, reflection papers, attendance
• 25% - Course project, in the following breakdown
• 5% - Project proposal (3 pages max, intro to problem, proposed model and assumptions, references)
• 8% - Presentation of final project (15 minutes max)
• 12% - Written report of final project (approx. 10 pages with figures and references)

Project: All project components should be typed using a word processor, or using LaTeX.

Participation: This grade consists of attendance, in-class presentations, and reflection papers. Students will be required to write a one page discussion on required readings that are discussed in class.