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.