Mathematical Techniques in Disease and Fluid Dynamics Modeling

1. Auflage 2027
ISBN: 978-1-394-39005-2
Verlag: John Wiley & Sons Inc

Buch, Englisch, 592 Seiten

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.

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.

Autoren/Hrsg.

Gupta, Reshu

Dhar, Biplab

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Epidemiologie, Medizinische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre

Inhaltsverzeichnis

Preface xvii
Acknowledgement xix
Aim and Scope xxi

1 Modeling Disease Transmission via Fluid Dynamics 1
G. Shirisha and Saroj Revankar

1.1 Introduction 2
1.2 Basic Principles of Fluid Dynamics 5
1.3 Intermolecular Aspects of Fluid 10
1.4 Choosing the Right Frame of Reference 11
1.5 Non-Dimensionalization in Epidemics 11
1.6 Inviscid Fluid Assumption in Epidemic Flow 11
1.7 The External Force 12
1.8 Comparison of Fluid Flow with Disease Transmission 12
1.9 Model Formulation 13
1.10 Numerical Treatment 15
1.11 Observations 20
1.12 Case Studies of Disease Transmission Using Fluid Dynamics 23

2 The SIR Model and Its Adaptations for Dengue 31
Naresh Kumar Jothi, Lakshmi A., Sukumaran D., Vivekanandan T. and Saravanakumar G.

2.1 Introduction 32
2.2 Experimental Methods and Materials 33
2.3 Stability of the System 37
2.4 Numerical Simulation 40
2.5 Conclusion 42

3 A Gompertz Model for the Average and Median Values of the Endometrial Thicknesses of Women Suffering from Abnormal Uterine Bleeding 45
Lalit Mohan Upadhyaya and Sudhanshu Aggarwal

3.1 Introduction 46
3.2 Data for the Study 48
3.3 A Gompertz Model for the Measurements of the Average and Median Values of the ET for Patients Suffering with AUB 48
3.4 Features of the Covariance Matrix of the Proposed Gompertz Model 57
3.5 Solutions of Some Systems of Differential Equations Associated with the Covariance Matrix A and the Matrix of Its Eigenvectors 64
3.6 Conclusion 70

4 Formulating the Zika Virus Transmission Model 75
Lakshmi A., Naresh Kumar Jothi, Sukumaran D., Vivekanandan T. and Saravanakumar G.

4.1 Introduction 76
4.2 The Model of the Equation 77
4.3 Parameters of the Equations 77
4.4 Disease Free Equilibrium Points (DFEP) 78
4.5 Endemic Equilibrium Points 78
4.6 The Systems Stability 79
4.7 Numerical Analysis 83
4.8 Conclusion 85

5 Stability Analysis of Human–Dog Rabies Dynamics 89
Anusha Muruganandham, Naresh Kumar Jothi, Deepa S., Vivekanandan T. and Saravanakumar G.

5.1 Introduction 90
5.2 Assumption of the Model 91
5.3 Disease-Free Equilibrium 92
5.4 Endemic Equilibrium 93
5.5 Reproduction Number 93
5.6 Stability of the System 95
5.7 Theorem 97
5.8 Conclusion 100

6 Control Strategies and Stability in Diseases Caused by Aedes aegypti 105
Naresh Kumar Jothi, Anusha Muruganandham, Deepa S., Vivekanandan T. and Saravanakumar G.

6.1 Introduction 106
6.2 The Mathematical Model 107
6.3 Model Diagram 108
6.4 Disease-Free Equilibrium 109
6.5 Stability of the System 111
6.6 Global Stability of Endemic Equilibrium 112viii Contents
6.7 Theorem 113
6.8 Numerical Reproductions 114
6.9 Conclusion 117

7 Ethical Considerations in Mathematical Modeling 121
Sachin Mishra, Raj Kumar, Sakshi Saxena, Kunj Bihari Pandey and Ajai Singh Yadav

7.1 Introduction 122
7.2 Theoretical Study of Lubricants and Bearings 124
7.3 Nomenclature 125
7.4 Analysis 126
7.5 Definition of Flow Rate 129
7.6 Weight Bearing Capacity 132
7.7 Pressure Distribution 132
7.8 Lubrication Flow Rate 132
7.9 Frictional Torque 133
7.10 Bearing Design 133
7.11 Results and Discussion 133
7.12 Conclusion and Future Scope 137

8 Hyperbolic PDEs in Biofluid Mechanics 143
Shivani Kumari

8.1 Introduction 145
8.2 Theoretical Foundations of Hyperbolic PDEs 149
8.3 Governing Equations in Biofluid Systems 155
8.4 Solution Techniques for Hyperbolic PDEs 160
8.5 Applications and Case Studies 166
8.6 Challenges in Biofluid Modeling 172
8.7 Advancements and Future Directions 176
8.8 Conclusion 181

9 Comparative Analysis of Newtonian and Non-Newtonian Blood Flow in Arteries 189
S. R. Prathiba and A. Karthika

9.1 Introduction 190
9.2 Composition and Properties of Blood 191
9.3 Blood Flow in Large Arteries-Newtonian Fluid 191
9.4 Blood as a Non-Newtonian Fluid 193
9.5 Results and Discussion 205
9.6 Conclusion 207

10 Models of Tumor-Immune Drug Interaction 213
Kaushik Dehingia, Animesh Phukan and Lovely Borah

10.1 Introduction 213
10.2 Preliminaries of Cancer Modeling 215
10.3 Modeling of Tumor-Immune Interactions 218
10.4 Mathematical Models with Treatment Strategies 222
10.5 Other Studies and Approaches 226
10.6 Conclusion 229

