Epidemics

Statistical and mathematical models are important tools for analyzing the spread of infectious diseases. This article begins with some historical remarks on the application of mathematical methods in infectious disease epidemiology. Subsequently, types of data occurring in infectious disease epidemiology are discussed, methodological concepts like the basic reproduction number are introduced, and important applications of mathematical modeling for assessing the effectiveness of interventions are presented. An important example for the latter is vaccination, where statistical analysis of serological and surveillance data are used to evaluate the impact of vaccination on immune status of a population and transmission dynamic models are used for estimating long-term effects on prevalence. Particular attention is then paid to analysis of HIV/AIDS, as the changing epidemiology of this infectious disease and the increasing availability of treatment options have inspired the development of many new methods in the field of statistics and modeling since the onset of the epidemic.