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This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.

Stochastic processes --- Biomathematics. Biometry. Biostatistics --- General ecology and biosociology --- Mathematics --- Ecology --- Genetics --- Distribution (Probability theory) --- Mathématiques --- Ecologie --- Distribution (Théorie des probabilités) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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Biomathematics. Biometry. Biostatistics

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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 ).

Epidemiologic Methods. --- Models, Theoretical. --- Public Health. --- Epidemiology --- Public health --- Biomathematics. --- Mathematical models. --- Epidémiologie --- Biomathématiques --- Modèles mathématiques --- Biomathematics --- Mathematical models --- Models, Theoretical --- Public Health --- Epidemiologic Methods --- Health --- Environment and Public Health --- Medicine --- Investigative Techniques --- Health Occupations --- Population Characteristics --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Health Care --- Disciplines and Occupations --- Epidemiology & Epidemics --- Health & Biological Sciences --- 51-7 --- 51:37 --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Santé publique --- 51:37 Mathematics-:-Opvoeding en onderwijs --(algemeen) --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Models, Mathematical --- Biology --- Community health --- Health services --- Hygiene, Public --- Hygiene, Social --- Public health services --- Public hygiene --- Sanitary affairs --- Social hygiene --- Mathematics --- Medicine. --- Epidemiology. --- Mathematical analysis. --- Analysis (Mathematics). --- Dynamics. --- Ergodic theory. --- Differential equations. --- Probabilities. --- Medicine & Public Health. --- Probability Theory and Stochastic Processes. --- Analysis. --- Genetics and Population Dynamics. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.91 Differential equations --- Differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 517.1 Mathematical analysis --- Mathematical analysis --- Diseases --- Clinical sciences --- Medical profession --- Human biology --- Life sciences --- Medical sciences --- Pathology --- Physicians --- Human services --- Biosecurity --- Health literacy --- Medicine, Preventive --- National health services --- Sanitation --- Simulation methods --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Distribution (Probability theory. --- Global analysis (Mathematics). --- Genetics --- Differential Equations. --- Differentiable dynamical systems. --- Mathematics. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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