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Mathematical Modeling in Bioscience
Theory and Applications
- 1st Edition - March 27, 2025
- Editor: Hemen Dutta
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 4 5 - 4
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 5 4 4 6 - 1
Mathematical Modeling in Bioscience: Theory and Applications provides readers with tools and techniques for mathematical modeling in bioscience through a wide range of novel and in… Read more
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Request a sales quoteMathematical Modeling in Bioscience: Theory and Applications provides readers with tools and techniques for mathematical modeling in bioscience through a wide range of novel and intriguing topics. The book concentrates on larger elements of mathematical modeling in bioscience, including topics such as modeling of the Topp--Leone new power generalized Weibull-G distribution family, vector-borne disease modeling, transmission modeling of SARS-COV-2 among other infectious diseases, pattern formulation models, compartmental models for HIV/AIDS transmission, population models, irrigation scheduling models, and predator--prey models. The readers will discover a variety of new methods, approaches, and techniques, as well as a wide range of applications demonstrating key concepts in bioscience modeling. This book provides a leading-edge resource for researchers in a variety of scientific fields who are interested in mathematical modeling, including mathematics, statistics, biology, biomedical engineering, computer science, and applied sciences.
- Provides key concepts for advanced mathematical methods for modeling in bioscience
- Includes statistical, delay, random, and stochastic mathematical models
- Focuses on broader aspects of mathematical models in bioscience
- Provides the readers with several types of dynamic representative applications
Mathematicians, researchers in computational modelling and computational biology, computer scientists, engineers, as well as researchers in biomedical engineering and other biological sciences
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Contributors
- 1: Analysis of the impact of time delay incorporation in mathematical models of cellular population dynamics
- 1.1. Introduction
- 1.2. The mathematical model for autoimmunity with time delay
- 1.2.1. The non-delayed model
- 1.2.2. The model with time delay
- 1.2.3. Equilibrium states of the model with delay
- 1.3. Local asymptotical stability of the equilibrium states
- 1.3.1. Local stability of E0
- 1.3.2. Local stability of E1
- 1.3.3. Local stability of E3
- 1.4. Global stability of the equilibrium states
- 1.5. Numerical results
- 1.6. Summary and perspectives
- 2: Alternative food for predators: elucidating their impact on a predation model with Allee effect on prey
- 2.1. Introduction
- 2.2. The model
- 2.2.1. Topological equivalence
- 2.2.2. Equilibrium points
- 2.3. Main results
- 2.3.1. Model with strong Allee effect
- 2.3.2. Model with special weak Allee effect
- 2.3.3. Model with weak Allee effect
- 2.3.4. Model without Allee effect
- 2.4. Numerical simulations
- 2.5. Conclusions
- 3: Modeling and analysis of an eco-epidemiological model with Caputo–Fabrizio derivative
- 3.1. Introduction
- 3.2. Mathematical model
- 3.2.1. Fractional model
- 3.3. Existence and uniqueness
- 3.4. Numerical scheme
- 3.4.1. Numerical results
- 3.5. Conclusion
- 4: The Topp–Leone-exponentiated half logistic-generalized-G family of distributions with applications
- 4.1. Introduction
- 4.2. The new family
- 4.2.1. Sub-families
- 4.3. Properties
- 4.3.1. Quantile function
- 4.3.2. Series expansion of the density function
- 4.3.3. Moments
- 4.3.4. Probability weighted moments
- 4.3.5. Stochastic ordering
- 4.3.6. Distribution of order statistics
- 4.3.7. Entropy
- 4.4. Parameter estimation
- 4.5. Specific cases
- 4.5.1. Topp–Leone-exponentiated half logistic generalized-log-logistic (TL-EHL-GLLo) distribution
- 4.5.2. Topp–Leone-exponentiated half logistic generalized-Weibull (TL-EHL-GW) distribution
- 4.5.3. Topp–Leone-exponentiated half logistic generalized-power (TL-EHL-GP) distribution
- 4.6. Monte Carlo simulations
- 4.7. Some applications
- 4.7.1. Waiting times of bank customers data
- 4.7.2. Remission times of cancer patients data
- 4.8. Concluding remarks
- Appendix 4.A.
- 5: A mathematical model for the dynamics of visceral leishmaniasis disease with time delay
- 5.1. Introduction
- 5.2. The mathematical model
- 5.2.1. Some basic properties
- 5.2.2. Basic reproduction number
- 5.3. Equilibrium points
- 5.3.1. Characteristic equation
- 5.4. Stability of the system for τ=0
- 5.5. Stability of the system for τ>0
- 5.6. Sensitivity analysis
- 5.7. Numerical simulations
- 5.8. Discussion and conclusion
- 6: Fractalization through stochasticization processes in epileptic dynamics
- 6.1. Introduction
- 6.2. Operational procedure 1: analysis of epileptic and eclamptic seizures by applying non-linear dynamics methods
- 6.3. Operational procedure 2: the reconstruction of EEG signals through scale relativity theory
- 6.4. Conclusions
- 7: Mathematical model of Alzheimer disease using the nonlocal and nonsingular fractional operators
- 7.1. Introduction
- 7.2. Useful preliminaries
- 7.3. Model formulation of AD with the ABC derivative
- 7.4. A model integrating fractional calculus and stochastic processes to depict the propagation of Alzheimer's disease
- 7.5. Numerical schemes
- 7.5.1. The ABC operator
- 7.6. Numerical experiments and results
- 7.7. Conclusion
- Declaration of competing interest
- 8: From bubble nucleation to oscillatory denaturation: understanding complex DNA dynamics through nonlinear modeling
- 8.1. Introduction
- 8.2. Novel computational solutions
- 8.2.1. Khater II method implementation's results
- 8.2.2. Auxiliary equation method implementation's results
- 8.2.3. Solutions' stability
- 8.3. Graphical illustrations of solution sets
- 8.4. Results and discussion
- 8.5. Conclusion
- 9: Inertial projective Mann algorithm for split equilibrium problems in Parkinson's screening
- 9.1. Introduction
- 9.2. Preliminaries
- 9.3. Main results
- 9.4. Application to data classification problem
- 9.5. Conclusion
- Data availability
- Index
- No. of pages: 300
- Language: English
- Edition: 1
- Published: March 27, 2025
- Imprint: Academic Press
- Paperback ISBN: 9780443154454
- eBook ISBN: 9780443154461
HD
Hemen Dutta
Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.
Affiliations and expertise
Professor, Department of Mathematics, Gauhati University, India