Epidemics: Modelling with mathematics

Measles is back in the UK.  In many countries, it has never gone away.

With a cheap, effective vaccine available since the 1960s, we might have hoped that it would be totally eliminated by now.  But between January and mid-April 2011, there were more than 6,500 cases of measles in 33 countries (figures from the World Health Organisation).

Mathematicians use mathematical models to make predictions about epidemics.  Government health departments and hospitals use these to ensure they have the resources they need to deal with epidemics - so this is vitally important maths.

But how does it work?  How do mathematicians develop these models?  In the video clips in this pack, Dr Julia Gog and Dr Andrew Conlan, of the University of Cambridge, explain using a variety of simple models.  The accompanying activities will help students to understand what a mathematical model is, and how we can build up increasingly complex models from the simplest of starting points.  They will also be better equipped to understand why vaccination is important in preventing the spread of epidemics.

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The resources in this pack complement the video clips, providing activities designed to help students understand how the maths they are taught in school can help them to become better informed about such issues.  Answers and additional notes are also provided.

The video clips and easier follow-up resources labelled * can be used with most 12-14 year-old secondary students.  Those labelled *** may be more suitable for older students preparing for public exams, such as GCSE or equivalent, at higher levels.

Any of these resources can be used alone - although students will find it easier to understand them if they have seen the preceding video clip(s). 

• Download all videos (zip file, 67MB)
• Download all pdf files

Type of Resource	Resource Name	Difficulty	Notes
	Teacher notes and worksheet answers		Start here!
	Modelling with Mathematics: Introduction	*	Introductory video clip (3 min 2 secs) - Dr Julia Gog
	Standing Disease	*	Activity: The simplest of models - what does it tell us that's helpful, how could it be improved?
	Counter Plague	*	Activity: Developing the model - how is this model better, how could it be improved?
	Counter Plague: demonstration	*	Video clip (3 min 47 secs) - you could omit this if the activity instructions are clear without it, or use it as a teacher resource.
	Models of Epidemics	**	Video clip (3 mins 10 secs) - Dr Julia Gog
	Graphs of epidemics	**	The graphs Julia Gog talks about in Models of Epidemics, plus questions for class discussion.
	Refining the Models	***	Video clip (4 mins 30 secs) - Dr Andrew Conlan
	26-Card Disease	**	Activity: Refining the model to take account of immunity (natural or induced through vaccination)
	26-Card Disease	**	Video clip (7 mins 37 secs) - you could omit this if the activity instructions are clear without it, or use it as a teacher resource.
	Why do epidemics terminate?	***	Video clip (2 mins 42  secs) - Dr Julia Gog
	Understanding Counter Plague	***	Presentation: screenshots from e-Counter Plague to help students interpret the model, and to understand what we might expect to happen, given particular dice settings.  Students should have tried the activity Counter Plague first.
	e-Counter Plague	***	Activity: a set of 4 online simulations to help investigate variations on Counter Plague.  Students should have tried the activity Counter Plague first.  It would also be helpful if they worked through the presentation, Understanding Counter Plague, as preparation for investigating these animations.