Spatiotemporal Patterns in Ecology and Epidemiology

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

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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 more

Product details

  • Hardback | 464 pages
  • 150 x 226 x 26mm | 458.14g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 140 black & white illustrations, 17 colour illustrations, 2 black & white tables, 24 black & white halftones
  • 1584886749
  • 9781584886747
  • 2,423,265

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 Indexshow more