The Stages Involved in The Formulation of a Mathematical Model

1)

In your own words, define a mathematical model. Describe the stages involved in the formulation of mathematical models.

Mathematical modelling is when a person or group uses past data and mathematical methods to predict or model future events or behaviour. This simply means that somebody looks at what has happened previously, does some maths and is then able to work out what might happen in the future.

In order to create a mathematical model there are a number of steps that need to be taken: Description of the problem.

Assumptions.

Mathematical formulation of problem.

Solution of mathematical formulation

Interpretations of mathematical solution. At this point there are two options depending on whether the model works:

A)

If it is a satisfactory mathematical model, then:

Ability to make further predictions.

OR B)

If it is not a satisfactory mathematical model, then:

Revision of model.

To create a working mathematical model you would begin by working out what the problem or issue you are trying to predict or solve is. When doing this you would describe the system and work out any variables that might be needed. You must then simplify the model by making assumptions about what changes might affect the overall outcome. This step means your first solution is much simpler than real life is and you would then make the model more complicated as needed.

Next you would create mathematical equations that link to what you are trying to solve. If you are looking at the rate of change in more than one variable you will end up with some differential equations that need to be derived.

Once you have created your equations you then need to solve them. Nowadays equations are becoming so complex that it will often take vast and powerful super com...

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...f increase is dependant on the number of infected swans, if there are more infected swans there will be a greater number of animals spreading the disease. Likewise if there are more uninfected swans that are susceptible there is a greater chance of an infected swan coming across a susceptible swan and infecting it.

b)

Write down a differential equation for the rates of increase of infections with time.

State what I know: s = total number of swans = 1000

I(t) = Infected swans

N(t) = Non-infected swans t = time s = I(t) + N(t)

N(t) = 1000 – I(t)

Create an equation for that:

Substitute in what I know:

Rearrange it:

Hence:

And then I was stuck.

Bibliography:

[1]: http://en.wikipedia.org/wiki/Epidemic_model

[2]: http://www.samsi.info/sites/default/files/SAMSI_math_infectious_disease.pdf

Images:

[1]: http://plus.maths.org/content/mathematics-diseases