Mathematical models determine how the system changes from one state to the next and describe the interdependence of the variables (or factors) involved. In contrast, statistical analyses characterise numerical data and attempt at estimating probabilistic future behaviour of a system based on its past behaviour. Mathematical models are generally exact and given by equations, whereas statistical models are generally given by data and the probability of the dataset matching the statistical assumptions. Some goals may be shared between the two approaches, but the key difference between mathematical models and statistical models lies in their underlying assumptions and objectives. Mathematical models are based on established principles, laws, and theories of the physical world. They aim to describe and predict the behaviour of a system using mathematical equations and relationships. These models typically involve variables, parameters, and deterministic functions that capture the underlying mechanics and dynamics of the system. The goal of a mathematical model is to provide a comprehensive, theoretically grounded representation of the system.