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The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution under clonal reproduction (that is, we simply ignore the importance of genes and sex). Another basic assumption is that mutation occurs on a time scale which is long relative to the time scale of convergence...
A decision analytical model is presented and analysed to assess the effectiveness and
cost-effectiveness of routine vaccination against varicella and herpes-zoster, or
shingles. These diseases have as common aetiological agent the varicella-zoster virus
(VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity.
The general concern is that universal varicella vaccination might lead to more cases of
zoster: with more...
A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase.
The CDC launched the National Plan to Eliminate Syphilis from the USA in October 1999
[4]. In order to reach this goal, a good
understanding of the transmission dynamics of the disease is necessary. Based on a SIRS
model Breban et al.
[3] provided
some evidence that supports the feasibility of the plan proving that no recurring
outbreaks should occur for syphilis. We study in this work a syphilis model that includes
partial...
We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.
A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.
A possible control strategy against the spread of an infectious disease is the treatment
with antimicrobials that are given prophylactically to those that had contact with an infective person.
The treatment continues until recovery or until it becomes obvious that there was no infection
in the first place. The model considers susceptible, treated uninfected exposed, treated infected,
(untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that
treated uninfected...
Previous work has shown that intracellular delay needs to be taken into account to
accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay
also effects the estimated value for the infected T-cell loss rate when we assume that the drug is
not completely effective [19]. Models of virus infection that include intracellular delay are more
accurate representations of the biological data.
We analyze a non-linear model of the human immunodeficiency virus (HIV)...
Recently, adult stem cells have become a focus of intensive biomedical research, but the
complex regulation that allows a small population of stem cells to replenish depleted tissues is still
unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells
undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that
a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum
Sensing) suffices...
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