Faculty of Science AMSI Summer School 2013

ANZIAM SS2013 subject: Mathematical epidemiology: stochastic models and their statistical calibration

Johua Ross
The University of Adelaide


Synopsis

Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology one of the most exciting topics in applied mathematics. During the summer school, you will be introduced to mathematical epidemiology and some fundamental theory required for studying and parametrising stochastic models of infection dynamics, which will provide an ideal basis for addressing key research questions in this area; several such questions will be introduced and explored in this course.

Course content:


Contact hours

28 hours spread over the four weeks, with consultation as required.


Prerequisites

Ideally, some previous study of the qualitative analysis of ordinary differential equations models, a second (or even better third) year course in probability & statistics, and some prior experience of programming (ideally in MATLAB).

Background reading prior to the summer school is:

As examples will be provided in MATLAB (this is because it is a relatively easy to use language which is ideally suited to dealing with matrices which form the basis of the models we will be considering), students wishing to take this course, who have no prior programming experience, should attempt to learn the basics of MATLAB prior to the summer school; Googling "Introduction to MATLAB" should provide several good sources.


Assessment

Three assignments worth 15% each, and a 3-hour exam worth 55%. Example exam questions.


Resources

Lecture notes are available for download. These will also be provided in hardcopy. Additional readings, including relevant journal articles, will be provided during the course.

There are no specific texts required for this course, though students are expected to supplement the lecture material with additional reading. Some relevant texts are:

  1. Daley and Gani, Epidemic modelling: an introduction, Cambridge University Press, 2001.
  2. Grimmett and Stirzaker, Probability and random processes,, Oxford University Press, 2001.
  3. Keeling and Rohani, Modeling infectious diseases in humans and animals, Princeton University Press, 2008.
  4. Gilks, Richardson and Spiegelhalter, Markov Chain Monte Carlo in practice, Chapman and Hall/CRC, 1996.
  5. Kreyszig, Advanced engineering mathematics, multiple years.

A formula sheet is now available for download.


Code

The course does have a substantial component of implementing theory computationally. If students do have a laptop, then they should check with their home institution about installing MATLAB on it, or download and install the free Scilab software.

Prac 1:

Prac 2:

Prac 3:

Lecture 21:


About Joshua Ross

Joshua Ross is a lecturer in applied mathematics at the University of Adelaide. Before coming to Adelaide he was a Zukerman research fellow in mathematical and economic epidemiology at King's College, University of Cambridge. Joshua was awarded a PhD in mathematics from the University of Queensland in 2007 following research in the area of stochastic modelling of ecological systems under the advice of Professor Phil Pollett and Professor Hugh Possingham. He then spent a year at the University of Warwick working with Professor Matt Keeling on developing methods for studying stochastic models of infectious disease dynamics before taking up his fellowship at Cambridge, where he continued research in mathematical and statistical methods for biological systems. You can read more on his webpage.

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