Delay Differential Equations and Applications to Biology

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 new edition introduces advanced numerical techniques for solving pantograph-type DDEs, including stability analyses. The book also integrates recent research on stochastic models of DDEs, particularly from the fields of immunology and cancer modeling. In addition, the book includes updated case studies from biological and medical sciences, such as glucose-insulin interaction models and infectious disease dynamics. This book is particularly valuable to mathematicians, researchers, and professionals in the fields of mathematical biology, life sciences, immunology, and epidemiology.

1. Qualitative Features of Delay Differential Equations. - 2. Continuous Runge-Kutta Methods for Delay Differential Equations. - 3. Stability Concepts of Numerical Solutions of Delay Differential Equations. - 4. Mono-Implicit Runge-Kutta Methods for Volterra Delay Integro-Differential Equations. - 5. Parameter Estimation with Delay Differential Equations. - 6. Sensitivity Analysis of Delay Differential Equations. - 7. Stochastic Delay Differential Equations. - 8. Continuous Runge-Kutta Schemes for Pantograph Delay Differential Equations. - 9. Split-Step -Method for Stochastic Pantograph Differential Equations. - 10. Delay Differential Equations with Infectious Diseases. - 11 Delay Differential Equations of Tumor-Immune System with Treatment and Control. - 12 Delay Differential Equations of Ecological Systems with Allee Effect. - 13 Fractional-Order Delay Differential Equations with Predator-prey Systems. - 14 Fractional-Order Delay Differential Equations of Hepatitis C Virus. - 15 Stochastic Delay Differential Model for Coronavirus Infection COVID-19. - 16 Delay Differential Equations with Glucose-Insulin Dynamics. - 17 Remarks and Current Challenges.