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Submit a ProposalMathematical Techniques in Disease and Fluid Dynamics Modeling
One Line Description
By integrating classical mathematical foundations with cutting-edge machine learning and high-performance computing, this definitive guide provides the complete toolkit needed to translate complex fluid mechanics and epidemiological theory into actionable, real-world solutions.
Description
The complexities of disease dynamics and fluid mechanics pose significant challenges in fields ranging from public health to environmental management. Understanding the spread of infectious diseases, optimizing control strategies, and modeling biological processes require interdisciplinary approaches that combine mathematical modeling, computational tools, and practical applications. This book provides a unified framework that bridges theoretical foundations, computational methods, and practical applications, resolving the disconnect between mathematical modeling and real-world problem-solving by introducing readers to core principles like conservation laws, Navier-Stokes equations, and epidemiological models while advancing their understanding through topics such as bifurcation analysis, stochastic modeling, and machine learning. Practical approaches, including numerical methods, optimization, and data-driven analytics, enable readers to tackle real-world challenges, such as airborne and waterborne pathogen spread, pollution modeling, and vaccination strategies. The book integrates classical techniques like perturbation and fractional calculus with cutting-edge methods like machine learning and high-performance computing, offering a comprehensive toolkit for interdisciplinary research. By combining traditional techniques with contemporary computational tools, this book equips readers to address complex problems in disease and fluid dynamics modeling effectively.
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The complexities of disease dynamics and fluid mechanics pose significant challenges in fields ranging from public health to environmental management. Understanding the spread of infectious diseases, optimizing control strategies, and modeling biological processes require interdisciplinary approaches that combine mathematical modeling, computational tools, and practical applications. This book provides a unified framework that bridges theoretical foundations, computational methods, and practical applications, resolving the disconnect between mathematical modeling and real-world problem-solving by introducing readers to core principles like conservation laws, Navier-Stokes equations, and epidemiological models while advancing their understanding through topics such as bifurcation analysis, stochastic modeling, and machine learning. Practical approaches, including numerical methods, optimization, and data-driven analytics, enable readers to tackle real-world challenges, such as airborne and waterborne pathogen spread, pollution modeling, and vaccination strategies. The book integrates classical techniques like perturbation and fractional calculus with cutting-edge methods like machine learning and high-performance computing, offering a comprehensive toolkit for interdisciplinary research. By combining traditional techniques with contemporary computational tools, this book equips readers to address complex problems in disease and fluid dynamics modeling effectively.
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Author / Editor Details
Reshu Gupta, PhD is an Associate Professor in the Applied Science Cluster at the University of Petroleum and Energy Studies, India. She has published more than 40 articles in international journals and conferences of repute. Her research focuses on numerical analysis, nanofluids, and heat and mass transfer.
Reshu Gupta, PhD is an Associate Professor in the Applied Science Cluster at the University of Petroleum and Energy Studies, India. She has published more than 40 articles in international journals and conferences of repute. Her research focuses on numerical analysis, nanofluids, and heat and mass transfer.
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Table of Contents
Preface
Acknowledgement
Aim and Scope
1. Modeling Disease Transmission via Fluid Dynamics
G. Shirisha and Saroj Revankar
1.1 Introduction
1.1.1 Overview of Disease Transmission
1.1.2 Significance of Fluid Dynamics in Understanding the Movement of Pathogens
1.2 Basic Principles of Fluid Dynamics
1.2.1 Navier-Stokes Equations
1.2.2 Transportation Theorem
1.2.3 Reynolds Transport Theorem
1.2.4 Divergence Theorem
1.2.5 Conservation of Mass
1.2.6 Conversation of Momentum
1.2.7 Equations of Motion
1.3 Intermolecular Aspects of Fluid
1.4 Choosing the Right Frame of Reference
1.5 Non-Dimensionalization in Epidemics
1.6 Inviscid Fluid Assumption in Epidemic Flow
1.7 The External Force
1.8 Comparison of Fluid Flow with Disease Transmission
1.9 Model Formulation
1.10 Numerical Treatment
1.10.1 Governing Equations
1.10.2 NSFD Scheme
1.10.3 Applying NSFD to the Equations
1.10.4 Solution Approach
1.11 Observations
1.11.1 Evolution of Infection Distribution in Space and Time
1.11.2 Infection Spread Dynamics
1.11.3 Impact of Fluid Motion on Disease Transmission
1.11.4 Role of NSFD Scheme
1.11.5 Final Infection Distribution
1.12 Case Studies of Disease Transmission Using Fluid Dynamics
1.12.1 COVID-19 Transmission
1.12.2 Influenza Spread
1.12.3 Measles Transmission
1.12.4 Waterborne Diseases (Cholera)
References
2. The SIR Model and Its Adaptations for Dengue
Naresh Kumar Jothi, Lakshmi A., Sukumaran D., Vivekanandan T. and Saravanakumar G.
