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10 Oct 2022

# Real World Examples Of Mathematical Modelling

Mathematics

Maths is one of the most versatile subjects. Applied in the right ways, mathematical modelling can be life-saving. Its developments have benefitted healthcare, policy-making and economics. This, in turn, is helping to make a more equitable and fair world. Yet, maths can be damaging, so understanding how it works is incredibly useful.

### What is a mathematical model?

A model is a simplification of a real-world situation. Mathematicians make assumptions about a situation, to produce a version which is more manageable to work with. Often, they start with an oversimplification and produce a system of equations to describe it. Then they introduce more complexity to the model. They build up the complexity until they are satisfied that the model accurately represents the situation. How accurate this needs to be, depends on why we use the model.

Recently, mathematical models have been key to managing the pandemic. Check out this video on modelling the spread of viruses, it has amazing visuals! >>

### Modelling power supply in South Africa

Researchers have used a mathematical model to produce advice. This advises the South African national power supplier, Eskom, on their energy tariffs.

When energy tariffs go up, wealthy households and businesses invest in alternative energy sources. By using alternative energy sources, such as solar power, they can produce their own electricity. So, the supplier receives less revenue, which would otherwise be used to subsidise the energy bills of the poorest households. This effect was proven using a mathematical model, demonstrating how mathematical modelling can be used in policy-making.

### How is mathematical modelling used to produce accurate weather forecasts?

1:  Apply the laws of physics

2: Next, put these laws into differential equations (super complicated differential equations!)

3: Get accurate data from weather stations and use this data as ‘initial conditions

4: Use a supercomputer to solve the differential equations to provide tomorrow’s weather

5: Convert this data into an understandable form

Mathematics
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