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Mathematical Learning and Cognition in Early Childhood: Integrating Interdisciplinary Research into Practice
by Katherine M. Robinson Helena P. Osana Donna KotsopoulosThis book explores mathematical learning and cognition in early childhood from interdisciplinary perspectives, including developmental psychology, neuroscience, cognitive psychology, and education. It examines how infants and young children develop numerical and mathematical skills, why some children struggle to acquire basic abilities, and how parents, caregivers, and early childhood educators can promote early mathematical development. The first section of the book focuses on infancy and toddlerhood with a particular emphasis on the home environment and how parents can foster early mathematical skills to prepare their children for formal schooling. The second section examines topics in preschool and kindergarten, such as the development of counting procedures and principles, the use of mathematics manipulatives in instruction, and the impacts of early intervention. The final part of the book focuses on particular instructional approaches in the elementary school years, such as different additive concepts, schema-based instruction, and methods of division. Chapters analyze the ways children learn to think about, work with, and master the language of mathematical concepts, as well as provide effective approaches to screening and intervention.Included among the topics:The relationship between early gender differences and future mathematical learning and participation.The connection between mathematical and computational thinking.Patterning abilities in young children.Supporting children with learning difficulties and intellectual disabilities.The effectiveness of tablets as elementary mathematics education tools. Mathematical Learning and Cognition in Early Childhood is an essential resource for researchers, graduate students, and professionals in infancy and early childhood development, child and school psychology, neuroscience, mathematics education, educational psychology, and social work.
Mathematical Methods for Cancer Evolution
by Takashi SuzukiThe purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
Mathematical Modeling and Computational Tools: ICACM 2018, Kharagpur, India, November 23–25 (Springer Proceedings in Mathematics & Statistics #320)
by Jitendra Kumar Somnath Bhattacharyya Koeli GhoshalThis book features original research papers presented at the International Conference on Computational and Applied Mathematics, held at the Indian Institute of Technology Kharagpur, India during November 23–25, 2018. This book covers various topics under applied mathematics, ranging from modeling of fluid flow, numerical techniques to physical problems, electrokinetic transport phenomenon, graph theory and optimization, stochastic modelling and machine learning. It introduces the mathematical modeling of complicated scientific problems, discusses micro- and nanoscale transport phenomena, recent development in sophisticated numerical algorithms with applications, and gives an in-depth analysis of complicated real-world problems. With contributions from internationally acclaimed academic researchers and experienced practitioners and covering interdisciplinary applications, this book is a valuable resource for researchers and students in fields of mathematics, statistics, engineering, and health care.
Mathematical Modeling and Validation in Physiology
by Mostafa Bachar Jerry J. Batzel Franz KappelThis volume synthesizes theoretical and practical aspects of both the mathematical and life science viewpoints needed for modeling of the cardiovascular-respiratory system specifically and physiological systems generally. Theoretical points include model design, model complexity and validation in the light of available data, as well as control theory approaches to feedback delay and Kalman filter applications to parameter identification. State of the art approaches using parameter sensitivity are discussed for enhancing model identifiability through joint analysis of model structure and data. Practical examples illustrate model development at various levels of complexity based on given physiological information. The sensitivity-based approaches for examining model identifiability are illustrated by means of specific modeling examples. The themes presented address the current problem of patient-specific model adaptation in the clinical setting, where data is typically limited.
Mathematical Modeling in Renal Physiology
by Anita T. Layton Aurélie EdwardsWith the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physiology. The models presented describe the main homeostatic functions performed by the kidney, including blood filtration, excretion of water and salt, maintenance of electrolyte balance and regulation of blood pressure. Each chapter includes an introduction to the basic relevant physiology, a derivation of the essential conservation equations and then a discussion of a series of mathematical models, with increasing level of complexity. This volume will be of interest to biological and mathematical scientists, as well as physiologists and nephrologists, who would like an introduction to mathematical techniques that can be applied to renal transport and function. The material is written for students who have had college-level calculus, but can be used in modeling courses in applied mathematics at all levels through early graduate courses.
