ArticleJournal of mathematical biology2022
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation.
Article in Journal of mathematical biology, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer.Bulletin of mathematical biology · 2021Article
- One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics.Acta applicandae mathematicae · 2021Article
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3 authors.
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Abstract
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.
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