The Basic Approach To Age Structured Population Dynamics
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The Basic Approach to Age Structured Population Dynamics
Author | : Mimmo Iannelli,Fabio Milner |
Publsiher | : Springer |
Total Pages | : 350 |
Release | : 2017-08-27 |
Genre | : Mathematics |
ISBN | : 9789402411461 |
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This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
Age Structured Population Dynamics in Demography and Epidemiology
Author | : Hisashi Inaba |
Publsiher | : Springer |
Total Pages | : 555 |
Release | : 2017-03-15 |
Genre | : Social Science |
ISBN | : 9789811001888 |
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This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.
Population Dynamics Algebraic And Probabilistic Approach
Author | : Utkir A Rozikov |
Publsiher | : World Scientific |
Total Pages | : 458 |
Release | : 2020-04-22 |
Genre | : Science |
ISBN | : 9789811211249 |
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A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.
Current Trends in Analysis its Applications and Computation
Author | : Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft |
Publsiher | : Springer Nature |
Total Pages | : 663 |
Release | : 2022-10-03 |
Genre | : Mathematics |
ISBN | : 9783030875022 |
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This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.
Mathematical Theory of Age structured Population Dynamics
Author | : Mimmo Iannelli |
Publsiher | : Giardini |
Total Pages | : 196 |
Release | : 1995 |
Genre | : Age distribution (Demography) |
ISBN | : CHI:46889805 |
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Structured Population Models in Marine Terrestrial and Freshwater Systems
Author | : Shripad Tuljapurkar,Hal Caswell |
Publsiher | : Springer Science & Business Media |
Total Pages | : 660 |
Release | : 1997-01-31 |
Genre | : Mathematics |
ISBN | : 0412072718 |
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Providing many examples of how models can be implemented and interpreted, this book describes the biology of the life cycle and follows the transitions of individuals through stages in the life cycle. The focus is on models as tools.
Gender structured Population Modeling
Author | : M. Iannelli,M. Martcheva,F. A. Milner |
Publsiher | : SIAM |
Total Pages | : 186 |
Release | : 2005-04-01 |
Genre | : Mathematics |
ISBN | : 9780898715774 |
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This book gives a unified presentation of, and mathematical framework for, modeling population growth by couple formation, summarizing both past and present modeling results. It provides results on model analysis, gives an up-to-date review of mathematical demography, discusses numerical methods, and puts deterministic modeling of human populations into historical perspective.
Age Structured Epidemic Modeling
Author | : Xue-Zhi Li,Junyuan Yang,Maia Martcheva |
Publsiher | : Springer Nature |
Total Pages | : 386 |
Release | : 2020-05-28 |
Genre | : Mathematics |
ISBN | : 9783030424961 |
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This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology. Chronological age and class-age play an important role in the description of infectious diseases and this text provides the tools for the analysis of this type of partial differential equation models. This book presents general theoretical tools as well as large number of specific examples to guide the reader to develop their own tools that they may then apply to study structured models in mathematical epidemiology. The book will be a valuable addition to the arsenal of all researchers interested in developing theory or studying specific models with age structure.