11 Modeling of SARS-CoV-19 237
Saravanakumar G., Naresh Kumar Jothi, Vadivelu V., Sukumaran D. and Vivekanandan T.

11.1 Introduction 238
11.2 The Model 238
11.3 Positivity and Boundedness of the System 240
11.4 The Basic Reproduction Number 242
11.5 Numerical Simulations and Discussion 248
11.6 Conclusion 251

12 Simulation Techniques for Fluid Dynamics Problems 253
Eny Tayang and Sahin Ahmed

12.1 Introduction 255
12.2 Mathematical Formulation 259
12.3 Results and Discussion 265
12.4 Conclusion 271

13 Darcy-Forchheimer Hybrid Nanofluid (Blood-Fe2O3+Au) Flow of Bio-Convective Couple Stress Model with Quadratic Thermal Radiation: Optimization Analysis and Homotopy Analysis 279
Seetalsmita Samal, Surender Ontela, Thirupathi Thumma and Pungja Mushahary

13.1 Introduction 280
13.2 Mathematical Modeling 284
13.3 Solution Methodology 290
13.4 Findings and Analysis 293
13.5 Optimization Analysis through RSM CCD Approach 301
13.6 Conclusion 308

14 Numerical Methods in Fluid Dynamics and Disease Modeling 315
Anil Nangkar, Sahin Ahmed and Bikash Das

14.1 Introduction 316
14.2 Mathematical Formulation 318Contents xi
14.3 Methodology and Grid Point Analysis 324
14.4 Results and Discussion 326
14.5 Conclusion 332

15 Numerical Simulation of Solar PV Panel Thermal Behavior with Nanofluid Cooling Techniques 337
Bikash Das, Sahin Ahmed and Anil Nangkar

15.1 Introduction 338
15.2 PV Panel Geometry 339
15.3 Mathematical Formulation 340
15.4 Power Output and Efficiency 342
15.5 Methodology, Grid Independence Test, and Validation 343
15.6 Results and Discussion 344
15.7 Conclusions 346

16 Applications to Public Health and Environmental Studies 351
Manjula Kuntigorla, Ega Chandra Shekar, Masma Shaik and Bommareddy Nagalakshmi

16.1 Fluid Dynamics 352
16.2 Fluid Dynamics Applications 366
16.3 Blood Circulation in Medicine 372xii Contents
16.4 Environmental Engineering 374
16.5 Extraction of Oil and Gas 375
16.6 Fire Suppression Systems 376
16.7 Applications of Fluid Dynamics in Systems of Fire Control 377
16.8 Cooling Mechanisms in Electronics 378
16.9 Desalination Methods 380

17 Complex Systems and Nonlinear Dynamics 385
Dahiru Abdurrahman, Maheshwar Pathak and Pratibha Joshi

17.1 Introduction 386
17.2 Modified Variational Iteration Method 389
17.3 Applications 392
17.4 Conclusion 409

18 Mathematical Techniques for Environmental Fluid Dynamics 413
Km Shelly Chaudhary and Lalit Mohan

18.1 Introduction 414
18.2 Preliminaries of FC 415
18.3 Solution Process by LADT 416
18.4 Numerical Application and Results 418
18.5 Conclusion 423

19 AI-Driven Multimodal Fusion for Predictive Disease Modeling and Clinical Insight Generation 425
Subhranil Das, Rashmi Kumari, Raghwendra Kishore Singh and Satvik Tiwari

19.1 Introduction 426
19.2 Types of Data in Disease Modeling 434
19.3 Techniques and Methodologies in Disease Modeling 439
19.4 Early-Warning Systems for Disease Outbreaks 442
19.5 Ethical Concerns and Privacy Issues 445
19.6 Explainable AI (XAI) in Healthcare 446
19.7 Federated Learning for Secure Data Sharing 448
19.8 Advancements in Genomic Medicine and AI 450

20 Clinical Implications of Couple Stress Nanofluid Flow in Arterial Stenosis 457
Pungja Mushahary, Thirupathi Thumma, Surender Ontela and Seetalsmita Samal

20.1 Introduction 459
20.2 Mathematical Modeling 464xiv Contents
20.3 Solution Methodology 469
20.4 Results and Discussion 471
20.5 Conclusions 485

21 Applications of Advanced Computational Techniques 493
Sahin Ahmed and Nava Jyoti Hazarika

21.1 Introduction 494
21.2 Mathematical Formulation 496
21.3 Method of Solution 500
21.4 Stability Analysis and Validation 502
21.5 Results and Discussion 503
21.6 Conclusion 509

22 Computational Fluid Dynamics in Biological Systems 515
Nasiru Musa Haruna, Abdulhalim Musa Abubakar, Yusufu Luka, Hamadou Mamoudou, Muhammad Tariq, Gaurav Kumar Pandit, Rezkallah Chafika and Zannatul Nayem

22.1 Introduction 516
22.2 Mathematical Models for CFD in Biological Systems 518
22.3 CFD in Cardiovascular Systems 520
22.4 CFD in Respiratory Systems 522
22.5 CFD in Cellular and Tissue-Level Fluid Dynamics 523
22.6 Integration of CFD with Medical Imaging 524
22.7 Challenges in CFD for Biological Systems 524
22.8 Case Studies and Practical Applications 525
22.9 Future Directions in CFD and Biological Systems 529
22.10 Conclusion 529

Nomenclature 530
References 531
Index 545

Über Autor(innen)

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.

Biplab Dhar, PhD is an Assistant Professor in the Applied Science Cluster at the University of Petroleum and Energy Studies, India. He has published 12 articles in international journals and conferences. His research interests include mathematical modeling, oncology, epidemiology, and infodemiology.