2.1 Introduction
2.2 Experimental Methods and Materials
2.3 Stability of the System
2.4 Numerical Simulation
2.5 Conclusion
References
3. A Gompertz Model for the Average and Median Values of the Endometrial Thicknesses of Women Suffering from Abnormal Uterine Bleeding
Lalit Mohan Upadhyaya and Sudhanshu Aggarwal
3.1 Introduction
3.1.1 Abbreviations Used in the Paper
3.2 Data for the Study
3.3 A Gompertz Model for the Measurements of the Average and Median Values of the ET for Patients Suffering with AUB
3.4 Features of the Covariance Matrix of the Proposed Gompertz Model
3.5 Solutions of Some Systems of Differential Equations Associated with the Covariance Matrix A and the Matrix of Its Eigenvectors
3.6 Conclusion
Acknowledgements
References
4. Formulating the Zika Virus Transmission Model
Lakshmi A., Naresh Kumar Jothi, Sukumaran D., Vivekanandan T. and Saravanakumar G.
4.1 Introduction
4.2 The Model of the Equation
4.3 Parameters of the Equations
4.4 Disease Free Equilibrium Points (DFEP)
4.5 Endemic Equilibrium Points
4.6 The Systems Stability
4.6.1 Disease-Free Equilibrium Local Stability
4.6.2 Positivity Solution
4.6.3 Global Stability of Disease Endemicity
4.7 Numerical Analysis
4.8 Conclusion
References
5. Stability Analysis of Human–Dog Rabies Dynamics
Anusha Muruganandham, Naresh Kumar Jothi, Deepa S., Vivekanandan T. and Saravanakumar G.
5.1 Introduction
5.2 Assumption of the Model
5.3 Disease-Free Equilibrium
5.4 Endemic Equilibrium
5.5 Reproduction Number
5.6 Stability of the System
5.6.1 Local Stability of Disease-Free Equilibrium
5.6.2 Global Stability of Endemic Equilibrium
5.7 Theorem
5.8 Conclusion
References
6. Control Strategies and Stability in Diseases Caused by Aedes aegypti
Naresh Kumar Jothi, Anusha Muruganandham, Deepa S., Vivekanandan T. and Saravanakumar G.
6.1 Introduction
6.2 The Mathematical Model
6.3 Model Diagram
6.4 Disease-Free Equilibrium
6.5 Stability of the System
6.6 Global Stability of Endemic Equilibrium
6.7 Theorem
6.8 Numerical Reproductions
6.9 Conclusion
References
7. Ethical Considerations in Mathematical Modeling
Sachin Mishra, Raj Kumar, Sakshi Saxena, Kunj Bihari Pandey and Ajai Singh Yadav
7.1 Introduction
7.2 Theoretical Study of Lubricants and Bearings
7.2.1 Lubricants and Non-Newtonian Lubricants
7.2.2 Externally Pressurized Circular Step Thrust Bearings
7.3 Nomenclature
7.4 Analysis
7.5 Definition of Flow Rate
7.6 Weight Bearing Capacity
7.7 Pressure Distribution
7.8 Lubrication Flow Rate
7.9 Frictional Torque
7.10 Bearing Design
7.11 Results and Discussion
7.12 Conclusion and Future Scope
Bibliography
8. Hyperbolic PDEs in Biofluid Mechanics
Shivani Kumari
Nomenclature
8.1 Introduction
8.2 Theoretical Foundations of Hyperbolic PDEs
8.2.1 Characteristics of Hyperbolic PDEs
8.2.2 Common Hyperbolic PDEs in Biofluid Mechanics
8.2.3 Initial and Boundary Conditions
8.3 Governing Equations in Biofluid Systems
8.3.1 Blood Flow in Arteries
8.3.2 Respiratory System Models
8.3.3 Wave Propagation in Tissues
8.3.4 Cerebrospinal Fluid Flow
8.4 Solution Techniques for Hyperbolic PDEs
8.4.1 Analytical Solutions
8.4.2 Numerical Approaches
8.4.3 Coupled Systems
8.5 Applications and Case Studies
8.5.1 Pulse Wave Propagation in Arterial Networks
8.5.2 Airway Flow Dynamics in Asthma and COPD
8.5.3 Wave-Based Imaging in Medical Diagnostics
