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Pierre Auger [15]Pierre M. Auger [5]
  1. Pierre Auger, Ali Moussaoui & Gauthier Sallet (forthcoming). Basic Reproduction Ratio for a Fishery Model in a Patchy Environment. Acta Biotheoretica.
    Abstract We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities (...)
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  2. Etienne Kouokam, Pierre Auger, Hassan Hbid & Maurice Tchuente (forthcoming). Effect of the Number of Patches in a Multi-Patch SIRS Model with Fast Migration on the Basic Reproduction Rate. Acta Biotheoretica.
    We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than (...)
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  3. Ángel Blasco, Luis Sanz, Pierre Auger & Rafael Bravo de la Parra (2002). Linear Discrete Population Models with Two Time Scales in Fast Changing Environments II: Non-Autonomous Case. Acta Biotheoretica 50 (1).
    As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from (...)
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  4. Ángel Blasco, Luis Sanz, Pierre Auger & Rafael Bravo de la Parra (2001). Linear Discrete Population Models with Two Time Scales in Fast Changing Environments I: Autonomous Case. Acta Biotheoretica 49 (4).
    In this work we consider a structured population with groups and subgroups of individuals. The intra-group dynamics is assumed to be fast in comparison with the inter-group dynamics. We study linear discrete models where the slow dynamics is represented by a single matrix and the fast dynamics is described by means of the first k terms of a converging sequence of different matrices. The number k can be interpreted as the ratio between the two time scales.The aim of this work (...)
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  5. Karine Chalvet-Monfray, Marc Artzrouni, Jean-Paul Gouteux, Pierre Auger & Philippe Sabatier (1998). A Two-Patch Model of Gambian Sleeping Sickness: Application to Vector Control Strategies in a Village and Plantations. Acta Biotheoretica 46 (3).
    A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below (...)
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  6. Alain L. Bardou, Pierre M. Auger, Jean-Luc Chasse & Renaud Seigneuric (1997). Theoretical Study of Cardiac Transient Conduction Blocks on Reentries Induction. Applications to Antiarrhythmic Drugs. Acta Biotheoretica 45 (3-4).
    Limitations of antiarrhythmic drugs on cardiac sudden death prevention appeared since the early 80's. The "Cardiac Arrhythmia Suppression Trial"(CAST) showed more recently that mortality was significantly higher inpatients treated with some particular antiarrhythmic drugs than in non-treated patients. In this field, our group recently demonstrated that a bolus of a Class 1B antiarrhythmic drug was able to trigger a ventricular fibrillation due to transient blocks induction. The aim of the present work was to systematically study, by use of the van (...)
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  7. Eva Sanchez, Pierre Auger & Rafael Bravo de la Parra (1997). Influence of Individual Aggressiveness on the Dynamics of Competitive Populations. Acta Biotheoretica 45 (3-4).
    Two populations are subdivided into two categories of individuals (hawks and doves). Individuals fight to have access to a resource which is necessary for their survival. Conflicts occur between individuals belonging to the same population and to different populations. We investigate the long term effects of the conflicts on the stability of the community. The modelis a set of ODE's with four variables corresponding to hawk and dove individuals of the two populations. Two time scales are considered. A fast time (...)
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  8. Pierre Auger & Jean-Christophe Poggiale (1996). Aggregation and Emergence in Hierarchically Organized Systems: Population Dynamics. Acta Biotheoretica 44 (3-4).
    The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. A (...)
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  9. Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4).
    Aggregation methods allow one to replace a large scale dynamical system (micro-system) by a reduced dynamical system (macro-system) governing a small number of global variables. This aggregation of variables can be performed when two time scales exist, a fast time scale and a slow time scale. Perturbation theory allows to obtain an approximated aggregated dynamical system which describes the behaviour of a few number of slow time varying variables which are constants of motion of the fast part of the micro-system. (...)
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  10. Pierre Auger & Bruno Faivre (1995). A Spatial Model of Interspecific Competition and Selective Predation: The Case of the Two Hippolais. Acta Biotheoretica 43 (1-2).
    Mutual exclusion between congeneric species has been observed such as the case of the grey and red squirrels in Great Britain and the case of the twoHippolais warbler speciesHippolais icterina andH. polyglotta in Europe. This process can lead to the formation of an extinction wave which propagates. Two main assumptions are tested, competition and selective predation. The aim of this work is to present spatial models of these two processes. The animals of two species are assumed to move on a (...)
