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