8.5.4 Modeling Shock Waves in Biofluids
8.6 Challenges in Biofluid Modeling
8.6.1 Nonlinear Dynamics
8.6.2 Interplay of Scales
8.6.3 Biological Uncertainty and Variability
8.7 Advancements and Future Directions
8.7.1 Computational Innovations
8.7.2 Integration with Experimental Data
8.7.3 Broader Applications
8.8 Conclusion
References
9. Comparative Analysis of Newtonian and Non-Newtonian Blood Flow in Arteries
S. R. Prathiba and A. Karthika
9.1 Introduction
9.2 Composition and Properties of Blood
9.3 Blood Flow in Large Arteries-Newtonian Fluid
9.4 Blood as a Non-Newtonian Fluid
9.4.1 Mild Stenosis
9.4.2 Double Stenoses
9.4.3 Two-Phase Stenosis Model
9.4.4 Inclined Stenosis with Nanoparticles
9.5 Results and Discussion
9.6 Conclusion
Nomenclature
References
10. Models of Tumor-Immune Drug Interaction
Kaushik Dehingia, Animesh Phukan and Lovely Borah
10.1 Introduction
10.2 Preliminaries of Cancer Modeling
10.3 Modeling of Tumor-Immune Interactions
10.4 Mathematical Models with Treatment Strategies
10.5 Other Studies and Approaches
10.6 Conclusion
References
11. Modeling of SARS-CoV-19
Saravanakumar G., Naresh Kumar Jothi, Vadivelu V., Sukumaran D. and Vivekanandan T.
11.1 Introduction
11.2 The Model
11.3 Positivity and Boundedness of the System
11.4 The Basic Reproduction Number
11.5 Numerical Simulations and Discussion
11.6 Conclusion
References
12. Simulation Techniques for Fluid Dynamics Problems
Eny Tayang and Sahin Ahmed
Nomenclature
Abbreviations
12.1 Introduction
12.2 Mathematical Formulation
12.3 Results and Discussion
12.4 Conclusion
Appendix
References
13. Darcy-Forchheimer Hybrid Nanofluid (Blood-Fe2O3+Au) Flow of Bio-Convective Couple Stress Model with Quadratic Thermal Radiation: Optimization Analysis and Homotopy Analysis
Seetalsmita Samal, Surender Ontela, Thirupathi Thumma and Pungja Mushahary
13.1 Introduction
13.2 Mathematical Modeling
13.2.1 Quantities of Physical Interests
13.3 Solution Methodology
13.4 Findings and Analysis
13.5 Optimization Analysis through RSM CCD Approach
13.6 Conclusion
Nomenclature
References
14. Numerical Methods in Fluid Dynamics and Disease Modeling
Anil Nangkar, Sahin Ahmed and Bikash Das
14.1 Introduction
14.2 Mathematical Formulation
14.3 Methodology and Grid Point Analysis
14.4 Results and Discussion
14.5 Conclusion
Nomenclature
Greek Symbols
Subscripts
References
15. Numerical Simulation of Solar PV Panel Thermal Behavior
with Nanofluid Cooling Techniques
Bikash Das, Sahin Ahmed and Anil Nangkar
15.1 Introduction
15.2 PV Panel Geometry
15.3 Mathematical Formulation
15.3.1 Heat Transfer in Solid
15.3.2 Fluid Flow and Heat Transmission in Fluid
15.4 Power Output and Efficiency
15.5 Methodology, Grid Independence Test, and Validation
15.6 Results and Discussion
15.7 Conclusions
Nomenclature
References
16. Applications to Public Health and Environmental Studies
Manjula Kuntigorla, Ega Chandra Shekar, Masma Shaik and Bommareddy Nagalakshmi
16.1 Fluid Dynamics
16.1.1 Importance of Fluid Dynamics
16.1.2 CFD to Environmental Flows
16.1.3 CFD in Groundwater Pollution Repair
16.1.4 CFD to Public Health
16.1.5 Fluid Dynamics in Biology
16.1.6 Fluid Dynamics in Astrophysics
16.1.7 Fluid Dynamics in Oceanography
16.1.8 Fluid Dynamics in Meteorology
16.1.9 Fluid Dynamics Applications in Engineering
