The asynchronous exponential growth property in a model for the kinetic heterogeneity of tumour cell populations

DOI10.1016/j.jmaa.2004.08.024zbMath1084.92020OpenAlexW1980921213MaRDI QIDQ1763816

Ovide Arino, Eva Sanchez, Carmela Sinisgalli, Alessandro Bertuzzi, Alberto Gandolfi

Publication date: 22 February 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.08.024

zbMATH Keywords

Asynchronous exponential growthCell kinetic heterogeneityCell population dynamics

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Medical applications (general) (92C50) Population dynamics (general) (92D25) Groups and semigroups of linear operators (47D03) Cell biology (92C37) Applications of operator theory in chemistry and life sciences (47N60)

Related Items

Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity ⋮ Estimating the total rate of DNA replication using branching processes ⋮ Principal spectral theory and asynchronous exponential growth for age-structured models with nonlocal diffusion of Neumann type ⋮ Well-posedness and stability of the repairable system with \(N\) failure modes and one standby unit ⋮ On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process ⋮ Nonlinear dynamics in tumor-immune system interaction models with delays ⋮ Asymptotically exponential solutions in nonlinear integral and differential equations ⋮ A model with `growth retardation' for the kinetic heterogeneity of tumour cell populations ⋮ On a size-structured population model with infinite states-at-birth and distributed delay in birth process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mathematical models of the cell cycle with a view to tumor studies
• A model with `growth retardation' for the kinetic heterogeneity of tumour cell populations
• One-parameter semigroups of positive operators
• A model of proliferating cell populations with inherited cycle length
• A nonlinear structured population model of tumor growth with quiescence
• Mathematical analysis of cancer chemotherapy
• A theory for the age and generation time distribution of a microbial population
• Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence