127 research outputs found
A system of state-dependent delay differential equation modelling forest growth I: semiflow properties
In this article we investigate the semiflow properties of a class of
state-dependent delay differential equations which is motivated by some models
describing the dynamics of the number of adult trees in forests. We investigate
the existence and uniqueness of a semiflow in the space of Lipschitz and
weighted functions. We obtain a blow-up result when the time approaches the
maximal time of existence. We conclude the paper with an application of a
spatially structured forest model
Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups
AbstractThe aim of this article is to derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues for linear functional differential equations (FDE) by using integrated semigroup theory. The idea is to formulate the FDE as a non-densely defined Cauchy problem and obtain an explicit formula for the integrated solutions of the non-densely defined Cauchy problem, from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues. The results are useful in studying bifurcations in some semi-linear problems
Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model
Cancer is a proliferation disease affecting a genetically unstable cell
population, in which molecular alterations can be somatically inherited by
genetic, epigenetic or extragenetic transmission processes, leading to a
cooperation of neoplastic cells within tumoral tissue. The efflux protein
P-glycoprotein (P gp) is overexpressed in many cancer cells and has known
capacity to confer multidrug resistance to cytotoxic therapies. Recently,
cell-to-cell P-gp transfers have been shown. Herein, we combine experimental
evidence and a mathematical model to examine the consequences of an
intercellular P-gp trafficking in the extragenetic transfer of multidrug
resistance from resistant to sensitive cell subpopulations. We report
cell-to-cell transfers of functional P-gp in co-cultures of a P-gp
overexpressing human breast cancer MCF-7 cell variant, selected for its
resistance towards doxorubicin, with the parental sensitive cell line. We found
that P-gp as well as efflux activity distribution are progressively reorganized
over time in co-cultures analyzed by flow cytometry. A mathematical model based
on a Boltzmann type integro-partial differential equation structured by a
continuum variable corresponding to P-gp activity describes the cell
populations in co-culture. The mathematical model elucidates the population
elements in the experimental data, specifically, the initial proportions, the
proliferative growth rates, and the transfer rates of P-gp in the sensitive and
resistant subpopulations. We confirmed cell-to-cell transfer of functional
P-gp. The transfer process depends on the gradient of P-gp expression in the
donor-recipient cell interactions, as they evolve over time. Extragenetically
acquired drug resistance is an additional aptitude of neoplastic cells which
has implications in the diagnostic value of P-gp expression and in the design
of chemotherapy regimensComment: 13 pages, 8 figures, 1 tabl
On a Vector-host Epidemic Model with Spatial Structure
In this paper, we study a reaction-diffusion vector-host epidemic model. We
define the basic reproduction number and show that is a threshold
parameter: if the disease free steady state is globally stable; if
the model has a unique globally stable positive steady state. We then
write as the spectral radius of the product of one multiplicative
operator and two compact operators with spectral radius equalling one.
Here corresponds to the basic reproduction number of the model without
diffusion and is thus called local basic reproduction number. We study the
relationship between and as the diffusion rates vary
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