We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation. We conclude by extending this framework to a spatial context, facilitating the modeling of traveling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.
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http://dx.doi.org/10.1103/PhysRevE.105.064411 | DOI Listing |
Phys Rev E
June 2022
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom.
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation.
View Article and Find Full Text PDFPLoS One
July 2020
Fisheries and Oceans Canada, Northwest Atlantic Fisheries Center, St. John's, Newfoundland and Labrador, Canada.
Populations often show complex spatial and temporal dynamics, creating challenges in designing and implementing effective surveys. Inappropriate sampling designs can potentially lead to both under-sampling (reducing precision) and over-sampling (through the extensive and potentially expensive sampling of correlated metrics). These issues can be difficult to identify and avoid in sample surveys of fish populations as they tend to be costly and comprised of multiple levels of sampling.
View Article and Find Full Text PDFJ Optim Theory Appl
December 2019
Wittgenstein Centre (IIASA, VID/ÖAW, WU), Vienna Institute of Demography, Vienna, Austria.
The paper presents a transformation of a multi-stage optimal control model with random switching time to an age-structured optimal control model. Following the mathematical transformation, the advantages of the present approach, as compared to a standard backward approach, are discussed. They relate in particular to a compact and unified representation of the two stages of the model: the applicability of well-known numerical solution methods and the illustration of state and control dynamics.
View Article and Find Full Text PDFMath Biosci Eng
June 2014
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China.
In this paper, an age-structured epidemic model is formulated to describe the transmission dynamics of cholera. The PDE model incorporates direct and indirect transmission pathways, infection-age-dependent infectivity and variable periods of infectiousness. Under some suitable assumptions, the PDE model can be reduced to the multi-stage models investigated in the literature.
View Article and Find Full Text PDFJ Theor Biol
June 2006
School of Chemical Engineering, Forney Hall of Chemical Engineering, 480 Stadium Mall Way, Purdue University, West Lafayette, IN 47907, USA.
An age-structured population balance model that explicitly models cell cycle phases is developed to investigate the effects of cell cycle specific (CCS) drugs. In particular, the benefits of timing CCS drug treatments in resonance chemotherapy are predicted and measured directly in vitro before evaluating likely in vivo scenarios. The phase transition rates are measured in vitro for the HL60 leukemia cell line and are used to predict the transient phase dynamics after exposure to the S phase specific drug, camptothecin.
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