Lecturer: Louise Dyson

Term(s): Term 2

Status for Mathematics students: List C

Commitment: 20 lectures, 10 lecturer-led classes and 9 TA-led classes

Assessment: 100% assessed through coursework

Formal registration prerequisites: None

Assumed knowledge:

• Knowledge of general behaviour/steady states of ODEs. To revise or check your background knowledge on ODEs we recommend reading the following textbook which is available online through Warwick’s library: An Introduction to Ordinary Differential Equations (James Robinson)”
• Basic programming skills (ODE solvers, functions, for/if/while loops, plotting, vectors and matrices)
• The module is taught in R but the first 2 weeks is aimed at getting everyone to a basic level either by refreshing their knowledge or by learning R given prior programming experience in another language
• Basic knowledge of key probability distributions and their properties (including gamma, Erlang, Poisson, binomial, beta, uniform, exponential, normal).

Useful background: There are no strict prerequisites, but other modules that could provide a useful background include those on modelling such as:

• MA254 Theory of ODEs
• MA256 Introduction to Systems Biology
• ST202 Stochastic Processes
• MA390 Topics in Mathematical Biology
• MA3J4 Mathematical Modelling with PDE

For programming:

• MA124 Maths by Computer
• MA117 Programming for Scientists
• MA261 Differential Equations: Modelling and Numerics 

Synergies: The following module goes well together with Epidemiology by Example:

• MA4E7 Population Dynamics - this is a complementary course which is recommended to be taken before or simultaneously with Epidemiology by Example. Population Dynamics provides a lot more detail on development of different ecological and epidemiological models and their behaviour (especially qualitative) and is assessed 100% through exam. Epidemiology by Example focuses on programming to tackle a series of real-world-inspired epidemiological problems, bringing in components like model fitting and health economics, which would not be able to be assessed through traditional written examination.

Content: Epidemiology by Example was a new module in 2020/21 which focuses on the application of numerical methods to address real-world problems in infectious diseases. Starting with programming for basic infectious disease models, the module will progress on to implementation of stochastic models, fitting models to real-world data, adaptive management of diseases and health economic analyses for decision making. The module is designed to give an overview of key methods currently used in epidemiology research and will be 100% assessed through coursework.

Programming language: R

Aims: Students taking this module will acquire hands-on experience of manipulating mathematical models, implementing appropriate numerical methods and fitting models to data, all of which are essential components of
modern-day modelling for research or industry. By the end of the module, students will have encountered a range of model types which can describe a broad range of important infection systems such as influenza, malaria, measles and soil transmitted helminths. Students will understand how to perform predictive analyses which could inform policy decision making - such as assessing future control interventions including adaptive strategies and health economic analyses.

Objectives:

By the end of the module the student will be able to:

• Adapt or create infection models within R and perform simulations
• Perform fitting to data using both frequentist and Bayesian approaches
• Implement and explain deterministic and stochastic modelling approaches and their situational appropriateness
• Demonstrate how modelling predictions can be performed and contrast future interventions including adaptive strategies
• Utilise basic health economic concepts (disability-adjusted life years, willingness to pay, etc.) and methodology
  communicate modelling outcomes in a clear and informative manner
• Appraise the suitability of different models and their predictions for real-world decision making
  evaluate the role of assumptions in influencing model outcomes

Outline of the module:

This 10-week programme will be partitioned into five, 2-week topics:

• Simple infectious disease model dynamics simulation and prediction
• Deterministic vs stochastic modelling approaches (endemic vs outbreak or elimination)
• Modelling fitting to data (frequentist and Bayesian methods)
• Health economics for dynamic models and decision making
• Adaptive management for improved intervention efficacy

There will be 2 formal lectures per week plus 1 structured, lecturer-lead lab session plus 1 support lab.

Coursework: Assessment will take the format of five worksheets to be submitted in weeks 3, 5, 7, 9 and 11. Weighting is 20% for each sheet. Marks will be returned in weeks 4, 6, 8, 10 and during the Easter break so feedback is received before submitting the next worksheet. Submitted documents will be a mixture of LaTeXed solutions and R code.

Suggested reading:

General: M.J. Keeling and P. Rohani, Modelling Infectious Diseases in Humans and Animals, Princeton University Press, 2007 (ISBN 0691116172)

Health Economics: Briggs, Claxton and Sculpher, Decision Modelling for Health Economic Evaluation (2006) (available in print through Warwick library)

Epidemiology Programming in R: Bjørnstad, Ottar N, Epidemics: models and data using R, Use R!, 2018 (Online at Warwick library)

Topic-specific research articles will be suggested as reading during the courseE

Additional Resources