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Topic 1: Key components of mathematical models

Now that you know more about how modeling is used in public health, you might be wondering what goes into models to produce the results.

Mathematical models describe the relationship between inputs and outputs in mathematical terms. They use data and assumptions to make projections about the future and to answer specific questions.

Click on the plus signs below to learn about the key components of mathematical models.

Input: data and assumptions used in the model

Data: concrete information inputted into a model. Examples include cost, population size or characteristics of how disease spreads.

Assumption: a modeler’s best guess at data that is unknown but required to construct a model. Can be expressed as a number or a relationship between elements of the model.

Output: the findings and results from the model. Outputs from the model can be anything from projections about the future to answers to the research questions the modelers were originally asking.

Mathematical models can be simple or complex. The degree of complexity required in a model depends on the research question. With greater complexity, models are increasingly flexible, but they:

  • Are more difficult to analyze
  • Are more difficult to validate
  • Require much more data
  • Have greater uncertainty

The best practice is to start simple, and gradually add complexity, but only if it also adds insight.

Let's look at an example of a simple mathematical model:

If we want to create a mathematical model for population growth in 2021, we might consider a model that looks at the population in 2019 + births in 2020.  This is a very simple model that we can compare to reality in 2021.

How could we make this simple mathematical model more complex?

We can add complexity to this simple model by incorporating things like:

Deaths in 2020

Fertility Rates