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.
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:
If it is a satisfactory mathematical model, then:
Ability to make further predictions.
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 computers some time to solve some of the equations.
The data that then comes out after you have solved your equations will need to be studied and possibly plotted into graphs to make for easier analysis. The predictions you have then produced will also need to be analysed by one of two methods:
1) A reality check, do the predictions you have created break reality or seem absurd?
2) Watching to see if your predictions become reality, If they do you will know your model works for this event.
If your predictions seem wild or do not happen you will then need to go back and change your model. This may include changing aspects or going back to when it last worked and trying again. You may also decide to make your model even simpler just so it will work and you can then go back and make it more complicated.
If your model works fine and seems realistic you could use the model to create more predictions or instead go back and see if there are any ways to make the model more complicated and more realistic.
Some examples of mathematical modelling of infectious diseases going on today include:
• Hepatitis C
• HIV and many other STI’s
Describe an SIR model as related to infectious diseases. In your own words, explain...