Does a mathematical modelling on Christofides algorithm exist, is it even possible to create one?
The mathematical model relevant for understanding Christofides' algorithm is not the algorithm itself but rather the problem it is trying to solving – the traveling salesman problem. This is a model for optimization problems which occur in practice.
Christofides' algorithm itself could also perhaps be considered a model, if it is supposed to represent the way that humans (or animals, or nature) solve the traveling salesman problem. But in fact, it doesn't – it was designed as an efficient algorithm for computers.