# Modeling Disease

'Modeling Disease saves lives - How and Why?'

Advantages of the activity: A very engaging context, accessible to all, which provides a physical world "memory" aid and conceptual context within which the study of patterns in number and their associated functions can be understood.

Medics follow the spread of diseases to stay informed on the potential threat of each to human populations. Watch the below four videos (click on the icon (bottom right) to enlarge and press "esc" to return to this page) on different diseases and rank them in order of which you think will spread the fastest to which will spread the slowest.

See the slide show/printout in the resources section below, can you match each disease to the number of human victims each week? To their graphs?

### Resources

Anything that can be measured can be modeled using a function and these functions, in turn, used to predict the future.

•  Having completed the matching activity try the "extension challenge" that follows. Alternatively, or after the extension challenge, you could try this activity Sequences - difference method.

Extension challenge: See if you can find the function for each of the sequences in the matching activity. Then plot the graph of each function (see the Help section below for video guidance on using graphing software to model functions) on the same axes to compare how quickly each disease will spread. Do your graphs confirm the policy decisions you took in the main part of the activity?

Here are some examples of the international measures implemented for the control of avian flu in 2006. Some diseases may need urgent attention to avoid an epidemic (or even pandemic!). The following example is from Japan (click on the "eye" icon) demonstrating the use of mathematics to model and analyse the spread of disease (you may want to mute/turn off the sound):

### Geogebra graphing help

You can watch the screencast on the following page if you need help with how to enter variable coefficients in Geogebra: Modelling Quadratics (Desmos is similar).

### Autograph graphing help

You can watch the screencast on the following page if you need help with how to enter variable coefficients in Autograph: Quadratic Movers.

The TiNspire and most other graphing software will be similar to one of these two approaches. Alternatively, students can try the Sequences - difference method activity before the extension challenge and then use the techniques learned to find a function for each of the "disease" sequences OR, they could try the "differences method" after the extension challenge as an alternative to finding functions using regression/transformation of graphs knowledge.

### Description

This resource is designed to provide students with a powerful example of the direct impact of sequences and function Mathematics on government policy and decisions which impact directly on their lives/well being.

• Students can work directly on the Powerpoint, matching a sequence with a disease and graph and writing a paragraph or so to explain their reasoning (e.g. on a class google doc or on large sheets of A3 stuck around the walls/A3 whiteboards for all to read) OR they can work with the printed version in groups OR a mixture of both within the one class, depending on computer availability and student preferences!
• The discussion following the matching activity is key. The aim of the resource is for students to develop an intuitive feel for how quickly linear (with different coefficients), quadratic and cubic sequences progress.
• Extension challenge: Once students have completed the They can use a graphing package e.g. Geogebra, Autograph, Desmos, TiNspire, LoggerPro, Graphing Calculators etc. to plot each function on the same axes for quick comparison (see Help section for videos on using Geogebra, Autograph etc). Alternatively, the teacher can allow them to use the graphing software's regression tools to find the function for students. This helps "scaffold" students who struggle to understand the differences (or other) analytical method, to gain an appreciation of which functions apply to which sequences.
• This activity provides a good opportunity for the final outcome to be a group presentation, or classroom display, of students' work. It also offers interesting cross-subject lesson/project opportunities.
• Having completed the above tasks the aim is that students now have some intuitive sense for what a linear, quadratic and cubic sequence look like and how they evolve.

Want more resources on this topic? Try Physical World Sequences.

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