Focusing on the mathematical foundations of outbreak dynamics and control, this book offers a comprehensive analysis that balances theory with practical applications. It introduces a unified framework related to the distribution theory of non-negative random variables, enhanced by contemporary topics in infectious disease modeling. Numerous examples throughout the text illustrate theoretical concepts, providing readers with a deeper understanding of the subject matter.
Contributions from epidemic modeling experts detail the creation of mathematical models and statistical forecasts to capture key aspects of emerging epidemics. Readers will explore various approaches to critical questions, such as the effectiveness of ring vaccination strategies for controlling Ebola, the speed required for case detection to manage outbreaks, and the potential for secondary outbreaks from West Africa. The text examines when to factor in disease-induced mortality in models and the influence of behavioral changes on Ebola dynamics. It also discusses optimal control theory for better understanding cholera and Ebola management, how to structure populations to reflect disease transmission dynamics, and methods for objectively determining the end of an epidemic. Additionally, the use of metapopulation models to analyze the impact of movement restrictions and migration patterns on disease spread is covered, as well as the role of household transmission in compartmental models. The effects of behavior-dependent vaccination on epidemic dynamics are also addressed. The derivation and analysis of these mathematical models provide a comprehensive overview of innovative methods for forecasting and mitigating emerging epidemics, appealing to researchers in mathematical epidemiology and public health professionals.
