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Age-structured and two-delay models for erythropoiesis
J Bélair1, M C Mackey, J M Mahaffy
1Département de Mathématiques et de Statistique, Université de Montréal, Québec, Canada.
Mathematical Biosciences
|July 1, 1995
Summary
This study models red blood cell production (erythropoiesis) using differential delay equations. The model predicts red blood cell dynamics and disease states like anemia, validated with human and rabbit data.
Area of Science:
- Mathematical Biology
- Hematology
- Dynamical Systems
Background:
- Erythropoiesis, the process of red blood cell production, is complex and involves feedback mechanisms.
- Mathematical modeling is crucial for understanding erythropoiesis regulation and its dysregulation in diseases.
Purpose of the Study:
- To develop and analyze an age-structured mathematical model for erythropoiesis.
- To investigate the model's behavior, including stability and bifurcations, under varying parameters.
Main Methods:
- Development of an age-structured model for erythropoiesis.
- Reduction to threshold-type differential delay equations using the method of characteristics.
- Parameter estimation from experimental data and simulation.
- Analysis of the characteristic equation for Hopf bifurcations.
Main Results:
- The model was successfully reduced to a system of delay differential equations with two delays.
- Simulations for a normal human subject after blood loss showed model predictability.
- Hopf bifurcations were identified, indicating potential for oscillatory dynamics in erythropoiesis.
- Numerical studies for a rabbit with autoimmune hemolytic anemia were performed and compared with experimental data.
Conclusions:
- The developed mathematical model provides a robust framework for studying erythropoiesis.
- The model captures key aspects of red blood cell dynamics, including responses to blood loss and disease states.
- Bifurcation analysis reveals critical thresholds influencing erythropoiesis stability.