What is a Model?

• A model is a construct invented as an aid to understand the system under study. A model is a formal statement of:
  
  
  • assumptions
    
    
  • conceptualizations
    
    
  • experimental design
    
    
• A mathematical model is a model which can be described by a set of mathematical equations.
  

The word "model" means different things to different people. Hence, we must define what we mean by a model. According to our definition, a model is a formal statement of assumptions about how the system functions, conceptualizations about how parts of the system are interconnected, and experimental design. The last statement means that, while you may know a great deal about the system you are studying, your experimental design may not permit you to resolve all of the fine detail you know are present, and hence a data-driven model may be an oversimplification of the truth (but useful anyway).

Everyone models! The modeling process provides a means by which each of us can categorize what we know about the system in a rational way. Our models may be different, but we cannot think in detail about a system without having some (qualitative, perhaps) picture in our mind of how it works.

The difference between a model and a mathematical model is that the mathematical model is described by a set of mathematical equations. You can think of this as taking your model, as defined above, and "gluing" it together using the language of mathematics. The trick is in dealing with the vagaries of biology and the precision of mathematics at the same time!