Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Contributors - p. ix 7. Chapter 1: Mathematical tools and techniques in the applied scientific disciplines - p. 1 8. Chapter 2: Fractional and fractal extensions of epidemiological models - p. 39 9. Chapter 3: Mathematical analysis of the COVID-19 pandemic dynamics in the emergence of resistant strains of SARS-CoV-2 in a vaccinated and non-vaccinated population: a real-world scenario in most countries - p. 63 10. Chapter 4: A fractional study on the vaccination effect to control the COVID-19 epidemic - p. 81 11. Chapter 5: An epidemiological model of the monkeypox virus and its quarantine effects - p. 105 12. Chapter 6: Dynamically consistent nonstandard discretization methods for some mathematical models of infectious diseases - p. 119 13. Chapter 7: A comparative study of different disease-incidence functions in the mathematical modeling of infectious diseases - p. 141 14. Chapter 8: Numerical investigation of HIV infection of CD4+ T-cells via fractional Vieta–Lucas wavelets - p. 159 15. Chapter 9: A numerical study of the fractional SIR epidemic model of an infectious disease via the reproducing kernel Hilbert space method - p. 177 16. Chapter 10: The numerical study of the cancer model in biological science - p. 191 17. Chapter 11: Mathematical analysis of the non-linear dynamics of bone mineralization - p. 207 18. Chapter 12: Mathematical analysis and computational study of a novel Covid-19 model in the presence of a nonsingular, non-local kernel - p. 227 19. Chapter 13: Parametric analysis of two reaction–diffusion models leading to pattern formation - p. 247 20. Chapter 14: Existence, uniqueness, and stability analysis results for the SIR epidemic model with a fractional operator - p. 267 21. Chapter 15: Analysis of the chaotic behavior of a fractional biological system: chaos control via a novel numerical method - p. 279 22. Index - p. 307
Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Contributors - p. ix 7. Chapter 1: Mathematical tools and techniques in the applied scientific disciplines - p. 1 8. Chapter 2: Fractional and fractal extensions of epidemiological models - p. 39 9. Chapter 3: Mathematical analysis of the COVID-19 pandemic dynamics in the emergence of resistant strains of SARS-CoV-2 in a vaccinated and non-vaccinated population: a real-world scenario in most countries - p. 63 10. Chapter 4: A fractional study on the vaccination effect to control the COVID-19 epidemic - p. 81 11. Chapter 5: An epidemiological model of the monkeypox virus and its quarantine effects - p. 105 12. Chapter 6: Dynamically consistent nonstandard discretization methods for some mathematical models of infectious diseases - p. 119 13. Chapter 7: A comparative study of different disease-incidence functions in the mathematical modeling of infectious diseases - p. 141 14. Chapter 8: Numerical investigation of HIV infection of CD4+ T-cells via fractional Vieta–Lucas wavelets - p. 159 15. Chapter 9: A numerical study of the fractional SIR epidemic model of an infectious disease via the reproducing kernel Hilbert space method - p. 177 16. Chapter 10: The numerical study of the cancer model in biological science - p. 191 17. Chapter 11: Mathematical analysis of the non-linear dynamics of bone mineralization - p. 207 18. Chapter 12: Mathematical analysis and computational study of a novel Covid-19 model in the presence of a nonsingular, non-local kernel - p. 227 19. Chapter 13: Parametric analysis of two reaction–diffusion models leading to pattern formation - p. 247 20. Chapter 14: Existence, uniqueness, and stability analysis results for the SIR epidemic model with a fractional operator - p. 267 21. Chapter 15: Analysis of the chaotic behavior of a fractional biological system: chaos control via a novel numerical method - p. 279 22. Index - p. 307