16.2 Fluid Dynamics Applications
16.2.1 Aerodynamics in Automotive Design
16.2.2 Weather Prediction
16.2.3 Storm Alerts
16.2.4 Taking to the Skies
16.3 Blood Circulation in Medicine
16.4 Environmental Engineering
16.5 Extraction of Oil and Gas
16.6 Fire Suppression Systems
16.7 Applications of Fluid Dynamics in Systems of Fire Control
16.8 Cooling Mechanisms in Electronics
16.9 Desalination Methods
References
17. Complex Systems and Nonlinear Dynamics
Dahiru Abdurrahman, Maheshwar Pathak and Pratibha Joshi
17.1 Introduction
17.2 Modified Variational Iteration Method
17.3 Applications
17.3.1 Velocity-Vorticity Interaction in 2D Flow
17.3.2 Multi-Population Disease Spread
17.3.3 Viral Infection Dynamics
17.3.4 Transfer of Energy in Turbulence
17.4 Conclusion
References
18. Mathematical Techniques for Environmental Fluid Dynamics
Km Shelly Chaudhary and Lalit Mohan
18.1 Introduction
18.2 Preliminaries of FC
18.3 Solution Process by LADT
18.4 Numerical Application and Results
18.5 Conclusion
References
19. AI-Driven Multimodal Fusion for Predictive Disease Modeling and Clinical Insight Generation
Subhranil Das, Rashmi Kumari, Raghwendra Kishore Singh and Satvik Tiwari
Nomenclature
19.1 Introduction
19.1.1 Overview of Disease Modeling
19.1.2 Types of Disease Models
19.1.3 Challenges in Disease Modeling
19.1.4 Role of AI, ML, and Big Data in Modern Healthcare
19.1.5 Big Data in Healthcare Decision-Making
19.1.6 Importance of Data Integration in Disease Management
19.1.7 Real-World Examples of Data Integration in Disease Management
19.2 Types of Data in Disease Modeling
19.2.1 Clinical Data
19.2.2 Genomic Data
19.2.3 Environmental and Behavioral Data
19.2.4 The Role of Data Integration in Disease Modeling
19.3 Techniques and Methodologies in Disease Modeling
19.3.1 Supervised Learning in Disease Modeling
19.3.2 Unsupervised Learning in Disease Modeling
19.3.3 Deep Learning Architectures for Disease Prediction
19.4 Early-Warning Systems for Disease Outbreaks
19.4.1 Predicting Disease Progression
19.4.2 Modeling Global Health Crises (e.g., COVID-19 Transmission)
19.4.3 AI in Drug Discovery and Vaccine Development
19.4.4 Personalized Medicine and Patient-Specific Trajectories
19.5 Ethical Concerns and Privacy Issues
19.5.1 Data Privacy and Security Risks
19.5.2 Privacy-Preserving AI Techniques
19.6 Explainable AI (XAI) in Healthcare
19.7 Federated Learning for Secure Data Sharing
19.8 Advancements in Genomic Medicine and AI
19.8.1 Ethical and Regulatory Considerations in AI-Driven Genomic Medicine
19.9 Conclusion
References
20. Clinical Implications of Couple Stress Nanofluid Flow in Arterial Stenosis
Pungja Mushahary, Thirupathi Thumma, Surender Ontela and Seetalsmita Samal
Nomenclature
Greek symbols
Subscripts
20.1 Introduction
20.2 Mathematical Modeling
20.2.1 Thermophysical Properties
20.2.2 Non-Dimensionalization
20.2.3 Nusselt Number
20.3 Solution Methodology
20.3.1 Convergence of HAM Solutions
20.4 Results and Discussion
20.4.1 Optimization Insights Using the Power of RSM-CCD
20.5 Conclusions
References
21. Applications of Advanced Computational Techniques
Sahin Ahmed and Nava Jyoti Hazarika
21.1 Introduction
21.2 Mathematical Formulation
21.3 Method of Solution
21.4 Stability Analysis and Validation
21.5 Results and Discussion
21.6 Conclusion
