Delay Differential Equations and Applications to Biology

Fathalla A. Rihan (Autor)

Buch | Softcover

286 Seiten

2022 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-0628-1 (ISBN)

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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.

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.

Part I Qualitative and Quantitative Features of Delay Differential Equations: 1. Delay Differential Equations.- 2. Numerical Solutions of Delay Differential Equations.- 3. Stability Concepts of Numerical Solutions of Delay Differential Equations.- 4. Parameter Estimation with Delay Differential Equations.- Part II Applications of Delay Differential Equations: 5. Delay Differential Equations with Infectious Diseases.- 6. Delay Differential Equations with Cell Growth Dynamics.- 7. Delay Differential Equations with Tumour-Immure Interactions and External Treatments.- 8. Delay Differential Equations with Ecological Systems.- 9. Fractional-Order Delay Differential Equations with Applications.- 10. Sensitivity Analysis.

“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)

Erscheinungsdatum	26.08.2022
Reihe/Serie	Forum for Interdisciplinary Mathematics
Zusatzinfo	62 Illustrations, color; 22 Illustrations, black and white; XVII, 286 p. 84 illus., 62 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Biological Systems • cell proliferations • continuous RK methods • continuous RK schemes • Covid-19 • Delay differential equations • Fractional-order • HIV • immunology • Infectious Diseases • least squares approach • Lyapunov functional • Mathematical Modelling • parameter estimations • Sensitivity • stability • stochastic DDEs • Time-Delays
ISBN-10	981-16-0628-5 / 9811606285
ISBN-13	978-981-16-0628-1 / 9789811606281
Zustand	Neuware