Methods of Mathematical Modelling
Infectious Diseases
- 1st Edition - June 10, 2022
- Imprint: Academic Press
- Editors: Harendra Singh, Hari M Srivastava, Dumitru Baleanu
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 9 8 8 8 - 8
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 9 9 4 7 - 2
Methods of Mathematical Modeling: Infectious Diseases presents computational methods related to biological systems and their numerical treatment via mathematical tools and techn… Read more
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Request a sales quoteMethods of Mathematical Modeling: Infectious Diseases presents computational methods related to biological systems and their numerical treatment via mathematical tools and techniques. Edited by renowned experts in the field, Dr. Hari Mohan Srivastava, Dr. Dumitru Baleanu, and Dr. Harendra Singh, the book examines advanced numerical methods to provide global solutions for biological models. These results are important for medical professionals, biomedical engineers, mathematicians, scientists and researchers working on biological models with real-life applications. The authors deal with methods as well as applications, including stability analysis of biological models, bifurcation scenarios, chaotic dynamics, and non-linear differential equations arising in biology.
The book focuses primarily on infectious disease modeling and computational modeling of other real-world medical issues, including COVID-19, smoking, cancer and diabetes. The book provides the solution of these models so as to provide actual remedies.
- Includes mathematical modeling for a variety of infectious diseases and disease processes, including SIR/SIRA, COVID-19, cancer, smoking and diabetes
- Offers a complete and foundational understanding of modeling algorithms and techniques such as stability analysis, bifurcation scenarios, chaotic dynamics, and non-linear differential equations
- Provides readers with datasets for applied learning of the various algorithms and modeling techniques
Biomedical engineers, computer scientists, data analysts, researchers, and clinicians in biology, neuroscience, biophysics, biochemistry, and applied mathematics; Research scientists and engineers in the fields of medical and biological sciences
- Cover image
- Title page
- Table of Contents
- Copyright
- Contributors
- 1: Epidemic theory: Studying the effective and basic reproduction numbers, epidemic thresholds and techniques for the analysis of infectious diseases with particular emphasis on tuberculosis
- Abstract
- Acknowledgment
- 1: Introduction
- 2: Basic and effective reproduction numbers
- 3: Significance and limitations of basic reproduction number
- 4: Herd immunity
- 5: Different methods to determine R0
- 6: Computation of R0 by the next-generation matrix method
- 7: Computation of BRN of a mathematical model on multidrug-resistant tuberculosis (MDR-TB)
- 8: Literature review on BRN of TB
- 9: Other measures to study an epidemic
- 10: Reproduction number using epidemic curve and serial interval distribution
- 11: Conclusions
- References
- 2: Numerical methods applied to a class of SEIR epidemic models described by the Caputo derivative
- Abstract
- 1: Introduction
- 2: On fractional operators in fractional calculus
- 3: Description of the model
- 4: Existence of the equilibrium points
- 5: Numerical schemes and applications
- 6: Stability analysis
- 7: Simulations and illustrations
- 8: Conclusion
- References
- Further reading
- 3: Mathematical model and interpretation of crowding effects on SARS-CoV-2 using Atangana-Baleanu fractional operator
- Abstract
- 1: Introduction
- 2: Spread of new SARS-CoV-2 variant in India
- 3: Model for crowding effects on COVID-19
- 4: Conclusions
- Availability of data and materials
- Competing interests
- Authors’ contributions
- References
- 4: Analysis for modified fractional epidemiological model for computer viruses
- Abstract
- 1: Introduction
- 2: Model description
- 3: Preliminaries
- 4: Outline of method
- 5: Stability analysis
- 6: Numerical discussion
- 7: Conclusions
- References
- 5: Analysis of e-cigarette smoking model by a novel technique
- Abstract
- 1: Introduction
- 2: Fundamental definitions
- 3: Analysis with the exponential-decay kernel
- 4: Numerical simulations
- 5: Conclusions
- References
- 6: Stability analysis of an unhealthy diet model with the effect of antiangiogenesis treatment
- Abstract
- 1: Introduction
- 2: Description of the antiangiogenic model
- 3: Invariant region
- 4: Existing equilibrium points of the system
- 5: Stability analysis
- 6: Global stability analysis at healthy equilibrium point E1
- 7: Diet-antiangiogenic drug model with delay
- 8: Positivity and boundedness of the solution
- 9: Existence of equilibrium points
- 10: Conclusion
- References
- 7: Analysis of the spread of infectious diseases with the effects of consciousness programs by media using three fractional operators
