"e. A simplified or idealized description or conception of a particular system, situation, or process (often in mathematical terms: so mathematical model) that is put forward as a basis for calculations, predictions, or further investigation."
Oxford English Dictionary

mathematical model
"either a physical representation of mathematical concepts or a mathematical representation of reality. Physical mathematical models include reproductions of plane and solid geometric figures made of cardboard, wood, plastic, or other substances; models of conic sections, curves in space, or three-dimensional surfaces of various kinds made of wire, plaster, or thread strung from frames; and models of surfaces of higher order that make it possible to visualize abstract mathematical concepts."
Encyclopędia Britannica

Model Types:

Reasons to Model: Features of a Good Model: Three approaches to mathematical modelling Another taxonomy of models: