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Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. The book fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. The book covers the latest research in mathematical modeling of infectious disease epidemiology; it integrates deterministic and stochastic approaches; and teaches skills in model construction, analysis, inference, and interpretation.

Despite decades of developments in immunization and drug therapy, tuberculosis remains one of the leading causes of human mortality, and no country has successfully eradicated the disease. Reenvisioning TB from the perspective of population biology, this book examines why the disease is so persistent and what must be done to fight it. Treating TB and its human hosts as dynamic, interacting populations, the book seeks new answers to key questions by drawing on demography, ecology, epidemiology, evolution, and population genetics. It uses simple mathematical models to investigate how cases and deaths could be reduced, and how interventions could lead to TB elimination. It reveals a striking gap between the actual and potential impact of current interventions, especially drug treatment, and suggests placing more emphasis on early case detection and the treatment of active or incipient TB. The book argues that the response to disappointingly slow rates of disease decline is not to abandon long-established principles of chemotherapy, but to implement them with greater vigor. Summarizing epidemiological insights from population biology, the book stresses the need to take a more inclusive view of the factors that affect disease, including characteristics of the pathogen, individuals and populations, health care systems, and physical and social environments. In broadening the horizons of TB research, the book demonstrates what must be done to prevent, control, and defeat this global threat in the twenty-first century.

When we think about viruses we tend to consider ones that afflict humans—such as those that cause influenza, HIV, and Ebola. Yet, vastly more viruses infect single-celled microbes. Diverse and abundant, microbes and the viruses that infect them are found in oceans, lakes, plants, soil, and animal-associated microbiomes. Taking a vital look at the “microscopic” mode of disease dynamics, this book establishes a theoretical foundation from which to model and predict the ecological and evolutionary dynamics that result from the interaction between viruses and their microbial hosts. The book addresses three major questions: What are viruses of microbes and what do they do to their hosts? How do interactions of a single virus–host pair affect the number and traits of hosts and virus populations? How do virus–host dynamics emerge in natural environments when interactions take place between many viruses and many hosts? Emphasizing how theory and models can provide answers, the book offers a cohesive framework for tackling new challenges in the study of viruses and microbes and how they are connected to ecological processes—from the laboratory to the Earth system. The book is an innovative exploration of the influence of viruses in our complex natural world.