- Abstract
- 1: Introduction
- 2: Preliminaries
- 3: Solution for FKDV equation
- 4: Results and discussion
- 5: Conclusion
- References
- 8: Modeling and analysis of computer virus fractional order model
- Abstract
- 1: Introduction
- 2: Basic concept of fractional order
- 3: Mathematical model formulations
- 4: Atangana-Baleanu Caputo sense
- 5: Result and discussion
- 6: Conclusion
- References
- 9: Stochastic analysis and disease transmission
- Abstract
- Acknowledgment
- 1: Introduction
- 2: Deterministic epidemic models
- 3: DTMC epidemic models
- 4: CTMC epidemic models formulation
- 5: SDE epidemic models formulation
- References
- Further reading
- 10: Analysis of the Adomian decomposition method to estimate the COVID-19 pandemic
- Abstract
- Funding
- Conflicts of interests
- 1: Introduction
- 2: Methodology
- 3: Theory and calculations
- 4: Results and discussion
- 5: Conclusion
- References
- 11: Study of a COVID-19 mathematical model
- Abstract
- 1: Introduction
- 2: Fundamental results
- 3: Feasibility of solution and stability analysis
- 4: Qualitative analysis
- 5: Series solution for model (2)
- 6: Numerical solution for Eq. (3)
- 7: Computational of the numerical solution of the COVID-19 model for model (2)
- 8: Graphical results and discussion for model (3)
- 9: Concluding remarks
- References
- Index
- Edition: 1
- Published: June 10, 2022
- Imprint: Academic Press
- No. of pages: 236
- Language: English
- Paperback ISBN: 9780323998888
- eBook ISBN: 9780323999472
HS
Harendra Singh
Dr. Harendra Singh is an Assistant Professor in the Department of Mathematics at Post-Graduate College Ghazipur, Uttar Pradesh, India. He teaches post-graduate mathematics courses including Real and Complex Analysis, Functional Analysis, Abstract Algebra, and Measure Theory. His research areas of interest include Mathematical Modelling, Fractional Differential Equations, Integral Equations, Calculus of Variations, and Analytical and Numerical Methods. He is the co-Editor with Dr. Srivastava of Special Functions in Fractional Calculus and Engineering, Taylor and Francis/CRC Press.
Affiliations and expertise
Assistant Professor, Department of Mathematics, Post-Graduate College, Ghazipur, IndiaHS
Hari M Srivastava
Dr. Hari M. Srivastava is Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria, British Columbia, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur, India. Dr. Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scientific research journals as the Lead or Joint Guest Editor, including the MDPI journal Axioms, Mathematics, and Symmetry, the Elsevier journals, Journal of Computational and Applied Mathematics, Applied Mathematics and Computation, Chaos, Solitons & Fractals, Alexandria Engineering Journal, and Journal of King Saud University – Science, the Wiley journal, Mathematical Methods in the Applied Sciences, the Springer journals, Advances in Difference Equations, Journal of Inequalities and Applications, Fixed Point Theory and Applications, and Boundary Value Problems, the American Institute of Physics journal, Chaos: An Interdisciplinary Journal of Nonlinear Science, and the American Institute of Mathematical Sciences journal, AIMS Mathematics, among many others. Dr. Srivastava has been a Clarivate Analytics (Web of Science) Highly-Cited Researcher since 2015. Dr. Srivastava’s research interests include several areas of Pure and Applied Mathematical Sciences, such as Real and Complex Analysis, Fractional Calculus and Its Applications, Integral Equations and Transforms, Higher Transcendental Functions and Their Applications, q-Series and q-Polynomials, Analytic Number Theory, Analytic and Geometric Inequalities, Probability and Statistics, and Inventory Modeling and Optimization. He has published 36 books, monographs, and edited volumes, 36 book (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1450 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals.
Affiliations and expertise
Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia, CanadaDB
Dumitru Baleanu
Dumitru Baleanu is a professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and a visiting staff member at the Department of Mathematics, Çankaya, University, Ankara, Turkey. He received his Ph.D. from the Institute of Atomic Physics in 1996. His fields of interest include Fractional Dynamics and its applications, Fractional Differential Equations and their applications, Discrete Mathematics, Image Processing, Bioinformatics, Mathematical Biology, Mathematical Physics, Soliton Theory, Lie Symmetry, Dynamic Systems on time scales, Computational Complexity, the Wavelet Method and its applications, Quantization of systems with constraints, the Hamilton-Jacobi Formalism, as well as geometries admitting generic and non-generic symmetries.
Affiliations and expertise
Professor, Institute of Space Sciences, Magurele-Bucharest, RomaniaRead Methods of Mathematical Modelling on ScienceDirect