Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation
Busse, Jan-Erik (Interdisciplinary Center for Scientific Computing and BIOQUANT Center, (Germany))
Cuadrado Gavilán, Sílvia (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Marciniak-Czochra, Anna (Interdisciplinary Center for Scientific Computing and BIOQUANT Center, (Germany))

Data:	2022
Resum:	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.
Ajuts:	Agencia Estatal de Investigación MTM2017-84214-C2-2-P Ministerio de Ciencia e Innovación RED2018-102650-T
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Selection mutation process ; Integro-differential equations ; Cell differentiation model ; Stationary solutions ; Asymptotic stability
Publicat a:	Journal of mathematical biology, Vol. 84, Issue 1-2 (January 2022) , art. 10, ISSN 1432-1416

DOI: 10.1007/s00285-021-01708-w
PMID: 34988700

Postprint 36 p, 5.2 MB

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