References
22. Computational Fluid Dynamics in Biological Systems
Nasiru Musa Haruna, Abdulhalim Musa Abubakar, Yusufu Luka, Hamadou Mamoudou, Muhammad Tariq, Gaurav Kumar Pandit, Rezkallah Chafika and Zannatul Nayem
22.1 Introduction
22.2 Mathematical Models for CFD in Biological Systems
22.3 CFD in Cardiovascular Systems
22.3.1 Blood Flow Dynamics in Arteries and Veins
22.3.2 CFD Applications in Cardiovascular Disease Diagnosis and Treatment
22.3.3 Case Studies: Aneurysms, Stenosis, and Blood Clots
22.4 CFD in Respiratory Systems
22.5 CFD in Cellular and Tissue-Level Fluid Dynamics
22.6 Integration of CFD with Medical Imaging
22.7 Challenges in CFD for Biological Systems
22.8 Case Studies and Practical Applications
22.8.1 Personalized Medicine Applications
22.8.2 Design of Medical Devices Using CFD
22.8.3 CFD in Surgical Planning and Outcome Prediction
22.9 Future Directions in CFD and Biological Systems c
22.10 Conclusion
Nomenclature
References
Index
Back to Top
Preface
Acknowledgement
Aim and Scope
1. Modeling Disease Transmission via Fluid Dynamics
G. Shirisha and Saroj Revankar
1.1 Introduction
1.1.1 Overview of Disease Transmission
1.1.2 Significance of Fluid Dynamics in Understanding the Movement of Pathogens
1.2 Basic Principles of Fluid Dynamics
1.2.1 Navier-Stokes Equations
1.2.2 Transportation Theorem
1.2.3 Reynolds Transport Theorem
1.2.4 Divergence Theorem
1.2.5 Conservation of Mass
1.2.6 Conversation of Momentum
1.2.7 Equations of Motion
1.3 Intermolecular Aspects of Fluid
1.4 Choosing the Right Frame of Reference
1.5 Non-Dimensionalization in Epidemics
1.6 Inviscid Fluid Assumption in Epidemic Flow
1.7 The External Force
1.8 Comparison of Fluid Flow with Disease Transmission
1.9 Model Formulation
1.10 Numerical Treatment
1.10.1 Governing Equations
1.10.2 NSFD Scheme
1.10.3 Applying NSFD to the Equations
1.10.4 Solution Approach
1.11 Observations
1.11.1 Evolution of Infection Distribution in Space and Time
1.11.2 Infection Spread Dynamics
1.11.3 Impact of Fluid Motion on Disease Transmission
1.11.4 Role of NSFD Scheme
1.11.5 Final Infection Distribution
1.12 Case Studies of Disease Transmission Using Fluid Dynamics
1.12.1 COVID-19 Transmission
1.12.2 Influenza Spread
1.12.3 Measles Transmission
1.12.4 Waterborne Diseases (Cholera)
References
2. The SIR Model and Its Adaptations for Dengue
Naresh Kumar Jothi, Lakshmi A., Sukumaran D., Vivekanandan T. and Saravanakumar G.
2.1 Introduction
2.2 Experimental Methods and Materials
2.3 Stability of the System
2.4 Numerical Simulation
2.5 Conclusion
References
3. A Gompertz Model for the Average and Median Values of the Endometrial Thicknesses of Women Suffering from Abnormal Uterine Bleeding
Lalit Mohan Upadhyaya and Sudhanshu Aggarwal
3.1 Introduction
3.1.1 Abbreviations Used in the Paper
3.2 Data for the Study
3.3 A Gompertz Model for the Measurements of the Average and Median Values of the ET for Patients Suffering with AUB
3.4 Features of the Covariance Matrix of the Proposed Gompertz Model
3.5 Solutions of Some Systems of Differential Equations Associated with the Covariance Matrix A and the Matrix of Its Eigenvectors
3.6 Conclusion
Acknowledgements
References
4. Formulating the Zika Virus Transmission Model
Lakshmi A., Naresh Kumar Jothi, Sukumaran D., Vivekanandan T. and Saravanakumar G.
