Jianhong Wu – författare

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Features modern research and methodology on the spread of infectious diseases and showcases a broad range of multi-disciplinary and state-of-the-art techniques on geo-simulation, geo-visualization, remote sensing, metapopulation modeling, cloud computing, and pattern analysisGiven the ongoing risk of infectious diseases worldwide, it is crucial to develop appropriate analysis methods, models, and tools to assess and predict the spread of disease and evaluate the risk. Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases features mathematical and spatial modeling approaches that integrate applications from various fields such as geo-computation and simulation, spatial analytics, mathematics, statistics, epidemiology, and health policy. In addition, the book captures the latest advances in the use of geographic information system (GIS), global positioning system (GPS), and other location-based technologies in the spatial and temporal study of infectious diseases.Highlighting the current practices and methodology via various infectious disease studies, Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases features: Approaches to better use infectious disease data collected from various sources for analysis and modeling purposesExamples of disease spreading dynamics, including West Nile virus, bird flu, Lyme disease, pandemic influenza (H1N1), and schistosomiasisModern techniques such as Smartphone use in spatio-temporal usage data, cloud computing-enabled cluster detection, and communicable disease geo-simulation based on human mobilityAn overview of different mathematical, statistical, spatial modeling, and geo-simulation techniques Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases is an excellent resource for researchers and scientists who use, manage, or analyze infectious disease data, need to learn various traditional and advanced analytical methods and modeling techniques, and become aware of different issues and challenges related to infectious disease modeling and simulation. The book is also a useful textbook and/or supplement for upper-undergraduate and graduate-level courses in bioinformatics, biostatistics, public health and policy, and epidemiology.

The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X.Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

​This collection covers a wide range of topics of infinitedimensional dynamical systems generated by parabolic partial differentialequations, hyperbolic partial differential equations, solitary equations,lattice differential equations, delay differential equations, and stochasticdifferential equations.Infinite dimensional dynamical systems are generated byevolutionary equations describing the evolutions in time of systems whosestatus must be depicted in infinite dimensional phase spaces. Studying thelong-term behaviors of such systems is important in our understanding of theirspatiotemporal pattern formation and global continuation, and has been amongmajor sources of motivation and applications of new developments of nonlinearanalysis and other mathematical theories. Theories of the infinite dimensionaldynamical systems have also found more and more important applications inphysical, chemical, and life sciences.This book collects 19 papers from 48 invited lecturers tothe International Conference on Infinite Dimensional Dynamical Systems held atYork University, Toronto, in September of 2008. As the conference was dedicatedto Professor George Sell from University of Minnesota on the occasion of his70th birthday, this collection reflects the pioneering work and influence ofProfessor Sell in a few core areas of dynamical systems, includingnon-autonomous dynamical systems, skew-product flows, invariant manifoldstheory,  infinite dimensional dynamicalsystems, approximation dynamics, and fluid flows.​

This book provides a crash course on various methods from the bifurcationtheory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self containedso the readers will find in this book all relevant materials inbifurcation, dynamical systems with symmetry, functional differentialequations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

This book provides a crash course on various methods from the bifurcationtheory of Functional Differential Equations (FDEs).

?This collection covers a wide range of topics of infinitedimensional dynamical systems generated by parabolic partial differentialequations, hyperbolic partial differential equations, solitary equations,lattice differential equations, delay differential equations, and stochasticdifferential equations.

This monograph introduces some current developments in the modelling of the spread of tick-borne diseases. Effective modelling requires the integration of multiple frameworks. Here, particular attention is given to the previously neglected issues of tick developmental and behavioral diapause, tick-borne pathogen co-feeding transmission, and their interactions. An introduction to the required basics of structured population formulations and delay differential equations is given, and topics for future study are suggested. The described techniques will also be useful in the study of other vector-borne diseases. The ultimate aim of this project is to develop a general qualitative framework leading to tick-borne disease risk predictive tools and a decision support system.The target audience is mathematical biologists interested in modelling tick population dynamics and tick-borne disease transmission, and developing computational tools for disease prevention and control.

Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research.

Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research.

