Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment

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Publisher : Springer Nature
ISBN 13 : 3030463060
Total Pages : 428 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment written by Rubem P. Mondaini and published by Springer Nature. This book was released on 2020-07-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; aspects of blood circulation modeling; multidimensional modeling approach via time-frequency analysis and Edge Based Compartmental Model; and more. This book builds upon the tradition of the previous BIOMAT volumes to foster interdisciplinary research in mathematical biology for students, researchers, and professionals. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 2019 edition of BIOMAT International Symposium received contributions by authors from 14 countries: Brazil, Cameroon, Canada, Colombia, Czech Republic, Finland, Hungary, India, Italy, Russia, Senegal, Serbia, United Kingdom and the USA. Selected papers presented at the 2017 and 2018 editions of this Symposium were also published by Springer, in the volumes "Trends in Biomathematics: Modeling, Optimization and Computational Problems" (978-3-319-91091-8) and "Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics" (978-3-030-23432-4).

Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models

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Publisher : Springer Nature
ISBN 13 : 3031125150
Total Pages : 421 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models written by Rubem P. Mondaini and published by Springer Nature. This book was released on 2023-01-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume convenes selected, peer-reviewed works presented at the BIOMAT 2021 International Symposium, which was virtually held on November 1–5, 2021, with its organization staff based in Rio de Janeiro, Brazil. In this volume the reader will find applications of mathematical modeling on health, ecology, and social interactions, addressing topics like probability distributions of mutations in different cancer cell types; oscillations in biological systems; modeling of marine ecosystems; mathematical modeling of organs and tissues at the cellular level; as well as studies on novel challenges related to COVID-19, including the mathematical analysis of a pandemic model targeting effective vaccination strategy and the modeling of the role of media coverage on mitigating the spread of infectious diseases. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2020 are also available by Springer.

Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

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Publisher : Springer Nature
ISBN 13 : 3031330501
Total Pages : 394 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics written by Rubem P. Mondaini and published by Springer Nature. This book was released on 2023-07-24 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers together selected peer-reviewed works presented at the BIOMAT 2022 International Symposium, which was virtually held on November 7-11, 2022, with an organization staff based in Rio de Janeiro, Brazil. Topics touched on in this volume include infection spread in a population described by an agent-based approach; the study of gene essentiality via network-based computational modeling; stochastic models of neuronal dynamics; and the modeling of a statistical distribution of amino acids in protein domain families. The reader will also find texts in epidemic models with dynamic social distancing; with no vertical transmission; and with general incidence rates. Aspects of COVID-19 dynamics: the use of an SEIR model to analyze its spread in Brazil; the age-dependent manner of modeling its spread pattern; the impact of media awareness programs; and a web-based computational tool for Non-invasive hemodynamics evaluation of coronary stenosis are also covered. Held every year since 2001, The BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2021 are also available by Springer.

Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells

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Publisher : Springer Nature
ISBN 13 : 303073241X
Total Pages : 395 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells written by Rubem P. Mondaini and published by Springer Nature. This book was released on 2021-07-27 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers together selected, peer-reviewed papers presented at the BIOMAT 2020 International Symposium, which was virtually held on November 1-6, 2020, with an organization staff based in Rio de Janeiro, Brazil. Topics covered in this volume include infection modeling, with an emphasis on different aspects of the COVID-19 and novel Coronavirus spread; a description of the effectiveness of quarantine measures via dynamic analysis of SLIR model; hemodynamic simulations in time-dependent domains; an optimal control model for the Ebola disease; and the co-existence of chaos and control in the context of biological models. Texts in agroforestry, economic development, and wastewater treatment processes complete this volume. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 20th edition of the BIOMAT International Symposium has received contributions by authors from 18 countries: Algeria, Brazil, Cameroon, Canada, Chile, China (Hong Kong), Colombia, Germany, Hungary, India, Italy, Morocco, Nigeria, Russia, Senegal, South Africa, USA, and Uzbekistan. Previous BIOMAT volumes with selected works from 2017, 2018, and 2019 were also published by Springer.

