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Cities of Workers, Children, or Seniors? : Age Structure and Economic Growth in a Global Cross-Section of Cities
Authors: --- ---
Year: 2019 Publisher: Washington, D.C. : The World Bank,

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Abstract

A large literature documents the positive influence of a city's skill structure on its rate of economic growth. By contrast, the effect of a city's age structure on its economic growth has been a hitherto largely neglected area of research. This paper hypothesizes that cities with more working-age adults are likely to grow faster than cities with more children or seniors. The paper sets out the potential channels through which such differential growth may occur. Using data from a variety of historical and contemporary sources, it shows that there exists marked variation in the age structure of the world's largest cities, across cities and over time. It then studies how age structure affects economic growth for a global cross-section of mega-cities. Using various identification strategies, the analysis finds that mega-cities with higher dependency ratios, that is, with more children and/or seniors per working-age adult, grow significantly slower. Such effects are particularly pronounced for cities with high shares of children. This result appears to be driven mainly by the direct, negative effects of a higher dependency ratio on the size of the working-age population and the indirect effects on work hours and productivity for working-age adults within a city.


Book
Applied Analysis of Ordinary Differential Equations
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ISBN: 3039217275 3039217267 Year: 2019 Publisher: MDPI - Multidisciplinary Digital Publishing Institute

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One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon this spirit: combining analysis with the applications of ordinary differential equations (ODEs). ODEs arise across a spectrum of applications in physics, engineering, geophysics, biology, chemistry, economics, etc., because the rules governing the time-variation of relevant fields is often naturally expressed in terms of relationships between rates of change. ODEs also emerge in stochastic models—for example, when considering the evolution of a probability density function—and in large networks of interconnected agents. The increasing ease of numerically simulating large systems of ODEs has resulted in a plethora of publications in this area; nevertheless, the difficulty of parametrizing models means that the computational results by themselves are sometimes questionable. Therefore, analysis cannot be ignored. This book comprises articles that possess both interesting applications and the mathematical analysis driven by such applications.


Book
Population Ecology of the Cooperatively Breeding Acorn Woodpecker. (MPB-24), Volume 24
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ISBN: 0691209626 Year: 2020 Publisher: Princeton, NJ : Princeton University Press,

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Ever since the acorn woodpecker was observed and described by Spanish explorers, its behavior--particularly the unique habit of caching acorns in specialized storage trees or granaries--has impressed observers. Acorn woodpeckers are also one of the few temperate zone species in which young are reared communally in family groups. This demographic study investigates the complexities of acorn storage and group living in acorn woodpeckers at Hastings Reservation in central coastal California. It is one of the most thorough studies of any avian social system to date.


Book
The Dynamics of Arthopod Predator-Prey Systems. (MPB-13), Volume 13
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ISBN: 0691209960 Year: 1978 Publisher: Princeton, N.J. : Baltimore, Md. : Princeton University Press, Project MUSE,

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In this study of arthropod predador-prey systems Michael Hassell shows how many of the components of predation may be simply modeled in order to reveal their effects on the overall dynamics of the interacting populations. Arthropods, particularly insects, make ideal subjects for such a study because their generation times are characteristically short and many have relatively discrete generations, inviting the use of difference equation models to describe population changes. Using analytical models framed in difference equations, Dr. Hassell is able to show how the detailed biological processes of insect predator-prey (including host-parasitoid) interactions may be understood. Emphasizing the development and subsequent stability analysis of general models, the author considers in detail several crucial components of predator-prey models: the prey's rate of increase as a function of density, non-random search, mutual interference, and the predator's rate of increase as a function of predator survival and fecundity. Drawing on the correspondence between the models and field and laboratory data, Dr. Hassell then discusses the practical implications for biological pest control and suggests how such models may help to formulate a theoretical basis for biological control practices.


Book
Models of Delay Differential Equations
Authors: --- ---
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering

Keywords

Research & information: general --- Mathematics & science --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation


Book
Mathematical Tools for Understanding Infectious Disease Dynamics
Authors: --- ---
ISBN: 1283578751 9786613891204 1400845629 9781400845620 9781283578752 9780691155395 0691155399 Year: 2012 Publisher: Princeton, NJ

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Mathematical 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 epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout

Keywords

Epidemiology --- Communicable diseases --- Contagion and contagious diseases --- Contagious diseases --- Infectious diseases --- Microbial diseases in human beings --- Zymotic diseases --- Mathematical models --- Mathematical models. --- Diseases --- Infection --- Epidemics --- Public health --- Bayesian statistical inference. --- ICU model. --- Markov chain Monte Carlo method. --- Markov chain Monte Carlo methods. --- ReedІrost epidemic. --- age structure. --- asymptotic speed. --- bacterial infections. --- biological interpretation. --- closed population. --- compartmental epidemic systems. --- consistency conditions. --- contact duration. --- demography. --- dependence. --- disease control. --- disease outbreaks. --- disease prevention. --- disease transmission. --- endemic. --- epidemic models. --- epidemic outbreak. --- epidemic. --- epidemiological models. --- epidemiological parameters. --- epidemiology. --- general epidemic. --- growth rate. --- homogeneous community. --- hospital infections. --- hospital patients. --- host population growth. --- host. --- human social behavior. --- i-states. --- individual states. --- infected host. --- infection transmission. --- infection. --- infectious disease epidemiology. --- infectious disease. --- infectious diseases. --- infectious output. --- infective agent. --- infectivity. --- intensive care units. --- intrinsic growth rate. --- larvae. --- macroparasites. --- mathematical modeling. --- mathematical reasoning. --- maximum likelihood estimation. --- microparasites. --- model construction. --- outbreak situations. --- outbreak. --- pair approximation. --- parasite load. --- parasite. --- population models. --- propagation speed. --- reproduction number. --- separable mixing. --- sexual activity. --- stochastic epidemic model. --- structured population models. --- susceptibility. --- vaccination.


Book
Models of Delay Differential Equations
Authors: --- ---
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering

Keywords

delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation

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