Computational and Mathematical Models in Biology (Nonlinear Systems and Complexity, 38)

✍ Scribed by Carla M.A. Pinto (editor), Clara Mihaela Ionescu (editor)

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 331
• Edition: 1st ed. 2023
• Category: Library

✦ Table of Contents

Contents
1 Numerical Simulations for Viscous Reactive Micropolar Real Gas Flow
1.1 Micropolar Fluids
1.1.1 Generalization of the Model in the Thermodynamic Sense
1.1.2 Literature Review
1.2 Mathematical Model for Micropolar Reactive Fluid
1.2.1 Micropolar Real Gas
1.2.2 One Dimensional Model
1.2.3 Reactive Gas
1.3 Local Existence of Generalized Solution
1.4 Approximate Solutions
1.5 Numerical Solution of the Model
1.5.1 Dependence of the Numerical Solution on the Initial Conditions
1.6 Conclusion
References
2 Digital Operators and Discrete Equations as Computational Tools
2.1 Introduction
2.2 Discrete Spaces and Digital Operators
2.3 Solvability of Discrete Equations and Discrete Boundary Value Problems
2.3.1 Periodic Wave Factorization
2.3.2 Solvability Conditions
2.3.3 Boundary Conditions
2.3.4 Classical Variant: The Dirichlet Discrete Boundary Condition
2.3.5 Nonlocal Discrete Boundary Condition
2.4 Continuous Boundary Value Problems
2.4.1 The Dirichlet Condition
2.4.2 Integral Condition
2.5 Error Estimates
2.5.1 The Discrete Dirichlet Problem
2.5.2 Nonlocal Discrete Boundary Value Problem
2.6 Conclusion
References
3 Lipschitz Quasistability of Impulsive Cohen–Grossberg Neural Network Models with Delays and Reaction-Diffusion Terms
3.1 Introduction
3.2 Model Description and Preliminaries
3.3 Uniform Lipschitz Quasistability Results
3.4 Examples
3.5 Concluding Notes
References
4 Rate-Induced Tipping and Chaos in Models of Epidemics
4.1 Introduction
4.1.1 Outline
4.2 Preliminaries
4.3 Rate-Induced Tipping
4.3.1 No Rate-Induced Tipping in a Smooth Unfolding of a Codimension Two Bifurcation of the DFE
4.3.2 Rate-Induced Tipping in a Non-smooth Unfolding
4.4 Periodically Forced Chaos
4.4.1 Chaos Between Two Endemic Equilibria in a Smooth SIR Model with Vital Dynamics
4.4.2 Chaos Between DFE and ENE in a Non-smooth SIRS Model
4.5 Conclusion
References
5 Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems
5.1 Introduction
5.2 The Dynamics Near the Infinity
5.2.1 The Poincaré Compactification
5.2.2 Application of the Poincaré Compactification to Predator-Prey Systems
A Kolmogorov System Obtained from the Rosenzweig-MacArthur System
A Kolmogorov System Obtained from the Spatial Lotka-Volterra Systems
5.3 A Desingularization Technique
5.3.1 Theoretical Introduction of the Directional Blow-Ups
Homogeneous Vertical Blow-Up
Homogeneous Horizontal Blow-Up
5.3.2 Application of the Directional Blow-Ups to Predator-Prey Systems
A Kolmogorov System Obtained from the Rosenzweig-MacArthur System
A Kolmogorov System Obtained from the Spatial Lotka-Volterra Systems
5.4 Conclusions
References
6 A Lotka–Volterra-Type Model Analyzed Through Different Techniques
6.1 Introduction
6.2 The Modified Lotka–Volterra Model
6.2.1 Model Description
6.2.2 Nonnegativity of Solutions and Conservation Law
6.2.3 Stability Analysis
6.2.4 Graphical Analysis
6.3 Euler's Numerical Scheme
6.3.1 Model Discretization
