Erect means build or upright. If you erect a house, you build it. If you stand erect, you hold your body as tall as possible.
A mathematical model is a description of a system using mathematical concepts and language.The process of building a mathematical model is termed mathematical modeling.Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence). mathematical model is a description of a system using mathematical concepts and language.
2. (Mathematics) (functioning as singular or plural) mathematical operations and processes involved in the solution of a problem or study of some scientific field. [C14: mathematik (n), via Latin from Greek (adj), from mathÄma a science, mathÄmatikos (adj); related to manthanein to learn]