Mathematical Model Building with an Application to Determine the Distribution of Dursban® Insecticide added to a Simulated Ecosystem

Publisher Summary This chapter presents a procedure for building a mechanistic model which represents an experimental reaction system. Starting with one or more plausible models, the principle of maximum likelihood is applied to the data collected in order to estimate the constants in the model and choose the best model among those originally postulated. Then, conventional statistical techniques are used to determine the suitability of this “best” model. If the model is inadequate, a technique is presented for identifying the specific limitations. Then the model builder must postulate additional physical meaningful models to accommodate this limitation and the procedure are repeated. The model building procedure is developed from elementary statistical principles. The important concept of maximum likelihood is introduced and illustrated with an example. The need for proper experimental design and an iterative experimentation-analysis program is presented with examples. The chapter illustrates the model building procedure by finding a model which describes the fate and distribution of Dursban ® insecticide added to a laboratory system which simulates pond of water.