A Comparative Analysis on the Mathematical Models of Pertussis and Measles

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The motivation of the study is based on the problems that arise from the mathe- matical model of Pertussis and Measles. The purpose is to depict the differences that occur in variations of mathematical systems. This is done by analyzing and interpreting this model, as well as a simpler model, and then comparing the solutions for the two. From the analysis, an insight to the theoretical and math- ematical description of spread and contamination patterns has been obtained. The two models are then compared to each other. The intention is to reveal the consequence of expanding upon a compartment model, and thus the system of di erential equations. The two models display a di erent level of detail which is re ected in the associated analysis. The simple model is a Measles model, and the pertussis model has the higher degree of detail. The analytic methods applied when describing the systems of differential equations appear to have a limited use in the expanded system. This leads to mathematical complications.
A Thesis submitted to the Institute of Distance Learning, Kwame Nkrumah University of Science and Technology in partial ful llment of the requirements for the degree of Master of Science, July-2013