Analysis of Some Mathematical Models of Cell Dynamics in Hematology Book, December 06, 2021 / Lorand Gabriel Parajdi
Author: Lorand Gabriel Parajdi
Title: Analysis of Some Mathematical Models of Cell Dynamics in Hematology
Publishing House: Casa Cărții de Știință
Year of Publication: 2021
The Book is available on Casa Cărții de Știință website:https://casacartii.ro/editura/carte/analysis-of-some-mathematical-models-of-cell-dynamics-in-hematology/
The Book is partially available on Google Books:https://books.google.com/lorand-gabriel-parajdi/analysis-of-some-mathematical-models-of-cell-dynamics-in-hematology/
Bringing new contributions to science might be challenging, however, this is our path to evolution. We cannot assume that we know everything, but it is only our curiosity that can lead us to answers. Therefore, we can and we should keep trying, seeking new and different paths. There is always a starting point: asking yourself „Why?”, and the answer will follow…
The purpose of the present book is the study of some mathematical models of cell dynamics and convex optimization problems applied to chronic myeloid leukemia, a type of leukemia also known as chronic myelogenous leukemia. We take into consideration basic concepts, methods and results from the theory of differential equations, such as: existence, uniqueness, monotonicity, boundedness, continuous dependence on data and stability of solutions.
This book was possible with the financial support offered by the “Babeș-Bolyai” University of Cluj-Napoca, through an AGC Grant, no. AGC35604 and AGC38848.
Chapter 2 Mathematical Modeling of Chronic Myeloid Leukemia 2.1 The basic mathematical model 2.2 Existence, uniqueness and continuous dependence on data 2.2.1 Existence and uniqueness 2.2.2 Monotonicity of the solutions 2.2.3 Boundedness of solutions 2.2.4 Continuous dependence on data 2.3 Steady states and local stability 2.3.1 Steady states 2.3.2 Local stability of steady states 2.4 Global stability 2.5 Numerical simulations 2.5.1 Parameter estimation 2.5.2 Numerical simulation of the model 2.6 The extended model to terminally differentiated cells
Chapter 3 Optimization Problems in Chronic Myeloid Leukemia 3.1 The optimization problem 3.2 Optimal personalized dosing of a selective drug 3.3 Non-specific drug optimization problems 3.4 Optimal personalized dosing of a selective drug based on the extended model to terminally differentiated cells
Chapter 4 Mathematical Modeling of Stem Cell Transplantation in Chronic Myeloid Leukemia 4.1 The mathematical model 4.2 Existence, uniqueness and continuous dependence on data 4.2.1 Existence and uniqueness 4.2.2 Monotonicity of the solutions 4.2.3 Boundedness of solutions 4.2.4 Continuous dependence on data 4.3 Steady states and stability 4.3.1 Steady states 4.3.2 Local stability of steady states 4.4 Numerical simulations 4.4.1 Numerical simulations in the chronic case 4.4.2 Numerical simulations in the accelerated-acute case