4.1 Introduction
4.2 The Model of the Equation
4.3 Parameters of the Equations
4.4 Disease Free Equilibrium Points (DFEP)
4.5 Endemic Equilibrium Points
4.6 The Systems Stability
4.6.1 Disease-Free Equilibrium Local Stability
4.6.2 Positivity Solution
4.6.3 Global Stability of Disease Endemicity
4.7 Numerical Analysis
4.8 Conclusion
References
5. Stability Analysis of Human–Dog Rabies Dynamics
Anusha Muruganandham, Naresh Kumar Jothi, Deepa S., Vivekanandan T. and Saravanakumar G.
5.1 Introduction
5.2 Assumption of the Model
5.3 Disease-Free Equilibrium
5.4 Endemic Equilibrium
5.5 Reproduction Number
5.6 Stability of the System
5.6.1 Local Stability of Disease-Free Equilibrium
5.6.2 Global Stability of Endemic Equilibrium
5.7 Theorem
5.8 Conclusion
References
6. Control Strategies and Stability in Diseases Caused by Aedes aegypti
Naresh Kumar Jothi, Anusha Muruganandham, Deepa S., Vivekanandan T. and Saravanakumar G.
6.1 Introduction
6.2 The Mathematical Model
6.3 Model Diagram
6.4 Disease-Free Equilibrium
6.5 Stability of the System
6.6 Global Stability of Endemic Equilibrium
6.7 Theorem
6.8 Numerical Reproductions
6.9 Conclusion
References
7. Ethical Considerations in Mathematical Modeling
Sachin Mishra, Raj Kumar, Sakshi Saxena, Kunj Bihari Pandey and Ajai Singh Yadav
7.1 Introduction
7.2 Theoretical Study of Lubricants and Bearings
7.2.1 Lubricants and Non-Newtonian Lubricants
7.2.2 Externally Pressurized Circular Step Thrust Bearings
7.3 Nomenclature
7.4 Analysis
7.5 Definition of Flow Rate
7.6 Weight Bearing Capacity
7.7 Pressure Distribution
7.8 Lubrication Flow Rate
7.9 Frictional Torque
7.10 Bearing Design
7.11 Results and Discussion
7.12 Conclusion and Future Scope
Bibliography
8. Hyperbolic PDEs in Biofluid Mechanics
Shivani Kumari
Nomenclature
8.1 Introduction
8.2 Theoretical Foundations of Hyperbolic PDEs
8.2.1 Characteristics of Hyperbolic PDEs
8.2.2 Common Hyperbolic PDEs in Biofluid Mechanics
8.2.3 Initial and Boundary Conditions
8.3 Governing Equations in Biofluid Systems
8.3.1 Blood Flow in Arteries
8.3.2 Respiratory System Models
8.3.3 Wave Propagation in Tissues
8.3.4 Cerebrospinal Fluid Flow
8.4 Solution Techniques for Hyperbolic PDEs
8.4.1 Analytical Solutions
8.4.2 Numerical Approaches
8.4.3 Coupled Systems
8.5 Applications and Case Studies
8.5.1 Pulse Wave Propagation in Arterial Networks
8.5.2 Airway Flow Dynamics in Asthma and COPD
8.5.3 Wave-Based Imaging in Medical Diagnostics
8.5.4 Modeling Shock Waves in Biofluids
8.6 Challenges in Biofluid Modeling
8.6.1 Nonlinear Dynamics
8.6.2 Interplay of Scales
8.6.3 Biological Uncertainty and Variability
8.7 Advancements and Future Directions
8.7.1 Computational Innovations
8.7.2 Integration with Experimental Data
8.7.3 Broader Applications
8.8 Conclusion
References
9. Comparative Analysis of Newtonian and Non-Newtonian Blood Flow in Arteries
S. R. Prathiba and A. Karthika
9.1 Introduction
9.2 Composition and Properties of Blood
9.3 Blood Flow in Large Arteries-Newtonian Fluid
9.4 Blood as a Non-Newtonian Fluid
9.4.1 Mild Stenosis
9.4.2 Double Stenoses
9.4.3 Two-Phase Stenosis Model
9.4.4 Inclined Stenosis with Nanoparticles
9.5 Results and Discussion
9.6 Conclusion
Nomenclature
References
10. Models of Tumor-Immune Drug Interaction
Kaushik Dehingia, Animesh Phukan and Lovely Borah
10.1 Introduction
10.2 Preliminaries of Cancer Modeling
10.3 Modeling of Tumor-Immune Interactions
10.4 Mathematical Models with Treatment Strategies
10.5 Other Studies and Approaches
10.6 Conclusion
References
11. Modeling of SARS-CoV-19
Saravanakumar G., Naresh Kumar Jothi, Vadivelu V., Sukumaran D. and Vivekanandan T.
