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ABSTRACT: In this paper, we propose a mathematical model to study a bacteria–fish system, based upon the interactions between Clostridium botulinum and tilapia, Oerochromis mossambicus. The fish population is divided into susceptible and infected, and the infected fish population is considered structured by the level of infection. The model is thus a system with the infected fish equation being an evolution equation, while those corresponding to the susceptible fish and bacteria in water are ordinary differential equations. The model is firstly transformed into a system with distributed delay for susceptible fish and bacteria and, further, under some assumptions, into a system with discrete delay. The study of this system gives us some results concerning the existence, uniqueness, positivity and boundedness of solutions; we also discuss the existence and stability of its equilibrium points, including conditions for the appearance of Hopf bifurcation. The theoretical results are illustrated by some numerical simulations.
Nonlinear Analysis Real World Applications 01/2009; 10:1662-1678. · 2.04 Impact Factor
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ABSTRACT: The aim of this paper is to put in evidence the onset of state-dependent delays in threshold models for structured population dynamics. A unified approach to these mod-els is provided, based on solving the corresponding balance law (hyperbolic P.D.E.) along the characteristic lines and showing the common underlying ideas. Size and age-structured models in different fields are presented: insect populations, cell proliferation and epidemics.
Mathematical Models and Methods in Applied Sciences. 01/2007; 17:877-900.
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ABSTRACT: The aim of this study was to analyze the results from the first pharmacology exam at the National Autonomous University of Mexico (UNAM). Defined performance criteria were considered from a database of 909 students containing the total number of correct answers, as well as their percentage related to each of the nine topics of the exam. Data were processed with the JMP statistical program to obtain student performance, using 60% of correct answers per topic as the test limit reference criterion. Only 21.5% of the students mastered at least 60% of each of the nine exam topics (satisfactory performance). Close to one fifth of the total number of students achieved comprehensive knowledge of exam topics. The students attending morning classes achieved four points higher than the mastered percentage reached by the total student population tested; far higher than the afternoon or evening classes. In this analysis, afternoon class reached the highest unsatisfactory performance percentage of all groups. We suggest that this information could be used to help students improve their learning process and could inform educational decision makers. INTRODUCTION The major purpose of this study was to analyze the results of the first pharmacology exam at UNAM, using formative assessment [1], trying to stress the importance to score the information about the students' behavior according to Glaser's [2] test limit reference criterion. This test limit reference criterion is commonly used to qualitatively analyze student achievement, and is based on the hypothesis that the professional learner encounters critical variables to fulfill their essential activities. Such variables cannot compensate for a deficiency in one area with a surpassing capacity in others. The students who do not reach the minimal essential ability required will surely fail, independently from their other existing talents [3]. For example, through medical instruction, a high global qualification due to high marks in some specific subject tasks may mask a grave knowledge deficiency, and it happens that such knowledge is intellectually indispensable to the clinical practice as it is with pharmacology knowledge. Achieving a global approbatory mark, even at the expense of high marks obtained in a partial examination, may be keeping occult, low qualifications which really reflect a poor specific knowledge management needed to continue learning, and, if this is not addressed, there may be the risk of a settling for a deficit in critical information. This learning evaluation procedure is considered as a kind of emergent assessment [4].
Proc. West. Pharmacol. Soc. 01/2006; 49:171-172.
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ABSTRACT: Submitted by William F. Ames This paper is devoted to the loving memory of our friend Ovide Arino, who passed away during the production of it Abstract The aim of this paper is to apply and justify the so-called aggregation of variables method for reduction of a complex system of linear delayed differential equations with two time scales: slow and fast. The difference between these time scales makes a parameter ε > 0 to appear in the formulation, being a mathematical problem of singular perturbations. The main result of this work consists of demonstrating that, under some hypotheses, the solution to the perturbed problem converges when ε → 0 to the solution of an aggregated system whose construction is proposed.
J. Math. Anal. Appl. 01/2006; 323:680-699.
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ABSTRACT: We present a model of two interacting populations using two individual strategies, hawk and dove. Individuals encounter each other frequently and can change tactics several times in their life. Conflicts occur between individuals belonging to the same population and to different populations. The general model is based on the replicator equations which are used to describe the variations of the hawk proportions of the two popula-tions. According to parameter values, namely the gain-, the intra-and inter-population costs, and the relative intra-population encounter rates, we classify the different phase portraits. We show that a decrease in the intra-population cost of a population provokes an increase in the hawk proportion in this population and of the dove proportion in the other population. An increase in the inter-population cost favors hawk strategy in the population which causes more injuries and dove strategy in the other. We also study the effects of the relative densities of the two populations on the stability of equilibria. In most cases, an increase in the relative density of a population leads to a decrease in hawk proportion in this population and of dove proportion in the other.
01/2001; 18(11):645-661.
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ABSTRACT: In this work we extend approximate aggregation methods in time discrete linear models to the case of time varying environments. Approximate aggregation consists of describing some features of the dynamics of a general system involving many coupled variables in terms of the dynamics of a reduced system with a few "global" variables. We present a time varying discrete model in which we distinguish two processes with different time scales. By defining the global variables as appropriate linear combinations of the state variables, we transform the system into a reduced one. The variables cor-responding to the original and reduced systems can be related, therefore allowing one the study of the former in terms of the latter. The property of weak ergodicity, which has to do with the capacity of a system to become asymptotically independent of initial conditions, is explored for the original and reduced systems. The general method is also applied to aggregate a time-dependent multiregional model which appears in the field of population dynamics in two different cases: Fast migration with respect to demography and fast demography with respect to migration.
01/2001; 11(11):1203-1235.
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Nonlinear Analysis Real World Applications 01/2000; 1:89-122. · 2.04 Impact Factor