Mathematical Modeling of Biosensors: An Introduction For Chemists And Mathematicians (Springer Series on Chemical Sensors and Biosensors #9)
by Juozas Kulys Romas Baronas Feliksas IvanauskasThis newly designed and enlarged edition offers an up-to-date presentation of biosensor development and modeling from both a chemical and a mathematical point of view. An entire new chapter in particular is dedicated to optimal design of biosensors. Two more new chapters discuss biosensors which utilize microbial cells and are based on carbon nanotubes respectively. All the other chapters have been revised and updated. The book contains unique modeling methods for amperometric, potentiometric and optical biosensors based mainly on biocatalysts . It examines processes that occur in the sensors' layers and at their interface, and it provides analytical and numerical methods to solve equations of conjugated enzymatic (chemical) and diffusion processes. The action of single enzyme as well as polyenzyme biosensors and biosensors based on chemically modified electrodes is studied. The modeling of biosensors that contain perforated membranes and multipart mass transport profiles is critically investigated. Furthermore, it is fully described how signals can be biochemically amplified, how cascades of enzymatic substrate conversion are triggered, and how signals are processed via a chemometric approach and artificial neuronal networks. The results of digital modeling are compared with both proximal analytical solutions and experimental data.
Mathematical Modeling of Pharmacokinetic Data
by DavidW.A. BourneA concise guide to mathematical modeling and analysis of pharmacokinetic data, this book contains valuable methods for maximizing the information obtained from given data. It is an ideal resource for scientists, scholars, and advanced students.
Mathematical Modeling of the Healthy and Diseased Lung: Linking Structure, Biomechanics, and Mechanobiology
by Béla Suki Jason H. BatesThe lung is a complex multiscale organ that serves as the primary interface between the environment and the tissues of the body. Homeostatic maintenance of lung function throughout life is essential for health. While failure of lung homeostasis underlies many of the most common chronic diseases that afflict mankind, the precise pathophysiologic mechanisms involved are often unclear. Investigative techniques such as microscopic imaging and atomic force microscopy are providing new insights into lung tissue properties at the micro scale. It nevertheless remains to be seen how this growing body of information can be integrated into a comprehensive picture of the lung. Mathematical and computational modeling has emerged as an essential tool for gaining such a holistic understanding. This book introduces the reader to the art of modeling as a means of linking lung structure to function over multiple length scales from the intracellular level to that of the whole organ, with specific attention given to the pathophysiology of a number of common lung diseases and aging.
Mathematical Modelling and Analysis of Infectious Diseases (Studies in Systems, Decision and Control #302)
by Hemen Dutta Khalid HattafThis book discusses significant research and study topics related to mathematical modelling and analysis of infectious diseases. It includes several models and modelling approaches with different aims, such as identifying and analysing causes of occurrence and re-occurrence, causes of spreading, treatments and control strategies. A valuable resource for researchers, students, educators, scientists, professionals and practitioners interested in gaining insights into various aspects of infectious diseases using mathematical modelling and mathematical analysis, the book will also appeal to general readers wanting to understand the dynamics of various diseases and related issues. Key FeaturesMathematical models that describe population prevalence or incidence of infectious diseasesMathematical tools and techniques to analyse data on the incidence of infectious diseasesEarly detection and risk estimate models of infectious diseasesMathematical models that describe the transmission of infectious diseases and analyse dataDynamical analysis and control strategies for infectious diseasesStudies comparing the utility of particular models in describing infected diseases-related issues such as social, health and economic
Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics
by Leszek Pstras Jacek WaniewskiBeginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy.Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes.Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy.
Mathematical Models for Dental Materials Research
by Alex Fok Hooi Pin ChewThis book presents a mechanistic approach—mathematical modeling—for carrying out dental materials research. This approach allows researchers to go beyond the null hypothesis and obtain a solution that is more general and therefore predictive for conditions other than those considered in a study. Hence it can be used either on its own or to complement the commonly used statistical approach. Through a series of practical problems with wide-ranging application, the reader will be guided on:How to construct a mathematical model for the behavior of dental materials by making informed assumptions of the physical, chemical, or mechanical situationHow to simplify the model by making suitable simplificationsHow to calibrate the model by calculating the values of key parameters using experimental resultsHow to refine the model when there are discrepancies between predictions and experimentsOnly elementary calculus is required to follow the examples and all the problems can be solved by using MS Excel© spreadsheets.This is an ideal book for dental materials researchers without a strong mathematical background who are interested in applying a more mechanistic approach to their research to give deeper insight into the problem at hand. Advance praise for Mathematical Models for Dental Materials Research:“This is a nice addition for research students on how to conduct their work and how to manage data analysis. It brings together a number of important aspects of dental materials investigations which has been missing in the literature. The practical examples make it much easier to understand.” – Michael F. Burrow, Clinical Professor in Prosthodontics, The University of Hong Kong“The great strengths of this volume are the real world examples of dental materials research in the successive chapters. In turn, this is an outcome of the outstanding expertise of both authors. I warmly recommend this book to the dental biomaterials community worldwide.” – David C. Watts, Professor of Biomaterials Science, University of Manchester, UK
Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission
by Priti Kumar RoyThe book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are presented in the book would serve to reveal the consequences of the logical structure of the disease transmission, quantitatively as well as qualitatively. One of the chapters introduces the optimal control approach towards the mathematical models, describing the optimal drug dosage process that is discussed with the basic deterministic models dealing with stability analysis. Another one chapter deals with the mathematical analysis for the perfect drug adherence for different drug dynamics during the treatment management. The last chapter of the book consists the stochastic approach to the disease dynamics on HIV/AIDS. This method helps to move the disease HIV/AIDS to extinction as the time to increase. This book will appeal to undergraduate and postgraduate students, as well as researchers, who are studying and working in the field of bio-mathematical modelling on infectious diseases, applied mathematics, health informatics, applied statistics and qualitative public health, etc. Social workers, who are working in the field of HIV, will also find the book useful for complements.
