Mathematical and Computational Methods in Biology and Finance : With numerical applications to Graph Theory

The topic of this book is the mathematical analysis of biological and financial systems. Firstly we develop some methods for analyzing the data that are furnished into matrix form. In particular we analyze the adjacency matrix of some well-known networks in the pertinent literature. We perform a general matrix analysis with the main aim to study the possible linear relantionship between the eigenvector associated with the highest eigenvalue (principal eigenvector) and the degree vector. We furnish some theoretical results that establish when the linear relation between the principal eigenvector and the degree vector is possible. Secondly this book is concerned with the simulation of biological systems viewed as solution of differential models. Specifically the analysis of a delayed ODE-based model for wound healing disease under the action of the immune system, is performed, and the conditions under which a Hopf bifurcation occurs are investigated. Moreover by employing the thermostatted kinetic theory, a model for the development of therapies against keloid is considered.