Recent Advances in Polynomials

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Publisher : BoD – Books on Demand
ISBN 13 : 183969758X
Total Pages : 168 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Recent Advances in Polynomials by : Kamal Shah

Download or read book Recent Advances in Polynomials written by Kamal Shah and published by BoD – Books on Demand. This book was released on 2022-05-18 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of recent developments in polynomials and their applications. It includes eight chapters that address such topics as characteristic functions of polynomials, permutations, Gon?arov polynomials, irreducible factors, polynomial regression algorithms, and the use of polynomials in fractional calculus, and much more.

Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells

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Publisher :
ISBN 13 : 9783030732424
Total Pages : 0 pages
Book Rating : 4.7/5 (324 download)

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Book Synopsis Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells written by Rubem P. Mondaini and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers together selected, peer-reviewed papers presented at the BIOMAT 2020 International Symposium, which was virtually held on November 1-6, 2020, with an organization staff based in Rio de Janeiro, Brazil. Topics covered in this volume include infection modeling, with an emphasis on different aspects of the COVID-19 and novel Coronavirus spread; a description of the effectiveness of quarantine measures via dynamic analysis of SLIR model; hemodynamic simulations in time-dependent domains; an optimal control model for the Ebola disease; and the co-existence of chaos and control in the context of biological models. Texts in agroforestry, economic development, and wastewater treatment processes complete this volume. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 20th edition of the BIOMAT International Symposium has received contributions by authors from 18 countries: Algeria, Brazil, Cameroon, Canada, Chile, China (Hong Kong), Colombia, Germany, Hungary, India, Italy, Morocco, Nigeria, Russia, Senegal, South Africa, USA, and Uzbekistan. Previous BIOMAT volumes with selected works from 2017, 2018, and 2019 were also published by Springer.

Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models

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Publisher : Springer
ISBN 13 : 9783031125171
Total Pages : 0 pages
Book Rating : 4.1/5 (251 download)

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Book Synopsis Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models written by Rubem P. Mondaini and published by Springer. This book was released on 2024-01-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume convenes selected, peer-reviewed works presented at the BIOMAT 2021 International Symposium, which was virtually held on November 1–5, 2021, with its organization staff based in Rio de Janeiro, Brazil. In this volume the reader will find applications of mathematical modeling on health, ecology, and social interactions, addressing topics like probability distributions of mutations in different cancer cell types; oscillations in biological systems; modeling of marine ecosystems; mathematical modeling of organs and tissues at the cellular level; as well as studies on novel challenges related to COVID-19, including the mathematical analysis of a pandemic model targeting effective vaccination strategy and the modeling of the role of media coverage on mitigating the spread of infectious diseases. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2020 are also available by Springer.

Structured Population Models in Biology and Epidemiology

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Publisher : Springer Science & Business Media
ISBN 13 : 3540782729
Total Pages : 314 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Structured Population Models in Biology and Epidemiology by : Pierre Magal

Download or read book Structured Population Models in Biology and Epidemiology written by Pierre Magal and published by Springer Science & Business Media. This book was released on 2008-04-30 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.

Trends in Biomathematics: Exploring Epidemics, Eco-Epidemiological Systems, and Optimal Control Strategies

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Publisher : Springer
ISBN 13 : 9783031590719
Total Pages : 0 pages
Book Rating : 4.5/5 (97 download)

