Mathematical Modeling: Proposal of a General Methodology and Application of This Methodology to Epidemiology

We propose a general methodology allowing modeling the natural phenomena mathematically. After having to clarify the concepts and to propose a classification of the models according to their functions of description, prediction and comprehension, we give a definition of the mathematical model which integrates prediction and comprehension. Thereafter, we propose with details the great stages of mathematical modeling. An application of methodology suggested is made in a general way in epidemiology. Finally we proceed in example to the modeling and mathematical analyis of influenza epidemic in a heterogeneous environment taking account the mobility of the individuals.