Blood Cell Dynamics: Half of a Century of Modelling
From MaRDI portal
Publication:4607480
DOI10.1051/mmnp/201611106zbMath1384.92027OpenAlexW2279648767MaRDI QIDQ4607480
Publication date: 14 March 2018
Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1051/mmnp/201611106
delay differential equationsmathematical modelinghematopoiesisblood cellstructured partial differential equation
Dynamical systems in biology (37N25) Developmental biology, pattern formation (92C15) Cell biology (92C37) First-order hyperbolic equations (35L02)
Related Items
DISCRETE MATURITY AND DELAY DIFFERENTIAL-DIFFERENCE MODEL OF HEMATOPOIETIC CELL DYNAMICS WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA, Bistability, bifurcations and chaos in the Mackey-Glass equation, Adaptive dynamics of hematopoietic stem cells and their supporting stroma: a model and mathematical analysis, Stochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation, Convergence of a class of nonlinear time delays reaction-diffusion equations, Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations, Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling, Control in dormancy or eradication of cancer stem cells: mathematical modeling and stability issues, Origins of oscillation patterns in cyclical thrombocytopenia, Response of an oscillatory differential delay equation to a periodic stimulus, Moving the boundaries of granulopoiesis modelling, Analysis of a system describing proliferative-quiescent cell dynamics, Dynamical properties of feedback signalling in B lymphopoiesis: a mathematical modelling approach, Distributed Delay Differential Equation Representations of Cyclic Differential Equations, Asymptotic Convergence in Delay Differential Equations Arising in Epidemiology and Physiology, Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods, Why are periodic erythrocytic diseases so rare in humans?, Stochastic models of stem cells and their descendants under different criticality assumptions
Cites Work
- Optimal linear stability condition for scalar differential equations with distributed delay
- Age-structured and delay differential-difference model of hematopoietic stem cell dynamics
- Characterization of stem cells using mathematical models of multistage cell lineages
- Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulations
- Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: mathematical modelling guides dose optimisation to minimise neutropenia
- Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases
- Existence and stability of equilibria in age-structured population dynamics
- On the stability of hematopoietic model with feedback control
- Globally asymptotic properties of proliferating cell populations
- On the stability of the cell size distribution
- Noncompact semigroups of operators generated by cell kinetics models
- Stability of limit cycles in a pluripotent stem cell dynamics model
- A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate
- High frequency spikes in long period blood cell oscillations
- Structured population models in biology and epidemiology.
- An age-and-cyclin-structured cell population model for healthy and tumoral tissues
- Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics
- Asymptotic behavior and stability switch for a mature-immature model of cell differentiation
- Stability and Hopf bifurcation in an approachable haematopoietic stem cells model
- Dynamic hematological disease: a review
- Parameter estimation in a structured erythropoiesis model
- Numerical integration of a mathematical model of hematopoietic stem cell dynamics
- An ``age-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia
- Age-size structure in populations with quiescence
- The extinction of slowly evolving dynamical systems
- Minimizing therapeutically induced anemia
- Asynchronous exponential growth of semigroups of nonlinear operators
- A mathematical model of neutrophil production and control in normal man
- A new criterion for the global stability of simultaneous cell replication and maturation processes
- Cell division and the stability of cellular populations
- Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant
- Global stability in a delayed partial differential equation describing cellular replication
- Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence
- Global stability of a partial differential equation with distributed delay due to cellular replication
- A nonlinear cellular proliferation model: cells dying out and invariance
- A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation
- Asynchronous exponential growth in an age structured population of proliferating and quiescent cells
- Mathematical model for G-CSF administration after chemotherapy
- Mathematical study of feedback control roles and relevance in stress erythropoiesis
- A biomathematical model of human thrombopoiesis under chemotherapy
- Stability of a model of human granulopoiesis using continuous maturation
- On the stability of a nonlinear maturity structured model of cellular proliferation
- Modeling and optimal regulation of erythropoiesis subject to Benzene intoxication
- Modelling human granulopoiesis under poly-chemotherapy with G-CSF support
- Modeling erythroblastic islands: using a hybrid model to assess the function of central macrophage
- Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis
- Understanding cyclical thrombocytopenia: a mathematical modeling approach
- Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response
- A semilinear transport equation with delays
- Age-structured and two-delay models for erythropoiesis
- A nonlinear age and maturity structured model of population dynamics. II: Chaos
- A nonlinear age and maturity structured model of population dynamics. I: Basic theory
- A delay differential-difference system of hematopoietic stem cell dynamics
- Oscillations in cyclical neutropenia: new evidence based on mathematical modeling
- Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses
- A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia
- A mathematical model of hematopoiesis. II: Cyclical neutropenia
- Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1
- Periodic oscillations in leukopoiesis models with two delays
- Stabilization of telomeres in nonlinear models of proliferating cell lines
- A model for stem cell population dynamics with regulated maturation delay
- Neutrophil dynamics in response to chemotherapy and G-CSF
- Delay equation formulation of a cyclin-structured cell population model
- Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle
- G-CSF control of neutrophils dynamics in the blood
- A mathematical model of multistage hematopoietic cell lineages
- Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay
- Existence, positivity and stability for a nonlinear model of cellular proliferation
- Global asymptotic stability and Hopf bifurcation for a blood cell production model
- Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces
- The role of spatial organization of cells in erythropoiesis
- Understanding, treating and avoiding hematological disease: better medicine through mathematics?
- Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
- Asymptotic behavior of a singular transport equation modelling cell division
- A singular transport model describing cellular division
- On a Model of Leukemia Development with a Spatial Cell Distribution
- Analysis of a Population Model Structured by the Cells Molecular Content
- Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia
- A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy
- Local Controllability of Models of Combined Anticancer Therapy with Delays in Control
- Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics
- Stability Analysis of Cell Dynamics in Leukemia
- A STOCHASTIC MODEL OF STEM CELL PROLIFERATION, BASED ON THE GROWTH OF SPLEEN COLONY-FORMING CELLS
- AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION
- Asynchronous Exponential Growth in Transition Probability Models of the Cell Cycle
- Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay
- Control of Oscillations in Hematopoiesis
- Relaxation Oscillations in a Class of Delay Differential Equations
- Stability and Hopf Bifurcation for a First-Order Delay Differential Equation with Distributed Delay
- A Structured Population Model of Cell Differentiation
- Hybrid Model of Erythropoiesis and Leukemia Treatment with Cytosine Arabinoside
- A numerical approach for investigating the stability of equilibria for structured population models
- A didactical note on the advantage of using two parameters in Hopf bifurcation studies
- Oscillations in a Maturation Model of Blood Cell Production
- Stochastic Differential Delay Equation, Moment Stability, and Application to Hematopoietic Stem Cell Regulation System
- Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics
- Modeling the Cancer Stem Cell Hypothesis
- DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA
- Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
- On the Dynamics of an Impulsive Model of Hematopoiesis
- Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments
- Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models
- Dynamics of Erythroid Progenitors and Erythroleukemia
- Stability analysis of models of cell production systems
- Asymptotic Analysis of a Cell Cycle Model Based on Unequal Division
- An Abstract Delay-Differential Equation Modelling Size Dependent Cell Growth and Division
- An Operator-Theoretic Formulation of Asynchronous Exponential Growth
- Comparison of Approaches to Modeling of Cell Population Dynamics
- Hypercyclic and chaotic semigroups of linear operators
- Hypercyclicity of solutions of a transport equation with delays
- A Survey of Cell Population Dynamics
- Cyclical Thrombocytopenia: Characterization by Spectral Analysis and a Review
- Oscillation and Chaos in Physiological Control Systems
- Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling
- Mathematical Models of Hematopoietic Reconstitution After Stem Cell Transplantation
- Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics
- Numerical Modelling of Cell Distribution in Blood Flow
- Chaoticity of the blood cell production system
- A multi-scale model of erythropoiesis
- Bifurcation and Bistability in a Model of Hematopoietic Regulation
- A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia
- Optimal Control of Leukemic Cell Population Dynamics
- Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division
- Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia
- Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia
- Long Period Oscillations in aG0Model of Hematopoietic Stem Cells
- Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays
- Optimal Proliferation Rate in a Cell Division Model
- Observations on the Pathophysiology and Mechanisms for Cyclic Neutropenia
- Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis
- Cell Modelling of Hematopoiesis
- Diagnostics of the AML with immunophenotypical data
- Sufficient conditions for stability of linear differential equations with distributed delay
- Multistability in an age-structured model of hematopoiesis: cyclical neutropenia
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