Mathematical Models for Therapeutic Approaches to Control Psoriasis (SpringerBriefs in Applied Sciences and Technology)
by Priti Kumar Roy Abhirup DattaThis book discusses several mathematical models highlighting the disease dynamics of psoriasis and its control. It explains the control of keratinocyte concentration through a negative feedback mechanism and the effect of including a realistic time delay in that system. The effect of cytokine release is described in a mathematical model of psoriasis and further elucidated in two different mathematical pathways: the ordinary differential equation model system, and the fractional-order differential equation model system. The book also identifies the role of CD8+ T-cells in psoriasis by investigating the interaction between dendritic cells and CD8+ T-cells. Presenting an approach to control the fractional-order system to prevent excess production of keratinocyte cell population, the book is intended for researchers and scientists in the field of applied mathematics, health informatics, applied statistics and qualitative public health, as well as bio-mathematicians interested in the mathematical modeling of autoimmune diseases like psoriasis.
Mathematical Models in the Biosciences I
by Michael FrameAn award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students.
Mathematical Models of Cancer and Different Therapies: Unified Framework (Series in BioEngineering)
by Regina Padmanabhan Nader Meskin Ala-Eddin Al MoustafaThis book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind.In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.
Mathematical Models of Exoskeleton: Dynamics, Strength, Control (Studies in Systems, Decision and Control #431)
by Andrey Valerievich Borisov Anatoly Vlasovich ChigarevThis book presents the current state of the problem of describing the musculoskeletal system of a person. Models of the destruction of the endoskeleton and the restoration of its functions using exoskeleton are presented. A description is given of new approaches to modeling based on the use of weightless rods of variable length with concentrated masses. The practical application to the tasks of numerical simulation of the movements of the musculoskeletal system of a person is described. Exoskeleton models with variable-length units based on absolutely hard sections and sections that change their telescopic type length have been developed.The book is intended for specialists in the field of theoretical mechanics, biomechanics, robotics and related fields. The book will be useful to teachers, as well as graduate students, undergraduates and senior students of higher educational institutions, whose research interests lie in the modeling of anthropomorphic biomechanical systems.
Mathematical Models of Tumor-Immune System Dynamics
by Peter Kim Amina Eladdadi Dann MalletThis collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences.
Mathematical Oncology 2013
by Alberto D'Onofrio Alberto GandolfiWith chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion-consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways. Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.
Mathematical Structures of Ergodicity and Chaos in Population Dynamics (Studies in Systems, Decision and Control #312)
by Paweł J. MitkowskiThis book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus pandemic, when models are intensively studied in order to help predict its behaviour within human population. The structures of population dynamics models and practical methods of finding their solutions are discussed. Finally, the hypothesis of the existence of non-trivial ergodic properties of the model of erythropoietic response dynamics formulated by A. Lasota in the form of delay differential equation with unimodal feedback is analysed. The research can be compared with actual medical data, as well as shows that the structures of population models can reflect the dynamic structures of reality.
Mathematical Tools for Neuroscience: A Geometric Approach (Lecture Notes in Morphogenesis)
by Richard A. ClementThis book provides a brief but accessible introduction to a set of related, mathematical ideas that have proved useful in understanding the brain and behaviour. If you record the eye movements of a group of people watching a riverside scene then some will look at the river, some will look at the barge by the side of the river, some will look at the people on the bridge, and so on, but if a duck takes off then everybody will look at it. How come the brain is so adept at processing such biological objects? In this book it is shown that brains are especially suited to exploiting the geometric properties of such objects. Central to the geometric approach is the concept of a manifold, which extends the idea of a surface to many dimensions. The manifold can be specified by collections of n-dimensional data points or by the paths of a system through state space. Just as tangent planes can be used to analyse the local linear behaviour of points on a surface, so the extension to tangent spaces can be used to investigate the local linear behaviour of manifolds. The majority of the geometric techniques introduced are all about how to do things with tangent spaces.Examples of the geometric approach to neuroscience include the analysis of colour and spatial vision measurements and the control of eye and arm movements. Additional examples are used to extend the applications of the approach and to show that it leads to new techniques for investigating neural systems. An advantage of following a geometric approach is that it is often possible to illustrate the concepts visually and all the descriptions of the examples are complemented by comprehensively captioned diagrams.The book is intended for a reader with an interest in neuroscience who may have been introduced to calculus in the past but is not aware of the many insights obtained by a geometric approach to the brain. Appendices contain brief reviews of the required background knowledge in neuroscience and calculus.
