- **Model derivation stage:** We have discussed before what we mean with a mathematical model. The process of deriving involve identifying suitable variables and relating them, which requires a good understanding of the system’s behaviour and properties. There is a purpose behind the efforts related to some questions on the system, and outcome is a mathematical problem. - **Solution stage:** This is the application are for mathematics. Modellers usually have certain solution techniques in mind when using certain methods to describe systems and relate the variables. However, some problems might be tricky to crack and require sophisticated tools or even further development of mathematical methods, thus motivating mathematical research. - **Validation stage**: Once we have obtained the solution to the problem and, possibly, further post-processed any results to draw further conclusions, we need to check whether the outcome meets the expectations and answers what we wanted to learn. This implies the assumption that we can do so. In fact, the generation of experimentally testable predictions is a hallmark of good mathematical modelling attempts. Testing against observations can be of qualitative nature, by which we mean that typical features and properties of the phenomenon are reproduced by the model. If detailed measurements and data are at hand then the model can be quantitatively validated by comparison with the values produced by solving the associated mathematical problem.