Mathematical modeling is an important device to analyze and control the spread of infectious diseases increase in a society. In these models there are parameters and other variables of the problem. Mathematical models have important tools in analyzing the spread and control of infectious diseases. The model formulation process clarifies assumptions, variables, and parameters; moreover, models provide conceptual results such as thresholds, basic reproduction numbers, contact numbers and replacement numbers. This book shows the applications of mathematical modeling in epidemic disease. By using mathematical modeling we can analyze and control the spread of infectious diseases increase in a society. One of the fundamental questions of mathematical epidemiology is to nd threshold conditions that determine whether or not an infectious disease will spread in a susceptible population when the disease is introduced into the population. The threshold conditions are characterized by the so called reproductive number. In this book we derive an explicit formula for the reproductive number employing the spectral radius of the next generation operator."

Various types of methods have been developed for solving the special second order ODEs which is not explicitly dependent on the first derivative of the solution. The solution to the equation can be obtained by reducing it to an equivalent first order system of twice the dimension and solved using a standard numerical methods. However it is often advantageous to solve them directly. This book focused on the derivation of the block methods for solving the special second order ODEs directly. The early section of the book is devoted to the derivation of the methods using linear operator. Then the derivation of the method is done using Newton-Gregory backward interpolation formula. Numerical results of the methods are compared with the existing methods which shows that they are computationally more efficient. Block methods are suitable for parallel implementation, hence parallel codes of the methods are developed for solving large systems of ODEs. The performance of the methods using sequential and parallel codes are compared which clearly shows that the parallel codes produced better speedup and efficiency.