Author: Michael Y. Li Publisher: Springer ISBN: 3319721224 Category : Mathematics Languages : en Pages : 163
Book Description
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.
Author: O. Diekmann Publisher: John Wiley & Sons ISBN: 9780471492412 Category : Mathematics Languages : en Pages : 324
Book Description
Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are unravelled. Conceptual clarity is attained, assumptions are stated clearly, hidden working hypotheses are attained and mechanistic links between different observables are exposed. Features: * Model construction, analysis and interpretation receive detailed attention * Uniquely covers both deterministic and stochastic viewpoints * Examples of applications given throughout * Extensive coverage of the latest research into the mathematical modelling of epidemics of infectious diseases * Provides a solid foundation of modelling skills The reader will learn to translate, model, analyse and interpret, with the help of the numerous exercises. In literally working through this text, the reader acquires modelling skills that are also valuable outside of epidemiology, certainly within population dynamics, but even beyond that. In addition, the reader receives training in mathematical argumentation. The text is aimed at applied mathematicians with an interest in population biology and epidemiology, at theoretical biologists and epidemiologists. Previous exposure to epidemic concepts is not required, as all background information is given. The book is primarily aimed at self-study and ideally suited for small discussion groups, or for use as a course text.
Author: Ivo M. Foppa Publisher: Academic Press ISBN: 0128024992 Category : Medical Languages : en Pages : 218
Book Description
A Historical Introduction to Mathematical Modeling of Infectious Diseases: Seminal Papers in Epidemiology offers step-by-step help on how to navigate the important historical papers on the subject, beginning in the 18th century. The book carefully, and critically, guides the reader through seminal writings that helped revolutionize the field. With pointed questions, prompts, and analysis, this book helps the non-mathematician develop their own perspective, relying purely on a basic knowledge of algebra, calculus, and statistics. By learning from the important moments in the field, from its conception to the 21st century, it enables readers to mature into competent practitioners of epidemiologic modeling. - Presents a refreshing and in-depth look at key historical works of mathematical epidemiology - Provides all the basic knowledge of mathematics readers need in order to understand the fundamentals of mathematical modeling of infectious diseases - Includes questions, prompts, and answers to help apply historical solutions to modern day problems
Author: Odo Diekmann Publisher: Princeton University Press ISBN: 0691155399 Category : Mathematics Languages : en Pages : 516
Book Description
This book 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.
Author: William E Schiesser Publisher: World Scientific ISBN: 9813238801 Category : Technology & Engineering Languages : en Pages : 460
Book Description
The intent of this book is to provide a methodology for the analysis of infectious diseases by computer-based mathematical models. The approach is based on ordinary differential equations (ODEs) that provide time variation of the model dependent variables and partial differential equations (PDEs) that provide time and spatial (spatiotemporal) variations of the model dependent variables.The starting point is a basic ODE SIR (Susceptible Infected Recovered) model that defines the S,I,R populations as a function of time. The ODE SIR model is then extended to PDEs that demonstrate the spatiotemporal evolution of the S,I,R populations. A unique feature of the PDE model is the use of cross diffusion between populations, a nonlinear effect that is readily accommodated numerically. A second feature is the use of radial coordinates to represent the geographical distribution of the model populations.The numerical methods for the computer implementation of ODE/PDE models for infectious diseases are illustrated with documented R routines for particular applications, including models for malaria and the Zika virus. The R routines are available from a download so that the reader can reproduce the reported solutions, then extend the applications through computer experimentation, including the addition of postulated effects and associated equations, and the implementation of alternative models of interest.The ODE/PDE methodology is open ended and facilitates the development of computer-based models which hopefully can elucidate the causes/conditions of infectious disease evolution and suggest methods of control.
Author: Xinzhi Liu Publisher: Springer ISBN: 3319532081 Category : Mathematics Languages : en Pages : 279
Book Description
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.
Author: Fred Brauer Publisher: SIAM ISBN: 9781611972429 Category : Mathematics Languages : en Pages : 288
Book Description
This graduate-level textbook appeals to readers interested in the mathematical theory of disease transmission models. It is self-contained and accessible to readers who are comfortable with calculus, elementary differential equations, and linear algebra. The book provides insight into modeling cross-immunity between different disease strains (such as influenza) and the synergistic interactions between multiple diseases (e.g., HIV and tuberculosis); diseases transmitted by viral agents, bacteria, and vectors (e.g., mosquitos transmitting malaria to humans); and both epidemic and endemic disease occurrences.
Author: Zhien Ma Publisher: World Scientific ISBN: 9814261254 Category : Medical Languages : en Pages : 355
Book Description
This book provides a systematic introduction to the fundamental methods and techniques and the frontiers of ? along with many new ideas and results on ? infectious disease modeling, parameter estimation and transmission dynamics. It provides complementary approaches, from deterministic to statistical to network modeling; and it seeks viewpoints of the same issues from different angles, from mathematical modeling to statistical analysis to computer simulations and finally to concrete applications.
Author: Guri I. Marchuk Publisher: Springer Science & Business Media ISBN: 9401587981 Category : Mathematics Languages : en Pages : 356
Book Description
Beginning his work on the monograph to be published in English, this author tried to present more or less general notions of the possibilities of mathematics in the new and rapidly developing science of infectious immunology, describing the processes of an organism's defence against antigen invasions. The results presented in this monograph are based on the construc tion and application of closed models of immune response to infections which makes it possible to approach problems of optimizing the treat ment of chronic and hypertoxic forms of diseases. The author, being a mathematician, had creative long-Iasting con tacts with immunologists, geneticist, biologists, and clinicians. As far back as 1976 it resulted in the organization of a special seminar in the Computing Center of Siberian Branch of the USSR Academy of Sci ences on mathematical models in immunology. The seminar attracted the attention of a wide circle of leading specialists in various fields of science. All these made it possible to approach, from a more or less united stand point, the construction of models of immune response, the mathematical description of the models, and interpretation of results.
Author: Michael Y. Li
Author: O. Diekmann
Author: Ivo M. Foppa
Author: Odo Diekmann
Author: William E Schiesser
Author: Xinzhi Liu
Author: Fred Brauer
Author: Zhien Ma
Author: Nita H. Shah
Author: Guri I. Marchuk