A mathematical model is an abstract model that uses mathematical language to describe the behavior of a system.
Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology and electrical engineering) but also in sobial sciences (such as economics, sociology and political sciences (such as economics, sociology and political science); physicists, engineers, computer scientists and economists use mathematical models most extensively.
Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing systems (or a system to be constructed ) which presents knowledge of that systems 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.
Since there can be many variables of each type, the variables are generally represented by vectors.
Mathematical modeling problems are often classified into black box or white box models, according to how much priori information is available of the system.
A black-box model is a system of which there is no a priori information available.
A white-box model (also called glass box or clear box) is a system where all necessary information is available.
Practically all systems are somewhere between the black-box and white-box models, so this concept only works as an intuitive guide for approach .
Usually it is preferable as much priori information as possible to make the model more appropriate.