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Salmonella strains colonize the digestive tract of farm livestock, such as chickens or pigs, without affecting them, and potentially infect food products, representing a threat for human health ranging from food poisoning to typhoid fever. It has been shown that the ability to excrete the pathogen in the environment and contaminate other animals is variable. This heterogeneity in pathogen carriage and shedding results from interactions between the host's immune response, the pathogen and the commensal intestinal microbiota. In this paper we propose a novel generic multiscale modeling framework of heterogeneous pathogen transmission in an animal population. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at between-host scale are added to obtain a drift-diffusion PDE model of the pathogen distribution at the population level. The model is further extended to represent transmission between several populations. The asymptotic behavior as well as the impact of control strategies including cleaning and antimicrobial administration are investigated through numerical simulation. [ABSTRACT FROM AUTHOR]

These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric. [ABSTRACT FROM AUTHOR]

Electroporation is a complex phenomenon that occurs when biological tissues are subjected to electric pulses. The clinical interest for the phenomenon has constantly increased for the last decades. Indeed, electroporation makes it possible to either kill directly the cells in the target region (tumor) or to introduce molecules into living cells. However, one of the main limitation of using electroporation in the clinical routine comes from the technical difficulties raised by such therapies, in particular it is difficult to well determine the treated zone. Numerical modeling of the electric field magnitude could provide a powerful strategy to assess the treatment efficacy: thanks to well-designed models, the computation of the distribution of the electric field is achievable, providing a numerical evaluation of the treatment. The main objective of this work is to go further on the patient-adapted numerical modeling of the electric field magnitude by laying the ground of the possible electroporation models - which will be compared qualitatively - and their calibrations. This will be done in the framework of bioelectrical measurements on rabbit livers that come from the literature. [ABSTRACT FROM AUTHOR]

Cell migration is a complex phenomenon that plays an important role in many biological processes. Our aim here is to build and study models of reduced complexity to describe some aspects of cell motility in tissues. Precisely, we study the impact of some biochemical and mechanical cues on the cell dynamics in a 2D framework. For that purpose, we model the cell as an active particle with a velocity solution to a particular Stochastic Differential Equation that describes the intracellular dynamics as well as the presence of some biochemical cues. In the 1D case, an asymptotic analysis puts to light a transition between migration dominated by the cell's internal activity and migration dominated by an external signal. In a second step, we use the contact algorithm introduced in [15,18] to describe the cell dynamics in an environment with obstacles. In the 2D case, we study how a cell submitted to a constant directional force that mimics the action of chemoattractant, behaves in the presence of obstacles. We numerically observe the existence of a velocity value that the cell can not exceed even if the directional force intensity increases. We find that this threshold value depends on the number of obstacles. Our result confirms a result that was already observed in a discrete framework in [3,4]. [ABSTRACT FROM AUTHOR]

We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically. [ABSTRACT FROM AUTHOR]

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructured grid. Finally, we describe an extension to three materials. [ABSTRACT FROM AUTHOR]

Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to their offspring. Consistent experimental evidence report that this phenomenon plays an essential role in the evolution of certain bacterias. In particular, HT is believed to be the main instrument of developing the antibiotic resistance. In this work, we consider several models which describe this phenomenon: a stochastic jump process (individual-based) and the deterministic nonlinear integrodifferential equation obtained as a limit for large populations. We also consider a Hamilton-Jacobi equation, obtained as a limit of the deterministic model under the assumption of small mutations. The goal of this paper is to compare these models with the help of numerical simulations. More specifically, our goal is to understand to which extent the Hamilton-Jacobi model reproduces the qualitative behavior of the stochastic model and the phenomenon of evolutionary rescue in particular. [ABSTRACT FROM AUTHOR]

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics. [ABSTRACT FROM AUTHOR]

