Mathematical Modelling Techniques

Models are concepts of reality

Mathematical Modelling is the mathematical technique of getting concepts mathematical which you only have a qualitative representation of linguistic description, a video recording, or any other possibility and striving a quantitative description where one should test against measurements of the phenomenon.

Mathematical treatment is essential if the dynamics of ecosystems are to be examined and predicted quantitatively. The approach is actually the same as that used in such fields as established in quantum mechanics, molecular biology and biophysics... One must not be fascinated by mathematical models; there is no character affiliated with them... physics and mathematics must be regarded as tools rather than references of knowledge, tools that are powerful, but nevertheless dangerous if misused.

Describe

Describe the real-world problem. Identify and understand the practical aspects of the situation.

Specify

Specify the mathematical problem. Frame the real-world scenario as an appropriate, related mathematical question(s).

Formulate

Formulate the mathematical model. Make simplifying assumptions, choose variables, estimate magnitudes of inputs, justify decisions made.

Solve

Solve the mathematics using software to get the solution.

Interpret

Interpret the solution. Consider mathematical results in terms of their real-world meanings.

Evaluate

Evaluate the model. Make a judgment as to the adequacy of the solution to the original question(s). Modify the model as necessary

Report and interpret

Report and interpret the solution of the mathematical model.

Communicate

Communicate clearly and fully your suggestions to address the real-world problem.

Different Models used for Mathematical Modelling

Deterministic vs. Stochastic models

Deterministic models have no components that are inherently uncertain, i.e., no parameters in the model are characterized by probability distributions, as opposed to

Qualitative vs. Quantitative Models

Qualitative models lead to a detailed, numerical prediction about responses, whereas qualitative models lead to general descriptions about the responses

Static vs. Dynamic Models

Static models are at an equilibrium or steady state, as opposed to dynamic models which change with respect to time.