For an SI type endemic model with one host and two parasite strains, we study thestability of the endemic coexistence equilibrium, where the host and both parasite strainsare present. Our model, which is a system of three ordinary differential equations,assumes complete cross-protection between the parasite strains and reduced fertility andincreased mortality of infected hosts. It also assumes that one parasite strain isexclusively vertically transmitted and cannot persists just by itself. We give severalsufficient conditions for the equilibrium to be locally asymptotically stable. One of themis that the horizontal transmission is of density-dependent (mass-action) type. If thehorizontal transmission is of frequency-dependent (standard) type, we show that, undercertain conditions, the equilibrium can be unstable and undamped oscillations can occur.We support and extend our analytical results by numerical simulations and bytwo-dimensional plots of stability regions for various pairs of parameters.

An analysis of all possible icosahedral viral capsids is proposed. It takes into accountthe diversity of coat proteins and their positioning in elementary pentagonal andhexagonal configurations, leading to definite capsid size. We show that theself-organization of observed capsids during their production implies a definitecomposition and configuration of elementary building blocks. The exact number of differentprotein dimers is related to the size of a given capsid, labeled by itsT-number. Simple rules determining these numbers for each value ofT are deduced and certain consequences concerning the probabilities ofmutations and evolution of capsid viruses are discussed.

This paper deals with the evolution Fokker-Planck-Smoluchowski configurationalprobability diffusion equation for the FENE dumbbell model in dilute polymer solutions. Weprove the exponential convergence in time of the solution of this equation to acorresponding steady-state solution, for arbitrary velocity gradients.

We consider an ecosystem in whichspiders may be transported by the wind from vineyards into thesurrounding woods and vice versa. The model takes into accountthis tranport phenomenon without building space explicitly intothe governing equations. The equilibria of the dynamical systemare analyzed together with their stability, showing thatbifurcations may occur. Then the effects of indiscriminatedspraying to keep pests under control is also investigated viasuitable simulations.

A traceless variant of the Johnson-Segalman viscoelastic model is presented and appliedto blood flow simulations. The viscoelastic extra stress tensor is decomposed into itstraceless (deviatoric) and spherical parts, leading to a reformulation of the classicalJohnson-Segalman model. The equivalence of the two models is established comparing modelpredictions for simple test cases. The new model is validated using several 2D benchmarkproblems, designed to reproduce difficulties that arise in the simulation of blood flow inblood vessels or medical devices. The structure and behaviour of the new model arediscussed and the future use of the new model in envisioned, both on the theoretical andnumerical perspectives.

The paper is devoted to a reaction-diffusion equation in an infinite two-dimensionalstrip with nonlinear boundary conditions. The existence of travelling waves is proved inthe bistable case by the Leray-Schauder method. It is based on a topological degree forelliptic problems in unbounded domains and on a priori estimates of solutions.

The formation, persistence and movement of self-organised biological aggregations aremediated by signals (e.g., visual, acoustic or chemical) that organisms use to communicatewith each other. To investigate the effect that communication has on the movement ofbiological aggregations, we use a class of nonlocal hyperbolic models that incorporatesocial interactions and different communication mechanisms between group members. Weapproximate the maximum speed for left-moving and right-moving groups, and shownumerically that the travelling pulses exhibited by the nonlocal hyperbolic modelsactually travel at this maximum speed. Next, we use the formula for the speed of atravelling pulse to calculate the reversal time for the zigzagging behaviour, and showthat the communication mechanisms have an effect on these reversal times. Moreover, weshow that how animals communicate with each other affects also the density structure ofthe zigzags. These findings offer a new perspective on the complexity of the biologicalfactors behind the formation and movement of various aggregations.

A finite volume method for the simulation of compressible aerodynamic flows is described.Stabilisation and shock capturing is achieved by the use of an HLLC consistent numericalflux function, with acoustic wave improvement. The method is implemented on anunstructured hybrid mesh in three dimensions. A solution of higher order accuracy isobtained by reconstruction, using an iteratively corrected least squares process, and by anew limiting procedure. The numerical performance of the complete approach is demonstratedby considering its application to the simulation of steady turbulent transonic flow overan ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraftconfiguration.

No other concepts have shaken so deeply the bases of engineering like those of positiveand negative feedback. They have played a most prominent role in engineering since the beginningof the previous century. The birth certificate of positive feedback can be traced back to a pair ofpatents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is alreadylost in time. We present in this paper a short review on the feedback's origins in the fields ofengineering and biology. Besides, we compare the main feedback's ideas in control theory andsystem biology in order to get a better understanding of the lactose and tryptophan operons' regulatorysystems (control systems). It is obvious that we need to know the genome of an organismin order to understand how it works, but that is only half of the puzzle, for we also need to knowhow the underlying genetic regulatory systems work in order to get a complete picture of the cell'sdynamics.

Mathematical and computational neuroscience have contributed to the brain sciences by thestudy of the dynamics of individual neurons and more recently the study of the dynamics ofelectrophysiological networks. Often these studies treat individual neurons as points orthe nodes in networks and the biochemistry of the brain appears, if at all, as someintermediate variables by which the neurons communicate with each other. In fact, manyneurons change brain function not by communicating in one-to-one fashion with otherneurons, but instead by projecting changes in biochemistry over long distances. Thisbiochemical network is of crucial importance for brain function and it influences and isinfluenced by the more traditional electrophysiological networks. Understanding howbiochemical networks interact with electrophysiological networks to produce brain functionboth in health and disease poses new challenges for mathematical neuroscience.