11.1 Introduction
11.2 The Model
11.3 Positivity and Boundedness of the System
11.4 The Basic Reproduction Number
11.5 Numerical Simulations and Discussion
11.6 Conclusion
References
12. Simulation Techniques for Fluid Dynamics Problems
Eny Tayang and Sahin Ahmed
Nomenclature
Abbreviations
12.1 Introduction
12.2 Mathematical Formulation
12.3 Results and Discussion
12.4 Conclusion
Appendix
References
13. Darcy-Forchheimer Hybrid Nanofluid (Blood-Fe2O3+Au) Flow of Bio-Convective Couple Stress Model with Quadratic Thermal Radiation: Optimization Analysis and Homotopy Analysis
Seetalsmita Samal, Surender Ontela, Thirupathi Thumma and Pungja Mushahary
13.1 Introduction
13.2 Mathematical Modeling
13.2.1 Quantities of Physical Interests
13.3 Solution Methodology
13.4 Findings and Analysis
13.5 Optimization Analysis through RSM CCD Approach
13.6 Conclusion
Nomenclature
References
14. Numerical Methods in Fluid Dynamics and Disease Modeling
Anil Nangkar, Sahin Ahmed and Bikash Das
14.1 Introduction
14.2 Mathematical Formulation
14.3 Methodology and Grid Point Analysis
14.4 Results and Discussion
14.5 Conclusion
Nomenclature
Greek Symbols
Subscripts
References
15. Numerical Simulation of Solar PV Panel Thermal Behavior
with Nanofluid Cooling Techniques
Bikash Das, Sahin Ahmed and Anil Nangkar
15.1 Introduction
15.2 PV Panel Geometry
15.3 Mathematical Formulation
15.3.1 Heat Transfer in Solid
15.3.2 Fluid Flow and Heat Transmission in Fluid
15.4 Power Output and Efficiency
15.5 Methodology, Grid Independence Test, and Validation
15.6 Results and Discussion
15.7 Conclusions
Nomenclature
References
16. Applications to Public Health and Environmental Studies
Manjula Kuntigorla, Ega Chandra Shekar, Masma Shaik and Bommareddy Nagalakshmi
16.1 Fluid Dynamics
16.1.1 Importance of Fluid Dynamics
16.1.2 CFD to Environmental Flows
16.1.3 CFD in Groundwater Pollution Repair
16.1.4 CFD to Public Health
16.1.5 Fluid Dynamics in Biology
16.1.6 Fluid Dynamics in Astrophysics
16.1.7 Fluid Dynamics in Oceanography
16.1.8 Fluid Dynamics in Meteorology
16.1.9 Fluid Dynamics Applications in Engineering
16.2 Fluid Dynamics Applications
16.2.1 Aerodynamics in Automotive Design
16.2.2 Weather Prediction
16.2.3 Storm Alerts
16.2.4 Taking to the Skies
16.3 Blood Circulation in Medicine
16.4 Environmental Engineering
16.5 Extraction of Oil and Gas
16.6 Fire Suppression Systems
16.7 Applications of Fluid Dynamics in Systems of Fire Control
16.8 Cooling Mechanisms in Electronics
16.9 Desalination Methods
References
17. Complex Systems and Nonlinear Dynamics
Dahiru Abdurrahman, Maheshwar Pathak and Pratibha Joshi
17.1 Introduction
17.2 Modified Variational Iteration Method
17.3 Applications
17.3.1 Velocity-Vorticity Interaction in 2D Flow
17.3.2 Multi-Population Disease Spread
17.3.3 Viral Infection Dynamics
17.3.4 Transfer of Energy in Turbulence
17.4 Conclusion
References
18. Mathematical Techniques for Environmental Fluid Dynamics
Km Shelly Chaudhary and Lalit Mohan
18.1 Introduction
18.2 Preliminaries of FC
18.3 Solution Process by LADT
18.4 Numerical Application and Results
18.5 Conclusion
References
19. AI-Driven Multimodal Fusion for Predictive Disease Modeling and Clinical Insight Generation
