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

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