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  11. Alain L. Bardou, Pierre M. Auger, Soumeya Achour, Philippe Dumee, Pierre J. Birkui & Marie-Claude Govaere (1995). Effect of Myocardial Infarction and Ischemia on Induction of Cardiac Reentries and Ventricular Fibrillation. Acta Biotheoretica 43 (4).
    The present work is aimed at investigating the effects of myocardial infarction and ischemia on induction of ventricular fibrillation. Electrophysiologic effects of global and local ischemia (variation of the dispersion of refractory periods as well as conduction velocity) on initiation of reentry mechanisms was studied by means of computer simulations based on a cellular automata model of propagation of activation wave through a ventricular surface element. A local area of ischemia where effects of the dispersion of refractory periods are investigated (...)
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  12. Jean-Christophe Poggiale, Pierre Auger & Robert Roussarie (1995). Perturbations of the Classical Lotka-Volterra System by Behavioral Sequences. Acta Biotheoretica 43 (1-2).
    The complexity and the variability of parameters occurring in ecological dynamical systems imply a large number of equations.Different methods, more or less successful, have been described to reduce this number of equations. For instance, in the paper of Auger and Roussarie (1993), the authors describe how to obtain a reduction by considering different time-scales. They consider a system which can be sub-divided into sub-systems such that the strengths of the intra-sub-systems interactions are much larger than those of the inter-sub-systems interactions. (...)
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  13. Eva Sánchez, Rafael Bravo Parra & Pierre Auger (1995). Linear Discrete Models with Different Time Scales. Acta Biotheoretica 43 (4).
    Aggregation of variables allows to approximate a large scale dynamical system (the micro-system) involving many variables into a reduced system (the macro-system) described by a few number of global variables. Approximate aggregation can be performed when different time scales are involved in the dynamics of the micro-system. Perturbation methods enable to approximate the large micro-system by a macro-system going on at a slow time scale. Aggregation has been performed for systems of ordinary differential equations in which time is a continuous (...)
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  14. Pierre M. Auger & Robert Roussarie (1994). Complex Ecological Models with Simple Dynamics: From Individuals to Populations. Acta Biotheoretica 42 (2-3).
    The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of (...)
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  15. Pierre M. Auger & Bruno Faivre (1993). Effects of Individual Activity Sequences on Prey-Predator Models. Acta Biotheoretica 41 (1-2).
    We study the influence of the individual behaviour of animals on predator-prey models. Populations of preys and predators are divided into sub-populations corresponding to different activity classes. The animals are assumed to do many activities all day long such as searching for food of different types. The preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study activity sequences of the animals and (...)
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  16. Bruno Faivre & Pierre M. Auger (1993). Competition and Predation Models Applied to the Case of the Sibling Birds Species Ofhippolais in Burgundy. Acta Biotheoretica 41 (1-2).
    We study the case of two sibling species ofHippolais(Aves). Very little differences can be observed in the morphology of both species. The breeding area of these species are complementary. Roughly, one species breeds North and East of Europe (Hippolais icterina) while the other breeds South and West of Europe (Hippolais polyglotta). There exitst a narrow zone of sympatry passing through Burgundy. Since several years, it has been observed that this area of sympatry was moving in the North-East direction at a (...)
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  17. Pierre Auger, Peter Dörmer & Joachim W. Ellwart (1992). Growth Factors and Cell Kinetics: A Mathematical Model Applied to Il-3 Deprivation on Leukemic Cell Lines. Acta Biotheoretica 40 (2-3).
    We assume the existence of a specific G1 protein which is an initiator of DNA replication. This initiator is supposed to be synthesized according to Michaelis-Menten kinetics. In order to start DNA replication, it is assumed that this G1 specific protein must be produced in a required amount. Intra-cellular growth inhibitors and extra-cellular growth factors control the production of the initiator. This model allows to calculate the average G1 phase time as a function of the various chemical concentrations of nutrients, (...)
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  18. Alain Bardou & Pierre Auger (1992). Preface. Acta Biotheoretica 40 (2-3).
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  19. Pierre Auger (1963). Scientific Cooperation in Western Europe. Minerva 1 (4):428-438.
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