6.3.2 Nonnegativity of Solutions and Conservation Law
6.3.3 Stability Analysis
6.3.4 Graphical Analysis
6.4 Mickens' Numerical Scheme
6.4.1 Model Discretization
6.4.2 Nonnegativity of Solutions and Conservation Law
6.4.3 Stability Analysis
6.4.4 Graphical Analysis
6.5 Fractional Calculus
6.5.1 Preliminaries on FC
6.5.2 Model Description
6.5.3 Existence and Uniqueness of Nonnegative Solutions
6.5.4 The Conservation Law
6.5.5 Stability Analysis
6.5.6 Graphical Analysis
6.6 Conclusion
References
7 From Duffing Equation to Bio-oscillations
7.1 Introduction
7.2 Genomic System
7.3 Genetic Systems of Low Dimensionality
7.3.1 Two-Dimensional Systems
7.4 Three-Dimensional Systems
7.5 Four-Dimensional System
7.5.1 Four-Dimensional System: 3+1
7.6 Artificial Neural Networks
7.7 Five-Dimensional (5D) Systems
7.8 Six-Dimensional (6D) Systems
7.9 Conclusions
References
8 Impact of Travel on Spread of Infection
8.1 Introduction
8.2 SIR Model with Two Different Travel Patterns
8.3 Theoretical Analysis of the SSIR Model
8.3.1 Positivity of Solutions
8.3.2 Equilibrium Points
8.3.3 Stability Analysis
8.3.4 Basic Reproduction Number
8.3.5 Transition Between Two Susceptible Sub-cohorts
8.4 Numerical Simulations
8.4.1 Selection of Parameters
8.4.2 Simulations for SIR and SSIR Models
8.5 Discussion
8.6 Conclusions
References
9 Mathematical Oncology: Tumor Evolution Models
9.1 Introduction
9.2 Methods
9.2.1 Hahnfeldt Model
9.2.2 Minimal Bilinear Model
9.2.3 Extended Bilinear Model
9.2.4 Predatory-Predator Model Without Delay in Conversion of Resting Cells of Hunting Cells
9.2.5 Predatory-Predator Model with Delay in Conversion of Resting Cells of Hunting Cells
9.2.6 Fractional-Order Models
9.3 Results
9.4 Discussion
9.5 Conclusions
References
10 A Model-Based Optimal Distributed Predictive Management of Multidrug Infusion in Lung Cancer Patient Therapy
10.1 Introduction
10.2 Model Description
10.3 Predictive Control Strategy
10.4 Optimality for Distributed Multidrug Predictive Control
10.5 Results and Discussion
10.6 Conclusions
References
11 Analysis of a Robust Fractional Order Multivariable Controller for Combined Anesthesia and Hemodynamic Stabilization
11.1 Introduction
11.2 Performance Specifications for Designing the FO-PIDs
11.3 Design Principles for Multivariable Robust FO-PID Controllers
11.4 FO-PIDs for Hemodynamic and Anesthesia Control
11.5 Robustness Analysis
11.6 Conclusion
References
12 Fractional-Order Event-Based Control Meets Biomedical Applications
12.1 Introduction
12.2 Suitability of Fractional Calculus and Event-Based Control in Biomedical Applications
12.3 Event-Based Control
12.4 Implementation Strategies of Event-Based Fractional-Order Control
12.4.1 The FOPID Controller
12.4.2 The FOIMC Controller
12.5 Case Study
12.6 Conclusions and Future Directions
References
13 Numerical Simulation and Validation of a Nonlinear Differential System for Drug Release Boosted by Light
13.1 Introduction
13.2 Preliminaries
13.3 Numerical Scheme
13.4 Numerical Examples: Convergence Behavior
13.5 Validation: Simulation Results Versus Experimental Data
13.5.1 Drug Release Enhanced by Light
13.5.2 In Vitro Experiment
13.5.3 Simulation Versus Experimental Data
13.6 Conclusions and Future Work
References
Index