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Mathematical Understanding of Infectious Disease Dynamics
An Original book with a comprehensive collection of many significant topics of the frontiers in applied presentation of many epidemic models with many real-life examples. presents an integration of interesting ideas from the well-mixed fields of statistics and mathematics. A valuable resource for researchers in wide range of disciplines to solve problems of practical interest.
Applied Mathematical Ecology
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. T...
Differential Equations and Applications in Ecology, Epidemics, and Population Problems
Differential Equations and Applications in Ecology, Epidemics, and Population Problems is composed of papers and abstracts presented at the 1981 research conference on Differential Equations and Applications to Ecology, Epidemics, and Population Problems held at Harvey Mudd College. The reported researches consist of mathematics that is either a direct outgrowth from questions in population biology and biomathematics, or applicable to such questions. The content of this volume are collected in four groups. The first group addresses aspects of population dynamics that involve the interaction between spatial and temporal effects. The second group covers other questions in population dynamics a...
Frontiers in Mathematical Biology
From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an...
Complex Population Dynamics
This collection of review articles is devoted to the modeling of ecological, epidemiological and evolutionary systems. Theoretical mathematical models are perhaps one of the most powerful approaches available for increasing our understanding of the complex population dynamics in these natural systems. Exciting new techniques are currently being developed to meet this challenge, such as generalized or structural modeling, adaptive dynamics or multiplicative processes. Many of these new techniques stem from the field of nonlinear dynamics and chaos theory, where even the simplest mathematical rule can generate a rich variety of dynamical behaviors that bear a strong analogy to biological populations.
Infectious Diseases of Humans
This book deals with infectious diseases -- viral, bacterial, protozoan and helminth -- in terms of the dynamics of their interaction with host populations. The book combines mathematical models with extensive use of epidemiological and other data. This analytic framework is highly useful for the evaluation of public health strategies aimed at controlling or eradicating particular infections. Such a framework is increasingly important in light of the widespread concern for primary health care programs aimed at such diseases as measles, malaria, river blindness, sleeping sickness, and schistosomiasis, and the advent of AIDS/HIV and other emerging viruses. Throughout the book, the mathematics ...
Mathematical Studies on Human Disease Dynamics
This volume contains the proceedings of the AMS-SIAM-IMS Joint Summer Research Conference on Modeling the Dynamics of Human Diseases: Emerging Paradigms and Challenges, held in Snowbird, Utah, July 17-21, 2005. The goal of the conference was to bring together leading and upcoming researchers to discuss the latest advances and challenges associated with the modeling of the dynamics of emerging and re-emerging diseases, and to explore various control strategies. The articles included in this book are devoted to some of the significant recent advances, trends, and challenges associated with the mathematical modeling and analysis of the dynamics and control of some diseases of public health impo...
Mathematical Epidemiology
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).