The bifurcation to one-dimensional weakly subcritical periodic patterns is described bythe cubic-quintic Ginzburg-Landau equation

       At = µA + Axx + i(a1|A|2Ax + a2A2Ax*) + b|A|2A - |A|4A.

These periodic patterns may in turn become unstable through one of two differentmechanisms, an Eckhaus instability or an oscillatory instability. We study the dynamicsnear the instability threshold in each of these cases using the corresponding modulationequations and compare the results with those obtained from direct numerical simulation ofthe equation. We also study the stability properties and dynamical evolution of differenttypes of fronts present in the protosnaking region of this equation. The results providenew predictions for the dynamical properties of generic systems in the weakly subcriticalregime.

It is shown that a real Hankel matrix admits an approximate block diagonalization inwhich the successive transformation matrices are upper triangular Toeplitz matrices. Thestructure of this factorization was first fully discussed in [1]. This approach isextended to obtain the quotients and the remainders appearing in the Euclidean algorithmapplied to two polynomials u(x) andv(x) of degree n andm, respectively, whith m <n

We show that simple diffusion processes are weak limits of piecewise continuous processesconstructed within a totally deterministic framework. The proofs are based on thecontinuous mapping theorem and the functional central limit theorem.

We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new modelthat incorporates the transcriptional feedback loops revealed so far in the network of thecircadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not usedto describe the regulation of genes, instead the explicit reactions of binding and unbindingprocesses of transcription factors to promoters are probabilistically modelled. The modelis described by a set of ordinary differential equations, and the parameters are estimatedfrom the in vitro experimental data of the clocks' components. The model is robust over awide range of parameter variations. Through the sensitivity analysis of the model, roles ofVRI and PDP1 feedback loops are investigated, and it is proposed that they increase therobustness of the clock.

The image's restoration is an essential step in medical imaging.Several Filters are developped to remove noise, the most interestingare filters who permits to denoise the image preserving semanticallyimportant structures. One class of recent adaptive denoising methodsis the nonlinear Partial Differential Equations who knows currently asignificant success. This work deals with mathematical study for aproposed nonlinear evolution partial differential equation for imageprocessing. The existence and the uniqueness of the solution areestablished. Using a finite differences method we experiment thevalidity of the proposed model and we illustrate the efficiently ofthe method using some medical images. The Signal to Noise Ration(SNR) number is used to estimate the quality of the restoredimages.

We propose and analyze a nonlinear mathematical model of hematopoiesis,describing the dynamics of stem cell population subject to impulsiveperturbations. This is a system of two age-structured partial differentialequations with impulses. By integrating these equations over theage, we obtain a system of two nonlinear impulsive differential equations withseveral discrete delays. This system describes the evolution of the totalhematopoietic stem cell populations with impulses. We first examine theasymptotic behavior of the model in the absence of impulsions.Secondly, we add the impulsive perturbations and we investigate the qualitativebehavior of the model including the global asymptotic stability of the trivialsolution and the existence of periodic solution in the case of periodicimpulsive perturbations. Finally, numerical simulations are carriedout to illustrate the behavior of the model. This study maybe helpful tounderstand the reactions observed in the hematopoietic system after differentforms of stress as direct destruction by some drugs or irradiation.

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool tomeasure lymphocyte proliferation. CFSE fluorescence precisely halves after each celldivision in a highly predictable manner and is thus highly amenable to mathematicalmodelling. However, there are several biological and experimental conditions that canaffect the quality of the proliferation data generated, which may be important to considerwhen modelling dye dilution data sets. Here we overview several of these variablesincluding the type of fluorescent dye used to monitor cell division, dye labellingmethodology, lymphocyte subset differences, in vitro versus in vivo experimental assays,cell autofluorescence, and dye transfer between cells.

Motivated by recent experiments on the electro-hydrodynamic instability of spin-castpolymer films, we study the undulation instability of a thin viscoelastic polymer filmunder in-plane stress and in the presence of either a close by contactor or an electricfield, both inducing a normal stress on the film surface. We find that the in-plane stressaffects both the typical timescale of the instability and the unstable wavelengths. Thefilm stability is also sensitive to the boundary conditions used at the film-substrateinterface. We have considered two conditions, either rigidly attaching the film to thesubstrate or allowing for slip.

The paper considers a methodology of mathematical modeling ofecological-economicprocesses at the regional level. The basis of the model is formed by equations,which describetwo interacting blocks: economic and ecological ones. Equations of the economicblock are representedby relations of generalized inter-branch balance, while the ecological part isdescribedin terms of differential equations with deviations with respect to some givenstate of natural resources.Issues of i) information support of the model, ii) techniques used foridentification of thecoefficients, iii) scenario analysis and iv) forecasting are analyzed.

We examine the theoretical and applications-specific issues relating to modelingthetemporal and spatial dynamics of forest ecosystems, based on the principles ofinvestigating dynamicalmodels. When developing the predictive dynamical models of forest resources,there is apossibility of achieving uniqueness of the solutions to equations by taking intoaccount the initialand boundary conditions of the solution, and the conditions of the geographicalenvironment. Wepresent the results of a computer modeling and predictive mapping for theregional and subregionalmodel of the forest resource dynamics.