Mathematical Tools for Telemedicine (TELe-Health)
by Michele NichelattiThis book is intended for professionals who must deal with telemedicine having little or no knowledge of matrix algebra and matrix calculus, and little or no knowledge of higher mathematics with special reference to differential equations: no other books cover these topics starting from scratch. It would therefore fill the gap existing between very simple and elementary textbooks and much more complicated ones, mainly adopting mathematical and on engineering approaches. Aims and objectives of this volume are to provide non-mathematicians and non-physicists with an almost complete coverage of the topic, from calculus and linear algebra to matrix derivatives, hat matrices, and regression models, as well as to give basic information about the description of a system by means of differential equations, which will be useful for a deeper understanding of telemedicine. The book is mainly addressing postgraduate students in medicine, biology, biostatistics, but it would also be a very useful tool researchers in other fields of a medical/biomedical curriculum.
Mathematical Tools for Understanding Infectious Disease Dynamics (Princeton Series in Theoretical and Computational Biology #7)
by Hans Heesterbeek Odo Diekmann Tom BrittonMathematical 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.Mathematical Tools for Understanding Infectious Disease Dynamics 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.Covers the latest research in mathematical modeling of infectious disease epidemiologyIntegrates deterministic and stochastic approachesTeaches skills in model construction, analysis, inference, and interpretationFeatures numerous exercises and their detailed elaborationsMotivated by real-world applications throughout
Mathematical and Computational Modelling of Covid-19 Transmission (River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering)
by Nita H. ShahInfectious diseases are leading threats and are of highest risk to the human population globally. Over the last two years, we saw the transmission of Covid-19. Millions of people died or were forced to live with a disability. Mathematical models are effective tools that enable analysis of relevant information, simulate the related process and evaluate beneficial results. They can help to make rational decisions to lead toward a healthy society. Formulation of mathematical models for a pollution-free environment is also very important for society. To determine the system which can be modelled, we need to formulate the basic context of the model underlying some necessary assumptions. This describes our beliefs in terms of the mathematical language of how the world functions. This book addresses issues during the Covid phase and post-Covid phase. It analyzes transmission, impact of coinfections, and vaccination as a control or to decrease the intensity of infection. It also talks about the violence and unemployment problems occurring during the post-Covid period. This book will help societal stakeholders to resume normality slowly and steadily.
Mathematical and Engineering Methods in Computer Science
by Jan Kofroň Tomáš VojnarThis volume contains the post-conference proceedings of the 10th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, MEMICS 2015, held in Telč, Czech Republic, in October 2015. The 10 thoroughly revised full papers were carefully selected out of 25 submissions and are presented together with 3 invited papers. The topics covered include: security and safety, bioinformatics, recommender systems, high-performance and cloud computing, and non-traditional computational models (quantum computing, etc. ).
Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases
by Gerardo Chowell James M. HymanThe contributions by epidemic modeling experts describe how mathematical models and statistical forecasting are created to capture the most important aspects of an emerging epidemic. Readers will discover a broad range of approaches to address questions, such as Can we control Ebola via ring vaccination strategies? How quickly should we detect Ebola cases to ensure epidemic control? What is the likelihood that an Ebola epidemic in West Africa leads to secondary outbreaks in other parts of the world? When does it matter to incorporate the role of disease-induced mortality on epidemic models? What is the role of behavior changes on Ebola dynamics? How can we better understand the control of cholera or Ebola using optimal control theory? How should a population be structured in order to mimic the transmission dynamics of diseases such as chlamydia, Ebola, or cholera? How can we objectively determine the end of an epidemic? How can we use metapopulation models to understand the role of movement restrictions and migration patterns on the spread of infectious diseases? How can we capture the impact of household transmission using compartmental epidemic models? How could behavior-dependent vaccination affect the dynamical outcomes of epidemic models? The derivation and analysis of the mathematical models addressing these questions provides a wide-ranging overview of the new approaches being created to better forecast and mitigate emerging epidemics. This book will be of interest to researchers in the field of mathematical epidemiology, as well as public health workers.