Subhranil Das, Rashmi Kumari, Raghwendra Kishore Singh and Satvik Tiwari
Nomenclature
19.1 Introduction
19.1.1 Overview of Disease Modeling
19.1.2 Types of Disease Models
19.1.3 Challenges in Disease Modeling
19.1.4 Role of AI, ML, and Big Data in Modern Healthcare
19.1.5 Big Data in Healthcare Decision-Making
19.1.6 Importance of Data Integration in Disease Management
19.1.7 Real-World Examples of Data Integration in Disease Management
19.2 Types of Data in Disease Modeling
19.2.1 Clinical Data
19.2.2 Genomic Data
19.2.3 Environmental and Behavioral Data
19.2.4 The Role of Data Integration in Disease Modeling
19.3 Techniques and Methodologies in Disease Modeling
19.3.1 Supervised Learning in Disease Modeling
19.3.2 Unsupervised Learning in Disease Modeling
19.3.3 Deep Learning Architectures for Disease Prediction
19.4 Early-Warning Systems for Disease Outbreaks
19.4.1 Predicting Disease Progression
19.4.2 Modeling Global Health Crises (e.g., COVID-19 Transmission)
19.4.3 AI in Drug Discovery and Vaccine Development
19.4.4 Personalized Medicine and Patient-Specific Trajectories
19.5 Ethical Concerns and Privacy Issues
19.5.1 Data Privacy and Security Risks
19.5.2 Privacy-Preserving AI Techniques
19.6 Explainable AI (XAI) in Healthcare
19.7 Federated Learning for Secure Data Sharing
19.8 Advancements in Genomic Medicine and AI
19.8.1 Ethical and Regulatory Considerations in AI-Driven Genomic Medicine
19.9 Conclusion
References
20. Clinical Implications of Couple Stress Nanofluid Flow in Arterial Stenosis
Pungja Mushahary, Thirupathi Thumma, Surender Ontela and Seetalsmita Samal
Nomenclature
Greek symbols
Subscripts
20.1 Introduction
20.2 Mathematical Modeling
20.2.1 Thermophysical Properties
20.2.2 Non-Dimensionalization
20.2.3 Nusselt Number
20.3 Solution Methodology
20.3.1 Convergence of HAM Solutions
20.4 Results and Discussion
20.4.1 Optimization Insights Using the Power of RSM-CCD
20.5 Conclusions
References
21. Applications of Advanced Computational Techniques
Sahin Ahmed and Nava Jyoti Hazarika
21.1 Introduction
21.2 Mathematical Formulation
21.3 Method of Solution
21.4 Stability Analysis and Validation
21.5 Results and Discussion
21.6 Conclusion
References
22. Computational Fluid Dynamics in Biological Systems
Nasiru Musa Haruna, Abdulhalim Musa Abubakar, Yusufu Luka, Hamadou Mamoudou, Muhammad Tariq, Gaurav Kumar Pandit, Rezkallah Chafika and Zannatul Nayem
22.1 Introduction
22.2 Mathematical Models for CFD in Biological Systems
22.3 CFD in Cardiovascular Systems
22.3.1 Blood Flow Dynamics in Arteries and Veins
22.3.2 CFD Applications in Cardiovascular Disease Diagnosis and Treatment
22.3.3 Case Studies: Aneurysms, Stenosis, and Blood Clots
22.4 CFD in Respiratory Systems
22.5 CFD in Cellular and Tissue-Level Fluid Dynamics
22.6 Integration of CFD with Medical Imaging
22.7 Challenges in CFD for Biological Systems
22.8 Case Studies and Practical Applications
22.8.1 Personalized Medicine Applications
22.8.2 Design of Medical Devices Using CFD
22.8.3 CFD in Surgical Planning and Outcome Prediction
22.9 Future Directions in CFD and Biological Systems c
22.10 Conclusion
Nomenclature
References
Index
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