# MATHEMATICAL MODELS

In the previous chapters, we have illustrated the importance and applicability of several of the mathematical concepts and methods introduced in this book by studying some mathematical models, in some cases briefly, and in some other cases, in great detail. Those applications and mathematical models include composite Bezier curves and postscript fonts, Google's PageRank, information retrieval, image compression, and predator–prey models with harvesting.

In this chapter, we introduce three mathematical models to further illustrate the process and importance of mathematical modeling to solve concrete problems. The first and second models, although quite different, fall within the area of optimization, the third model deals with an infection disease as a dynamical system, and finally on our last model, we consider a generalization of two interacting species models, where the interspecific relationships can change from mutualism to competition to host-parasite as certain parameters change.

Figure 8.1 Classic waste water management.

## 8.1 OPTIMIZATION OF A WASTE MANAGEMENT SYSTEM

In every city, region, or country of the world, authorities always pay great attention to dealing with waste water problem. They look for optimal ways of collecting and transporting waste water into purification plants in order to avoid the polluted water flowing into the rivers, ...

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