A brief definition of what a mathematical model

A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termedmathematical modelling(also modeling). Mathematical models are used not only in the natural sciences (such as physics, biology, earth,metereology) and engineering disciplines, but also in the social sciences (such as economics, psycology ,sociology and political science); physicists engineers,computer scientists, and economist use mathematical models most extensively.

Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form.

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models,differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.