Current Trends in Dynamical Systems in Biology and Natural Sciences

Preface
Contents
About the Editors
Modelling Ecological Systems from a Niche Theory to Lotka-Volterra Equations
	1 Introduction
	2 Definition of Lotka-Volterra Dynamical Model for an Ecological Niche
	3 Lotka-Volterra Dynamical Model for Interacting Niches in a Ecosystem
	4 The Master Equation and the Fluctuations in the Populations
	5 Numerical Simulations
	6 Conclusions
	References
Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species
	1 Introduction
	2 Model and Method
	3 Topological Characteristics of Spatial Pattern
		3.1 The Number of Objects
		3.2 The Fragmentation Rate and the Density of Objects
	4 Sensitivity of Spatial Pattern to the Cut-Off Parameter
	5 Reconstruction of Spatial Patterns from Sparse Data
	6 Conclusions
	References
Collocation Techniques for Structured Populations Modeled by Delay Equations
	1 Introduction
	2 Collocation to Improve Continuation
		2.1 Prototype Problem
			2.1.1 State-Dependency
	3 Collocation to Compute Periodic Solutions
		3.1 Experimental Results
	4 Conclusions and Future Work
	References
Herding Induced by Encounter Rate, with Predator Pressure Influencing Prey Response
	1 Introduction
	2 Intraspecific Interaction
	3 Modification of Well-Mixedness as a Result of Herding
	4 Interspecific Interactions
	5 The Specialist Predator Model
		5.1 Boundedness
		5.2 The No-Herding Counterpart of (13)
	6 The Generalist Predator Model
		6.1 Boundedness
		6.2 The No-Herding Counterpart of (32)
	7 Numerical Simulations
		7.1 The Specialist Predator Model
		7.2 The Generalist Predator Model
	8 Conclusions
	References
Harvesting Policies with Stepwise Effort and Logistic Growth in a Random Environment
	1 Introduction
	2 Variable Effort Optimal Policy
	3 Constant Effort Optimal Policy
	4 Comparison of Policies
	5 Conclusions
	References
Mathematical Modeling of the Population Dynamics of Long-Lived Raptor Species: Application to Eurasian Black Vulture Colonies
	1 Introduction
	2 The Model
	3 Estimation of p
	4 Application to Eurasian Black Vulture Colonies
	5 Concluding Remarks
	References
On the Role of Inhibition Processes in Modeling Control Strategies for Composting Plants
	1 Introduction
	2 The Aerobic Biodegradation Model
	3 Optimal Aeration Control Problem
	4 Modeling Oxygen Uptake
	5 Numerical Investigation of the Optimal Control Problem
		5.1 Optimal Time-Profiles
		5.2 Performance Indices
	6 The Bioeconomic Model
	7 Numerical Investigations of the Bioeconomic Problem
	8 Concluding Remarks
	References
Optimal Control of Invasive Species with Budget Constraint: Qualitative Analysis and Numerical Approximation
	1 Introduction
	2 An Optimal Control Model for Invasive Species
		2.1 Model Formulation
		2.2 First Order Necessary Conditions for Optimality
	3 The State-Control Optimality System
		3.1 Phase-Space Analysis in the State-Control Plane
		3.2 Analysis of the Optimal Solution Through the Phase-Space Analysis
	4 Numerical Approximation of the Temporal Dynamics
		4.1 Numerical Results
	5 Conclusions
	References
A Shape Optimization Problem Concerning the Regional Control of a Class of Spatially Structured Epidemics: Sufficiency Conditions
	1 Introduction
	2 Preliminaries
		2.1 A Spatially Structured Man-Environment-Man Epidemic Model
		2.2 A Regional Optimal Control Problem
	3 Dual Dynamic Programming Method for Problem (P)
	4 Sufficient Optimality Conditions
	5 Sufficient Conditions for -Optimality
		5.1 -Optimality
		5.2 Computational Algorithm
	6 Conclusions
	References
The Interplay Between Voluntary Vaccination and Reduction of Risky Behavior: A General Behavior-Implicit SIR Model for Vaccine Preventable Infections
	1 Introduction
	2 The SIR Model: Mandatory vs. Voluntary Vaccination
		2.1 The Case of Constant Vaccination Coverage
		2.2 Voluntary Vaccination: A Phenomenological Model
		2.3 Modeling the Information Index M(t)
	3 Behavior–Modulated Contact Rate
		3.1 Extending the Capasso–Serio Behavioral Model
	4 A General SIR Model Embedding Behavioral Feedbacks on Both Vaccination Propensity and the Contact Rate
		4.1 Modelling Human Behavior and Its Implications for Infection Control
		4.2 Behavioural Responses and Infection Dynamics
	5 Concluding Remarks
	References
PC-Based Sensitivity Analysis of the Basic Reproduction Number of Population and Epidemic Models
	1 Introduction
	2 The Basic Reproduction Number
		2.1 Definition
		2.2 Approximation
	3 PC-Based Global Sensitivity Analysis
		3.1 PCEs
		3.2 Sobol\' Decomposition and PC-Based Sobol\' Indices
	4 Examples
		4.1 Influenza Epidemic Model with Vaccination [27, 28]
		4.2 Age-Structured Epidemic Model [21]
	5 Conclusions
	References
Linear Dynamics of mRNA Expression and Hormone Concentration Levels in Primary Cultures of Bovine Granulosa Cells
	1 Introduction
	2 Experimental Materials and Methods
		2.1 Datasets
	3 Regulatory Function Approach: Gene and Hormone Regulatory Matrices (GHRMs)—Effect of Treatment on the Strength of the Interactions
		3.1 GHRM: Numerical Example
	4 Correlation Matrices
	5 Comparison Between GHRMs for Different Treatments
		5.1 Comparison Between GHRMs for Different Treatments for the Secondary Follicles
		5.2 Comparison Between GHRMs for Different Treatments for the Dominant Follicles
		5.3 Comparison Between Secondary and Dominant Follicles for Different Treatments Using GHRMs
	6 Conclusions
	References