Overview
- Discusses topics in delay differential equations, including theory, numerical methods, stability and control, and biological models
- Combines both qualitative and quantitative features of delay differential equations with real-life problems
- Provides interesting applications in infectious diseases, including COVID-19
Part of the book series: Forum for Interdisciplinary Mathematics (FFIM)
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About this book
This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.
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Keywords
- delay differential equations
- stability
- Lyapunov functional
- continuous RK methods
- time-delays
- mathematical modelling
- continuous RK schemes
- parameter estimations
- sensitivity
- infectious diseases
- cell proliferations
- least squares approach
- immunology
- HIV
- COVID-19
- biological systems
- fractional-order
- stochastic DDEs
Table of contents (14 chapters)
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Front Matter
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Qualitative and Quantitative Features of Delay Differential Equations
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Front Matter
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Applications of Delay Differential Equations in Biosciences
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Front Matter
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Back Matter
Reviews
“The author provides extensive references for each chapter … . It offers a breadth of ideas and approaches that could be fertile ground for further research.” (Bill Satzer, MAA Reviews, December 12, 2021)
Authors and Affiliations
About the author
FATHALLA A. RIHAN is Professor of Mathematics at the United Arab Emirates University, UAE, and Helwan University, Egypt. He received his D. Sc. in 2018 from the National University of Uzbekistan, Uzbekistan, in “Features of Delay Differential Equations and Their Application” and completed his Ph.D. in “Numerical Treatment of Delay Differential Equations in Biosciences” from the School of Mathematics, The University of Manchester, UK, in 2000. His research interests include numerical analysis, mathematical biology, mathematical modelling of real-life phenomena with memory (cell division, population dynamics, infectious diseases, etc.), parameter estimation, sensitivity analysis, qualitative and quantitative analysis of delay differential equations. He has published a considerable number of research articles in highly impacted journals and participated in more than 100 international conferences. He is also on the editorial board of many international journals and is a reviewer and member of American Mathematical Society. He has supervised several PhD students and is the principal investigator of many research projects. With an experience of more than 30 years of teaching mathematics to undergraduate and graduate students, Dr. Rihan is an expert in quality assurance and accreditation of higher education institutes.
Bibliographic Information
Book Title: Delay Differential Equations and Applications to Biology
Authors: Fathalla A. Rihan
Series Title: Forum for Interdisciplinary Mathematics
DOI: https://doi.org/10.1007/978-981-16-0626-7
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
Hardcover ISBN: 978-981-16-0625-0Published: 20 August 2021
Softcover ISBN: 978-981-16-0628-1Published: 21 August 2022
eBook ISBN: 978-981-16-0626-7Published: 19 August 2021
Series ISSN: 2364-6748
Series E-ISSN: 2364-6756
Edition Number: 1
Number of Pages: XVII, 286
Number of Illustrations: 22 b/w illustrations, 62 illustrations in colour
Topics: Analysis, Integral Equations