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Displaying 21 –
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107
A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour...
Since the release of the Bio 2010 report in 2003, significant emphasis has been placed on initiating changes in the way undergraduate biology and mathematics courses are taught and on creating new educational materials to facilitate those changes. Quantitative approaches, including mathematical models, are now considered critical for the education of the next generation of biologists. In response, mathematics departments across the country have initiated changes to their introductory calculus sequence,...
We derive a constitutive law for the myocardium from the description of both the geometrical arrangement of cardiomyocytes and their individual mechanical behaviour. We model a set of cardiomyocytes by a quasiperiodic discrete lattice of elastic bars interacting by means of moments. We work in a large displacement framework and we use a discrete homogenization technique. The macroscopic constitutive law is obtained through the resolution of a nonlinear self-equilibrum system of the discrete lattice...
We derive a constitutive law for the myocardium from the description of both the geometrical arrangement of
cardiomyocytes and their individual mechanical behaviour. We model a set of cardiomyocytes by a quasiperiodic discrete
lattice of elastic bars interacting by means of moments. We work in a large displacement framework and we use a discrete
homogenization technique. The macroscopic constitutive law is obtained through the resolution of a
nonlinear self-equilibrum system of the discrete lattice...
We study the growth rate of a cell population that follows an
age-structured PDE with time-periodic coefficients. Our motivation
comes from the comparison between experimental tumor growth curves
in mice endowed with intact or disrupted circadian clocks,
known to exert their influence on the cell division cycle.
We compare the growth rate of the model controlled by a time-periodic
control on its coefficients with the growth rate of stationary
models of the same nature, but with averaged coefficients....
Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with.Fortunately, there are many significant biological systems that are amenable to linear compartmental models which are often...
National policies regarding the BCG vaccine for tuberculosis vary greatly throughout the international community and several countries are currently considering discontinuing universal vaccination. Detractors of BCG point to its uncertain effectiveness and its interference with the detection and treatment of latent tuberculosis infection (LTBI). In order to quantify the trade-off between vaccination and treatment of LTBI, a mathematical model was designed and calibrated to data from Brazil, Ghana,...
Patients with acute myeloblastic leukemia (AML) are divided according to the French
American British (FAB) classification into eight subgroups (M0 to M7) on the basis of their degree
of maturation/differentiation. However, even if immunophenotypical characterization by flow cytometry
is routinely used to distinguish between AML and acute lymphoblastic leukemia (ALL), it
is not yet well established for the identification within the AML subgroups. Here we show that certain
subgroups of AML can be...
Chattopadhyay et al. [Biosystems (2003),
68, pp. 5-17] proposed and analyzed an N – P model in the presence
of viral infection on phytoplankton population. They studied the
dynamics under the constant nutrient input. The present paper deals
with the problem with seasonal variability on nutrient input. We use
a general periodic function for nutrient input. We observe the
dynamics of the system by considering (i) the infected phytoplankton
consumes nutrient and (ii) the infected phytoplankton is not...
Basic models suitable to explain the epidemiology of dengue fever have previously
shown the possibility of deterministically chaotic attractors, which might explain the observed
fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require
strong enhanced infectivity on secondary infection, motivated by experimental findings of
antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is
common knowledge among field researchers...
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107