Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation

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ISBN 9781584886747
Cat# C6749

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Features

  • Focuses on mathematical modeling and numerical simulations using basic conceptual models of population dynamics
  • Covers a wide range of nonspatial approaches to population dynamics and epidemiology, from elementary to state-of-the-art models
  • Introduces ecoepidemiological models where both the basic interspecies interactions of population dynamics and the impact of an infectious disease are considered within the same theoretical framework
  • Explores both deterministic and stochastic approaches to spatiotemporal pattern formation in population dynamics and epidemiology
  • Includes a CD-ROM with examples of MATLAB® codes for computer simulation of population dynamics
  • Summary

    Although the spatial dimension of ecosystem dynamics is now widely recognized, the specific mechanisms behind species patterning in space are still poorly understood and the corresponding theoretical framework is underdeveloped. Going beyond the classical Turing scenario of pattern formation, Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation illustrates how mathematical modeling and numerical simulations can lead to greater understanding of these issues. It takes a unified approach to population dynamics and epidemiology by presenting several ecoepidemiological models where both the basic interspecies interactions of population dynamics and the impact of an infectious disease are explicitly considered.

    The book first describes relevant phenomena in ecology and epidemiology, provides examples of pattern formation in natural systems, and summarizes existing modeling approaches. The authors then explore nonspatial models of population dynamics and epidemiology. They present the main scenarios of spatial and spatiotemporal pattern formation in deterministic models of population dynamics. The book also addresses the interaction between deterministic and stochastic processes in ecosystem and epidemic dynamics, discusses the corresponding modeling approaches, and examines how noise and stochasticity affect pattern formation.

    Reviewing the significant progress made in understanding spatiotemporal patterning in ecological and epidemiological systems, this resource shows that mathematical modeling and numerical simulations are effective tools in the study of population ecology and epidemiology.

    Table of Contents

    Introduction
    Ecological Patterns in Time and Space
    Local structures
    Spatial and spatiotemporal structures
    An Overview of Modeling Approaches
    Models of temporal dynamics
    Classical One Population Models
    Isolated populations models
    Migration models
    A glance at discrete models
    A peek into chaos
    Interacting Populations
    A two-species predator-prey population model
    The classical Lotka–Volterra model
    Other types of ecosystems
    Global stability
    A food web
    More about chaos
    Age-dependent populations
    A Case Study: Biological Pest Control in Vineyards
    The first model
    A more sophisticated model
    Modeling the ballooning effect
    Epidemic Models
    Basic epidemic models
    Other classical epidemic models
    An age- and stage-dependent epidemic system
    A case study: the Aujeszky disease
    Analysis of a disease with two states
    Ecoepidemic Systems
    Prey–diseased-predator interactions
    Predator–diseased-prey interactions
    Diseased competing species models
    Ecoepidemics models of symbiotic communities
    Diseased symbiotic species systems
    Spatiotemporal Dynamics and Pattern Formation: Deterministic Approach
    Spatial Aspect: Diffusion as a Paradigm
    Instabilities and Dissipative Structures
    Turing patterns
    Differential flow instability
    An ecological example: semiarid vegetation patterns
    Concluding remarks
    Patterns in the Wake of Invasion
    Invasion in a predator–prey system
    Dynamical stabilization of an unstable equilibrium
    Patterns in a competing species community
    Concluding remarks
    Biological Turbulence
    Self-organized patchiness and the wave of chaos
    Spatial structure and spatial correlations
    Ecological implications
    Concluding remarks
    Patchy Invasion
    The Allee effect, biological control, and 1-D patterns of species invasion
    Invasion and biological control in the 2-D case
    Biological control through infectious diseases
    Concluding remarks
    Spatiotemporal Patterns and Noise
    A Generic Model of Stochastic Population Dynamics
    Noise-Induced Pattern Transitions
    Transitions in a patchy environment
    Transitions in a uniform environment
    Epidemic Spread in a Stochastic Environment
    The model
    Strange periodic attractors in the lytic regime
    Local dynamics in the lysogenic regime
    The deterministic and stochastic spatial dynamics
    The local dynamics with deterministic switch from lysogeny to lysis
    The spatiotemporal dynamics with switches from lysogeny to lysis
    Noise-Induced Pattern Formation
    References
    Index

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    C6749_CD.zip Cross Platform March 18, 2014