Computational Methods for Biological Models (Studies in Computational Intelligence, 1109)

✍ Scribed by Harendra Singh (editor), Hemen Dutta (editor)

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 254
• Edition: 1st ed. 2023
• Category: Library

✦ Synopsis

This book discusses computational methods related to biological models using mathematical tools and techniques. The book chapters concentrate on numerical and analytical techniques that provide a global solution for biological models while keeping long-term benefits in mind. The solutions are useful in closely understanding biological models, and the results will be very useful for mathematicians, engineers, doctors, scientists and researchers working on real-life biological models. This book provides significant and current knowledge of biological models related to real-life applications. The book covers both methods and applications.

✦ Table of Contents

Preface
Contents
About the Editors
Exponential-Time-Differencing Method for the Solution of Diffusive HIV-I Model
1 Introduction
2 Numerical Techniques for Reaction-Diffusion Problems
2.1 Spectral Method for Spatial Discretization
2.2 The ETDRK4 Method
3 The HIV-I Model and Its Stability Analysis
4 Numerical Results and Discussions
4.1 One Dimensional Case
4.2 Two Dimensional Case
5 Conclusion
References
An Effective Technique for Solving a Model Describing Biological Species Living Together
1 Introduction
2 Development of the Methodology
2.1 Type-I
2.2 Type-II
3 Implementation and Numerical Results
4 Conclusion
References
Numerical Solution for a Tumor Cells Dynamics Within Their Micro-environment
1 Introduction
2 Mathematical Analysis
2.1 Solution Continuously Depending on the Data
2.2 Local Stability
2.3 Hopf Bifurcation Analysis
2.4 Global Stability Analysis
3 Derivation and Analysis of the Numerical Method
4 Numerical Results and Discussions
5 Conclusion
References
A Mathematical Model to Study Regulatory Properties and Dynamical Behaviour of Glycolytic Pathway Using Bifurcation Analysis
1 Introduction
2 Glycolytic Pathway, Mass Balance Equations, and S-System Representation
3 Interrelation Between Certain Parameters
4 Bifurcation Analysis of the Glycolytic Pathway
5 Second Pathway
5.1 When Forcing Coefficient is Equal to Zero i.e. f0 = 0
5.2 When Forcing Coefficient is Not Equal to Zero i.e. f0 neq0
6 Conclusion
7 Future Work
References
On Solutions of Biological Models Using Reproducing Kernel Hilbert Space Method
1 Introduction
2 Useful Mathematical Concepts
3 The RKHS Approach
4 Analysis of Convergence
5 Numerical Experiments
6 Computing Outcomes and Analysis
7 Conclusion
References
A Study of the Fractional Tumour–Immune Unhealthy Diet Model Using the Pseudo-operational Matrix Method
1 Introduction
2 Preliminaries
3 Fractional TIUNHD Model
4 Stability
5 Function Approximation
6 Pseudo-operational Matrix
7 Numerical Method to Solve the Fractional TIUNHD Model with Caputo's Derivative
8 Discussion of Numerical Results
9 Conclusion
References
Analysis of a Fractional Stage-Structured Model With Crowley–Martin Type Functional Response by Lagrange Polynomial Based Method
1 Introduction
2 Preliminaries
3 Mathematical Model Formulation
4 Boundedness
5 Existence and Uniqueness of Solutions of the Model
6 Existence and Stability of the Points of Equilibrium of the System (4)
6.1 Existence of Points of Equilibrium
6.2 Stability Analysis
7 Numerical Simulation
8 Conclusion
References
Qualitative Theory and Approximate Solution to Norovirus Model Under Non Singular Kernel Type Derivatives
1 Introduction
2 Formulation of Proposed Model
3 Preliminaries
4 Theoretical Results by Using CF Concept
5 Computational Results of (2)
6 Results and Discussion
7 Setting of Model (2) in Caputo and Atangana-Baleanu Piecewise Equations Fractional Derivative
8 Qualitative Analysis of (2) Using Piecewise Derivative
9 Approximate Results Using Piecewise Derivative Concept
10 Numerical Simulation and Discussion
11 Suberization of This Work
References
Study of the SIRI Model Utilizing the Caputo Derivative
1 Introduction
2 Fractional Calculus Operators
3 Fractional SIRI Model Under Caputo Operator
4 Stability Investigations
5 Results and Discussions
5.1 Solution Procedure
6 Conclusion
References
Implementation of Vaccination in an Epidemic Model for COVID-19
1 Introduction
2 Mathematical Hypothesis
3 Mathematical Model for Vaccination Epidemic Model
3.1 The Mathematical Equation of the Model
3.2 Mathematical Analysis
3.3 Positivity and Boundedness of the Solutions
4 Basic Reproduction Number
5 Stability Analysis
6 Global Stability for Infection-Free Equilibrium
7 Convergence Theorem for Lyapunov Stability
8 Global Stability for Endemic Equilibrium
9 Simulation and Discussion of Results
10 Limitations of the Model
11 Conclusion and Future Scope
References