A continuity equation for cell populations

Oldfield, D.

doi:10.1007/bf02476861

Cited by 24 publications

(8 citation statements)

References 2 publications

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“…Several continuous-time models with these properties originated in the study of populations of cells in tissue culture. Following Von Foerster's (1959) theoretical study of a population with age-dependent dynamics, Oldfield ( 1966) and Sinko and Streifer ( 1967) extended his model to include interactions between age and additional physiological variables such as size. Other authors (Stuart and Merkle 1965, Rubinow 1968, Weiss 1968, Gopalsamy 1978, Thompson and Cauley 1979, Iwasa 1981 have investigated models in which specific random processes govern the maturation of individuals in a population.…”

Section: Introductionmentioning

confidence: 99%

Demographic Models Based on Size, Not Age, For Organisms with Indeterminate Growth

Kirkpatrick¹

1984

Ecology

134

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In conventional demographic theory fecundity and survival are determined by the age of the individual, but for many organisms size is more important than age in determining life history characteristics. Continuous—time demographic models presented here explicitly account for growth, including individual variability in growth rate, and assume that size alone determines the birth and death rates. Growth and mortality processes are introduced that result in a normal distribution (on some scale of measurement) of the sizes of individuals within a cohort; this permits the cohort to be described in terms of only three variables; mean size, variance in size, and proportion of individuals surviving. Using general formulae for the intrinsic rate of population increase and the stable size distribution, applications of the models are presented illustrating the effects of individual growth rate variance and size—specific mortality on characteristics of the population.

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Section: Introductionmentioning

confidence: 99%

Demographic Models Based on Size, Not Age, For Organisms with Indeterminate Growth

Kirkpatrick¹

1984

Ecology

134

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“…Fortunately, in recent years reasonable agreement has coalesced concerning the equations that govern the aging of biological populations (Von Foerster 1959, Trucco 1965, Oldfield 1966, Frederickson et al, 1967, Sinko and Streiffer 1967, Langhaar 1972. It behooves us, therefore, in imitation of physics, to investigate all of the mathematical, i.e.…”

Section: Introductionmentioning

confidence: 99%

Models for Age‐Specific Interactions in a Periodic Environment

Oster¹,

Takahashi²

1974

Ecological Monographs

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In 1954 Hutchinson and S1obodkin suggested that populations can be viewed as feedback systems that could resonate in response to environmental fluctuation with a frequency o.f approximately one. generation time. In this paper we pursue this observation by con~tructmg several mathema~rcal models .based on the demographic equations governing populatr.on ag.e structure. The ~xrstence of thrs and several other effects of ecological importance are mvestrgated for populatrons coupled by age-specific interactions.

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“…where k is a nonnegative measurable function such that 1 a k(y, m) dy = 1 for all m. One of the areas in which such models have been used is that of cell replication and maturation and these applications have been around for over 50 years, [6,21,22,27,31,32]. A survey of many applications is given in the book edited by Metz and Diekmann [20].…”

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confidence: 99%

Asynchronous Exponential Growth of a General Structured Population Model

2011

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We consider a class of structured cell population models described by a first order partial differential equation perturbed by a general birth operator which describes in a unified way a wide class of birth phenomena ranging from cell division to the McKendrick model. Using the theory of positive stochastic semigroups we establish new criteria for an asynchronous exponential growth of solutions to such equations.

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A continuity equation for cell populations

Cited by 24 publications

References 2 publications

Demographic Models Based on Size, Not Age, For Organisms with Indeterminate Growth

Demographic Models Based on Size, Not Age, For Organisms with Indeterminate Growth

Models for Age‐Specific Interactions in a Periodic Environment

Asynchronous Exponential Growth of a General Structured Population Model

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