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Spatiotemporal Patterns in Ecology and Epidemiology

Theory, Models, and Simulation

By Horst Malchow, Sergei V. Petrovskii, Ezio Venturino

Series Editor: Jonathan L. Gross, Suzanne Lenhart, Philip K. Maini, Alison M. Etheridge, Eberhard O. Voit, Shoba Ranganathan, Hershel Safer

Published December 26th 2007 by Chapman and Hall/CRC – 464 pages

Series: Chapman & Hall/CRC Mathematical & Computational Biology

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Description

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.

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

Name: Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation (Hardback) – Chapman and Hall/CRC 
Description: By Horst Malchow, Sergei V. Petrovskii, Ezio VenturinoSeries Editor: Jonathan L. Gross, Suzanne Lenhart, Philip K. Maini, Alison M. Etheridge, Eberhard O. Voit, Shoba Ranganathan, Hershel Safer. 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...
Categories: Epidemiology, Mathematical Biology