This volume addresses SDG 3 from a mathematical standpoint, sharing novel perspectives of existing communicable disease modelling technologies of the next generation and disseminating new developments in modelling methodologies and simulation techniques. These methodologies are important for training and research in communicable diseases and can be applied to other threats to human health.  The contributions contained in this collection/book cover a range of modelling techniques that have been and may be used to support decision-making on critical health related issues such as:Resource allocationImpact of climate change on communicable diseasesInteraction of human behaviour change, and disease spreadDisease outbreak trajectories projectionPublic health interventions evaluationPreparedness and mitigation of emerging and re-emerging infectious diseases outbreaksDevelopment of vaccines and decisions around vaccine allocation and optimizationThe diseases and public health issues in this volume include, but are not limited to COVID-19, HIV, Influenza, antimicrobial resistance (AMR), the opioid epidemic, Lyme Disease, Zika, and Malaria. In addition, this volume compares compartmental models, agent-based models, machine learning and network. Readers have an opportunity to learn from the next generation perspective of evolving methodologies and algorithms in modelling infectious diseases, the mathematics behind them, the motivation for them, and some applications to supporting critical decisions on prevention and control of communicable diseases.This volume was compiled from the weekly seminar series organized by the Mathematics for Public Health (MfPH) Next Generation Network. This network brings together the next generation of modellers from across Canada and the world, developing the latest mathematical models, modeling methodologies, and analytical and simulation tools for communicable diseases of global public health concerns. The weekly seminar series provides a unique forum for this network and their invited guest speakers to share their perspectives on the status and future directions of mathematics of public health.

This volume addresses SDG 3 from a mathematical standpoint, sharing novel perspectives of existing communicable disease modelling technologies of the next generation and disseminating new developments in modelling methodologies and simulation techniques. These methodologies are important for training and research in communicable diseases and can be applied to other threats to human health.  The contributions contained in this collection/book cover a range of modelling techniques that have been and may be used to support decision-making on critical health related issues such as:Resource allocationImpact of climate change on communicable diseasesInteraction of human behaviour change, and disease spreadDisease outbreak trajectories projectionPublic health interventions evaluationPreparedness and mitigation of emerging and re-emerging infectious diseases outbreaksDevelopment of vaccines and decisions around vaccine allocation and optimizationThe diseases and public health issues in this volume include, but are not limited to COVID-19, HIV, Influenza, antimicrobial resistance (AMR), the opioid epidemic, Lyme Disease, Zika, and Malaria. In addition, this volume compares compartmental models, agent-based models, machine learning and network. Readers have an opportunity to learn from the next generation perspective of evolving methodologies and algorithms in modelling infectious diseases, the mathematics behind them, the motivation for them, and some applications to supporting critical decisions on prevention and control of communicable diseases.This volume was compiled from the weekly seminar series organized by the Mathematics for Public Health (MfPH) Next Generation Network. This network brings together the next generation of modellers from across Canada and the world, developing the latest mathematical models, modeling methodologies, and analytical and simulation tools for communicable diseases of global public health concerns. The weekly seminar series provides a unique forum for this network and their invited guest speakers to share their perspectives on the status and future directions of mathematics of public health.

This volume gathers contributions on modelling, analytical, numerical, and computational aspects of structured population dynamics and delay or functional equations in general, giving rise to infinite-dimensional dynamical systems. Starting from the basics, the most recent advances are discussed relying on functional analysis and semigroup theory, aiming at stability and bifurcation analysis also with the help of computational tools developed from advanced numerical analysis. The book serves as a useful tool for graduate students and researchers in the fields of structured population dynamics and time delay systems, with an interdisciplinary approach ranging from the abstract (theory) to the concrete (implementation).

In the design of a neural network, either for biological modeling, cognitive simulation, numerical computation or engineering applications, it is important to investigate the network's computational performance which is usually described by the long-term behaviors, called dynamics, of the model equations. The purpose of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons from the viewpoint of dynamical systems.

The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X.Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.

The express delivery industry plays a pivotal role in fostering social and economic advancements. The goal is to build a theory of operations for this industry that can facilitate management reform by improving standardization, optimizing overall functionality, and increasing efficiency