A Survey on Mathematical Modeling of Cancer Incidence Rates

Abstract

ABSTRACT: Bioinformatics is a novel interdisciplinary field which attempts to response the biological questions by the assist of other basic sciences as well as computer sciences. Cancer modeling is a real example of such these endeavors in order to help oncologists to find new ways to cure and prevent cancer diseases or predict, estimate, and analyze this hazard in order to step forward to a better future. In this arena mathematics and statistics have played great roles and enabled biology, oncology, and epidemiology to achieve new results by applying some mathematical and statistical methods such as various graphs and tools to compare the different criteria, curve fitting as well as analyzing and predicting the future data, time series and Markov processes to model the natural phenomena and study their behaviors. However this field is still like a young sapling which requires enough patience and care of scientists to bring forth. This thesis is mainly to make a survey generally on bioinformatics and specifically investigations on cancer cases as an application. First chapter provides a general overview about bioinformatics and its application. Then some preliminary concepts are explained including required biological information about cancer and its causes to comprehend the next concepts and implications better. Many scientists have tried to offer an applicable model for cancer incidence rate which can be acceptable and interpretable biologically. Second chapter provides some past findings about cancer incidence models as a background for readers with little biological information. In fact, the focus of this research is mainly on mathematical modeling of cancer incidence rates. In addition, chapter three is discussing about the cancer incidence. For instance some factors affecting on the process of cancer incidence such as the place and time period of living, sex, race, and the amount of development are checked. In chapter four some curve fittings are performed by MATLAB software, and also special mathematical model which is called Furrier model has been fitted to the real cancer incidence rates data with the best goodness of fit. Keywords: bioinformaics, biomathematics, cancer, incidence rate, mathematical modeling, curve fitting, Furrier model. ……………………………………………………………………………………………………………………………………………………………………………………………………………………

ÖZ: Biyoenfoformatik, son zamanlarda gelişen çoklu disiplinlerin içinde barındırıldığı bir başlıktır. Biyolojik veri tabanları üzerindeki bilgilerin incelenmesi ve onlar üzerinde kararların verilmesi oldukça önemli bir aşamayı içermektedir. Günümüzün en önemli sağlık vakalarından birisi durumundaki kanser olaylarının incelenmesi ve modellenmesi bu araştırma sahasının en önemli uygulamalarından biridir. Bu tez, biyoenformatik konusunda temel tanımlamaların daha önce yapılmış çalışmaların özetlendiği ve örnek olarak kanser vakalarıyla ilgili verilerin MATLAB paketi yardımıyla modellenmesini içeren bir çalışmadır. Anahtar kelimeler: biyoenformatik, biyomatematik, kanser, kanser vaka hızı, matematiksel modelleme, Fourier modeli.