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Book Synopsis Trends in Biomathematics: Exploring Epidemics, Eco-Epidemiological Systems, and Optimal Control Strategies by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Exploring Epidemics, Eco-Epidemiological Systems, and Optimal Control Strategies written by Rubem P. Mondaini and published by Springer. This book was released on 2024-07-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume convenes carefully selected, peer-reviewed papers presented at the BIOMAT 2023 International Symposium, which was virtually held on November 6-9, 2023, with an organization staff based in Rio de Janeiro, Brazil. In this volume, the reader will find studies on the epidemic model of the COVID-19 pandemic, aspects of risk-based testing and quarantine, as well as joint efforts in the search for the perfect vaccine. Additionally, the volume covers the influence of fear and the saturated fear cost in predator-prey dynamics, optimal control techniques applied to HPV infection and cervical cancer cells, generic epidemic models for disease propagation, discretized SIS model with no vertical transmission, dynamics of vibrio-phage interactions, and antibiotics treatment for septic arthritis. Comprehensive Reviews are also included on the applications of CHIRP ultrasound for the mathematical modeling of evaporation of nanodroplets and on Alternative Entropy Measures and their application in the studies of distributions of discrete probabilities of occurrence. These works aim to motivate Ph.D. students and new practitioners in the field of Biomathematics. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to foster the interdisciplinary exchange of results, ideas, and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2022 are also available by Springer.

Trends in Biomathematics: Modeling, Optimization and Computational Problems

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Publisher : Springer
ISBN 13 : 3319910922
Total Pages : 423 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Trends in Biomathematics: Modeling, Optimization and Computational Problems by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Modeling, Optimization and Computational Problems written by Rubem P. Mondaini and published by Springer. This book was released on 2018-08-16 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together carefully selected, peer-reviewed works on mathematical biology presented at the BIOMAT International Symposium on Mathematical and Computational Biology, which was held at the Institute of Numerical Mathematics, Russian Academy of Sciences, in October 2017, in Moscow. Topics covered include, but are not limited to, the evolution of spatial patterns on metapopulations, problems related to cardiovascular diseases and modeled by boundary control techniques in hemodynamics, algebraic modeling of the genetic code, and multi-step biochemical pathways. Also, new results are presented on topics like pattern recognition of probability distribution of amino acids, somitogenesis through reaction-diffusion models, mathematical modeling of infectious diseases, and many others. Experts, scientific practitioners, graduate students and professionals working in various interdisciplinary fields will find this book a rich resource for research and applications alike.

Mathematical Modeling in Economics, Ecology and the Environment

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Publisher : Springer Science & Business Media
ISBN 13 : 1441997334
Total Pages : 225 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Mathematical Modeling in Economics, Ecology and the Environment by : N.V. Hritonenko

Download or read book Mathematical Modeling in Economics, Ecology and the Environment written by N.V. Hritonenko and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ...

Mathematical Modeling and Control in Life and Environmental Sciences

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Publisher : Birkhäuser
ISBN 13 : 9783031499708
Total Pages : 0 pages
Book Rating : 4.4/5 (997 download)

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Book Synopsis Mathematical Modeling and Control in Life and Environmental Sciences by : Sebastian Aniţa

Download or read book Mathematical Modeling and Control in Life and Environmental Sciences written by Sebastian Aniţa and published by Birkhäuser. This book was released on 2024-04-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the use of mathematical modeling and control theory in a variety of contemporary challenges in mathematical biology and environmental sciences. Emphasizing an approach of learning by doing, the authors focus on a set of significant case studies emerging from real-world problems and illustrate how mathematical techniques and computational experiments can be employed in the search for sustainable solutions. The following topics are extensively discussed: Eradicability and control of a paradigmatic epidemic model, with a view to the existence of endemic states, their stability, and the existence of travelling waves A spatially structured epidemic model concerning malaria as an example of vector-borne epidemics Optimal harvesting problems for space-structured and age-structured population dynamics Controlling epidemics in agriculture due to pest insects The role of predators as a possible biocontrol agent of epidemics in agriculture Control by taxation of the environmental pollution produced by human activities The originality of this text is in its leitmotif – regional control – along the principle of “Think Globally, Act Locally.” Indeed, for example, in many real spatially structured ecosystems, it is practically impossible to control the relevant system by global interventions in the whole habitat. Proofs are given whenever they may serve as a guide to the introduction of new concepts. Each chapter includes a comprehensive description of the numerical methods used for the computational experiments, and MATLAB© codes for many of the numerical simulations are available for download. Several challenging open problems are also provided to stimulate future research. This text is aimed at mathematicians, engineers, and other scientists working in areas such as biology, medicine, and economics. Graduate and advanced undergraduate students of a quantitative subject related to the analysis and applications of dynamical systems and their control will also find it to be a valuable resource.

Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

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Publisher : Springer Nature
ISBN 13 : 3030234339
Total Pages : 437 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics by : Rubem P. Mondaini

Download or read book Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics written by Rubem P. Mondaini and published by Springer Nature. This book was released on 2019-10-03 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018. The topics covered include applications of mathematical modeling in hepatitis B, HIV and Chikungunya infections; tumor cell dynamics; inflammatory processes; chemotherapeutic drug effects; and population dynamics. Also discussing the application of techniques like the generalized stochastic Milevsky-Promislov model, numerical simulations and convergence of discrete and continuous models, it is an invaluable resource on interdisciplinary research in mathematical biology for students, researchers, and professionals. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 2018 edition of BIOMAT International Symposium received contributions by authors from seventeen countries: Algeria, Brazil, Cameroon, Canada, Chad, Colombia, France, Germany, Hungary, Italy, Mali, Morocco, Nigeria, Poland, Portugal, Russia, and Senegal. Selected papers presented at the 2017 edition of this Symposium were also published by Springer, in the volume “Trends in Biomathematics: Modeling, Optimization and Computational Problems” (978-3-319-91091-8).

Modeling Dynamic Biological Systems

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Publisher : Springer
ISBN 13 : 9783319307640
Total Pages : 0 pages
Book Rating : 4.3/5 (76 download)

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Book Synopsis Modeling Dynamic Biological Systems by : Bruce Hannon

Download or read book Modeling Dynamic Biological Systems written by Bruce Hannon and published by Springer. This book was released on 2014-07-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many biologists and ecologists have developed models that find widespread use in theoretical investigations and in applications to organism behavior, disease control, population and metapopulation theory, ecosystem dynamics, and environmental management. This book captures and extends the process of model development by concentrating on the dynamic aspects of these processes and by providing the tools such that virtually anyone with basic knowledge in the Life Sciences can develop meaningful dynamic models. Examples of the systems modeled in the book range from models of cell development, the beating heart, the growth and spread of insects, spatial competition and extinction, to the spread and control of epidemics, including the conditions for the development of chaos. Key features: - easy-to-learn and easy-to-use software - examples from many subdisciplines of biology, covering models of cells, organisms, populations, and metapopulations - no prior computer or programming experience required Key benefits: - learn how to develop modeling skills and system thinking on your own rather than use models developed by others - be able to easily run models under alternative assumptions and investigate the implications of these assumptions for the dynamics of the biological system being modeled - develop skills to assess the dynamics of biological systems

Research Awards Index

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Publisher :
ISBN 13 :
Total Pages : 742 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Research Awards Index by :

Download or read book Research Awards Index written by and published by . This book was released on 1989 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Models in Epidemiology

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Publisher : Springer Nature
ISBN 13 : 1493998285
Total Pages : 628 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Mathematical Models in Epidemiology by : Fred Brauer

Download or read book Mathematical Models in Epidemiology written by Fred Brauer and published by Springer Nature. This book was released on 2019-10-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.

Research Grants Index

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Publisher :
ISBN 13 :
Total Pages : 1212 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Research Grants Index by : National Institutes of Health (U.S.). Division of Research Grants

Download or read book Research Grants Index written by National Institutes of Health (U.S.). Division of Research Grants and published by . This book was released on 1975 with total page 1212 pages. Available in PDF, EPUB and Kindle. Book excerpt: