The Population Dynamics Of Infectious Diseases Theory And Applications

Since the beginning of this century there has been a growing interest in the study of the epidemiology and population dynamics of infectious disease agents. Mathematical and statistical methods have played an important role in the development of this field and a large, and sophisticated, literature exists which is concerned with the theory of epidemiological processes in popu lations and the dynamics of epidemie and endemie disease phenomena. Much ofthis literature is, however, rather formal and abstract in character, and the field has tended to become rather detached from its empirical base. Relatively little of the literature, for example, deals with the practical issues which are of major concern to public health workers. Encouragingly, in recent years there are signs of an increased awareness amongst theoreticians of the need to confront predictions with observed epidemiological trends, and to pay elose attention to the biological details of the interaction between host and disease agent. This trend has in part been stimulated by the early work of Ross and Macdonald, on the transmission dynamics of tropical parasitic infections, but a further impetus has been the recent advances made by ecologists in blending theory and observation in the study of plant and animal populations.

This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.

This book provides an introduction to the theory of ordinary differential equations and its applications to population dynamics. Part I focuses on linear systems. Beginning with some modeling background, it considers existence, uniqueness, stability of solution, positivity, and the Perron–Frobenius theorem and its consequences. Part II is devoted to nonlinear systems, with material on the semiflow property, positivity, the existence of invariant sub-regions, the Linearized Stability Principle, the Hartman–Grobman Theorem, and monotone semiflow. Part III opens up new perspectives for the understanding of infectious diseases by applying the theoretical results to COVID-19, combining data and epidemic models. Throughout the book the material is illustrated by numerical examples and their MATLAB codes are provided. Bridging an interdisciplinary gap, the book will be valuable to graduate and advanced undergraduate students studying mathematics and population dynamics.

The 1918-19 influenza epidemic killed more than fifty million people worldwide. The SARS epidemic of 2002-3, by comparison, killed fewer than a thousand. The success in containing the spread of SARS was due largely to the rapid global response of public health authorities, which was aided by insights resulting from mathematical models. Models enabled authorities to better understand how the disease spread and to assess the relative effectiveness of different control strategies. In this book, Lisa Sattenspiel and Alun Lloyd provide a comprehensive introduction to mathematical models in epidemiology and show how they can be used to predict and control the geographic spread of major infectious diseases. Key concepts in infectious disease modeling are explained, readers are guided from simple mathematical models to more complex ones, and the strengths and weaknesses of these models are explored. The book highlights the breadth of techniques available to modelers today, such as population-based and individual-based models, and covers specific applications as well. Sattenspiel and Lloyd examine the powerful mathematical models that health authorities have developed to understand the spatial distribution and geographic spread of influenza, measles, foot-and-mouth disease, and SARS. Analytic methods geographers use to study human infectious diseases and the dynamics of epidemics are also discussed. A must-read for students, researchers, and practitioners, no other book provides such an accessible introduction to this exciting and fast-evolving field.

This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.

The Second Autumn Course on Mathematical Ecology was held at the Intern ational Centre for Theoretical Physics in Trieste, Italy in November and December of 1986. During the four year period that had elapsed since the First Autumn Course on Mathematical Ecology, sufficient progress had been made in applied mathemat ical ecology to merit tilting the balance maintained between theoretical aspects and applications in the 1982 Course toward applications. The course format, while similar to that of the first Autumn Course on Mathematical Ecology, consequently focused upon applications of mathematical ecology. Current areas of application are almost as diverse as the spectrum covered by ecology. The topiys of this book reflect this diversity and were chosen because of perceived interest and utility to developing countries. Topical lectures began with foundational material mostly derived from Math ematical Ecology: An Introduction (a compilation of the lectures of the 1982 course published by Springer-Verlag in this series, Volume 17) and, when possible, progressed to the frontiers of research. In addition to the course lectures, workshops were arranged for small groups to supplement and enhance the learning experience. Other perspectives were provided through presentations by course participants and speakers at the associated Research Conference. Many of the research papers are in a companion volume, Mathematical Ecology: Proceedings Trieste 1986, published by World Scientific Press in 1988. This book is structured primarily by application area. Part II provides an introduction to mathematical and statistical applications in resource management.