Being able to monitor and forecast farm animal performances is a strategic problem in the agronomy industry. We use a Data-Model Coupling approach to build a biomimetic Statistical Learning tool taking into account some aspects of the biological dynamics of the animal body. The objective is to build a tool which is able to assimilate data about daily feed consumption and measured performances. The model encompasses several sub-models corresponding to compartments and permitting to mimic a kinetic process divided into several steps. Each sub-model contains parameters which can be learnt by using an optimization algorithm and data. The goal of the first application of the model on field data was to simulate and predict the growth of chickens. An experiment was performed during 70 days to collect every day the feed consumption and the weight gain of a male and a female chickens. After the learning of the model parameters, the model shows a very good approximation of the chicken's weight evolution over time. [ABSTRACT FROM AUTHOR]

We present a new method for defining and meshing patient-specific domains from medical images. Our approach is based on an atlas image segmentation technique, and relies on the modular registration algorithm of S. Bertoluzza et al. [25]. The mesh of the patient-specific domain is generated by deforming the corresponding mesh on an a priori segmented and meshed reference image (the atlas). Our method aims at automating the process at the interface of medical imaging and numerical simulation, thus reducing the computational cost in those situations where simulations have to be managed on numerous medical images of similar patients. [ABSTRACT FROM AUTHOR]

We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ finite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem. [ABSTRACT FROM AUTHOR]

We consider a reaction-diffusion-reproduction equation, modeling a population which is spatially heterogeneous. The dispersion of each individuals is influenced by its phenotype. In the literature, the asymptotic propagation speed of an asexual population has already been rigorously determined. In this paper we focus on the difference between the asexual reproduction case, and the sexual reproduction case, involving a non-local term modeling the reproduction. This comparison leads to a different invasion speed according to the reproduction. After a formal analysis of both cases, leading to a heuristic of the asymptotic behaviour of the invasion fronts, we give some numerical evidence that the acceleration rate of the spatial spreading of a sexual population is slower than the acceleration rate of an asexual one. The main difficulty to get sharper results on a transient comes from the non-local sexual reproduction term. [ABSTRACT FROM AUTHOR]

In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the population-level feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging. [ABSTRACT FROM AUTHOR]

In order to prevent the propagation of human diseases transmitted by mosquitoes (as dengue or zika), a solution is to release mosquitoes infected by Wolbachia. In this study, we model the release and the propagation over time and space of such infected mosquitoes in a population of uninfected ones. The aim of this study is to investigate the best location in space of the release to ensure invasion by the infected mosquitoes. [ABSTRACT FROM AUTHOR]

We study a model of cell segregation in a population composed of two cell types. Starting from a model initially proposed in [3], we aim to understand the impact of a cell division process on the system's segregation abilities. The original model describes a population of spherical cells interacting with their close neighbors by means of a repulsion potential and which centers are subject to Brownian motion. Here, we add a stochastic birth-death process in the agent-based model, that approaches a logistic growth term in the continuum limit. We address the linear stability of the spatially homogeneous steady states of the macroscopic model and obtain a precise criterion for the phase transition, which links the system segregation ability to the model parameters. By comparing the criterion with the one obtained without logistic growth, we show that the system's segregation ability is the result of a complex interplay between logistic growth, diffusion and mechanical repulsive interactions. Numerical simulations are presented to illustrate the results obtained at the microscopic scale. [ABSTRACT FROM AUTHOR]

Recent advances in the study of Alzheimer's Disease and the role of Aβ amyloid formation have caused the focus of biologists to progressively shift towards the smaller protein assemblies, the oligomers. These appear very early on in the disease progression and they seem to be the most infectious species for the neurons. We suggest a model of spatial propagation of Aβ oligomers in the vicinity of a few neurons, without considering the formation of large fibrils or plaques. We also include a simple representation of the oligomers neurotoxic effect. A numerical study reveals that the oligomers spatial dynamics are very sensitive to the balance between their diffusion and their replication, and that the outcome in terms of the progression of AD strongly depends on it. [ABSTRACT FROM AUTHOR]