Mathematical models provide a description of a system using mathematical concepts and language. Models explain how a system operates and predicts its behaviour with changing parameters and assumptions .
Mathematical models answer questions. In particular those relevant to ‘ What if‘ scenarios.
Models can describe:
- How a business performs using different operating frameworks.
- How finances change with different assumptions.
- How a pandemic affects a population.
When building a model you need to establish what questions need answering. Unless you have specific questions what is the point?
A mathematical model is only as good as its data and the assumptions used. With poor, incomplete or irrelevant data the validity of a model is questionable.
A model builder must not fall into the trap of wanting to support a predefined answer. A biased model includes data or facts that might support a particular conclusion and excludes data and facts that are non supportive. The phrase"Lies, damned lies, and statistics" describes how numbers can be manipulated to support an otherwise weak argument. Manipulating a model to force it to give that answer you want rather than an accurate answer leads to erroneous decisions.
A good model is only a reflection of reality. It is unlikely to include all things that impact it. Validation of the model occurs against the real world observations. Refinement ,where contradictory observations exist, is a reiterative process.
In the case of a pandemic possible questions could be:
- What would be the impact of doing nothing?
- Which scenarios result in the medical system collapsing?
- How long before we can ease up on restrictions?
- What if we relax restrictions too early?
- What if we move from suppression to elimination?
- What if no vaccine is developed?
- What if no immunisation is acquired after infection?
Models are valuable tools in the the decision making process.