Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation. (English) Zbl 1483.92058
Summary: 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.
MSC:
| 92C37 | Cell biology |
| 92D25 | Population dynamics (general) |
| 92C15 | Developmental biology, pattern formation |
| 45K05 | Integro-partial differential equations |
| 35B35 | Stability in context of PDEs |
Keywords:
selection mutation process; integro-differential equations; cell differentiation model; stationary solutions; asymptotic stabilityReferences:
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