Seminars LMAH 2025

• February 26 2026, 02:00 pm Jessie Levillain, CNES and INSA Toulouse.
  
  Title: Fokker-Planck based mathematical models for flagellar activation mechanisms.
  Abstract: Many micro-swimmers in nature achieve locomotion via active appendages-like organelles such as cilia or flagella, when moving inside fluids at a low Reynolds number. In order to swim as efficiently as possible in viscous fluids, these cilia and flagella all have a characteristic periodic motion. This motion arises from a active internal structure that runs along the entire length of the filament, known as the axoneme. Within the axoneme, forces are generated by molecular motors that act collectively to produce the filament’s curvature. After analyzing a first model for molecular motors, we will introduce several formulations of coupled partial differential equation systems describing activation within a small periodicity cell. We then prove the presence of a supercritical Hopf bifurcation in the system. Theoretical results will be complemented by numerical simulations.


• February 19 2026, 02:00 pm Leo Meyer, Vienna University, Austria.
  
  Title: Emergent Phase Transitions in Collective Dynamics: Numerical Approximation and Band Formation.
  Abstract: I will present the results of a collaboration with Pierre Degond and Sara Merino-Aceituno. We study the emergence of band patterns in the Vicsek model, a minimal agent-based model of alignment dynamics with noise. Agent-based simulations on periodic domains display coexisting ordered (high-density, aligned) bands and disordered (low-density, non-aligned) regions, a phenomenon not explained by classical parameter-driven phase transitions. We review prior kinetic and macroscopic results that identify an Emergent Phase Transition (EPT): depending on the local density ρ relative to a critical threshold ρ_c, different PDEs govern different spatial regions—Self-Organized Hydrodynamics (SOH) in the ordered regime (ρ > ρ_c) and a degenerate diffusive correction (at order ε) in the disordered regime (ρ < ρ_c). Building on this framework, we propose a model that couples the ordered and disordered macroscopic equations to simulate the continuum dynamics, with the goals of reproducing band formation at the macroscopic level, exploring pattern formation, and connecting the linear stability properties of the coupled model with those of SOH.


• February 5 2026, 02:00 pm Charles Elbar, Claude Bernard University, Lyon 1.
  
  Title: Deterministic particle approximation of a fourth-order PDE.
  Abstract: Many partial differential equations describe how a macroscopic density of particles/cells evolves in time. So, it is a natural question to ask whether there’s a microscopic (deterministic) model that leads to a given macroscopic PDE. For second-order aggregation–diffusion equations, this connection has been proved, starting with the porous medium equation in 2001. In this work, we extend that framework to a fourth-order equation, inspired by applications in cell–cell adhesion in biological systems. This is a joint work with Alejandro Fernandez-Jimenez.


• January 22 2026, 02:00 pm Thi Nhu Thao NGUYEN, Universitof Pau and Pays de l'Adour.
  
  Title: Applications of Multiscale Models to Population Dynamics.
  Abstract: In this presentation, I will discuss my PhD and postdoctoral research on the application of numerical methods in biology. We used an Individual-Based Model (IBM) to analyze the collective behavior of agents following simple rules, linking individual behaviors to spatial features and revealing emergent population dynamics. This approach was applied to multiscale models for voles, CD8 T cells, and neuroblastoma organoids. Inspired by the hybrid ODE–Multi-Agent model of Marilleau–Lang–Giraudoux [1], we developed a model to analyze vole population dynamics in France, using ordinary differential equations within square cells, without explicit spatial dynamics. When the density in a cell exceeds a threshold, young voles migrate and form an agent whose behavior is influenced by the topography and neighboring cells. We used a directed graph with transport equations for each colony and simulated transitions between colonies [2]. The simulations validated the simplified model, and we also explored more complex models for vole population density [3] and predator–prey interactions [4]. During my postdoctoral research, I used the Simuscale software [5] developed at INRIA to build multiscale models for CD8 T cells and neuroblastoma organoids. We modeled CD8 T cells using an IBM approach, including a genetic regulatory network described by a piecewise deterministic Markov process, which successfully reproduced the biological dynamics and allowed parameter sensitivity analysis [6]. For neuroblastoma organoids, a simple genetic network was developed, and the simulated 3D structures were validated through comparison with immunohistochemistry images, using quantitative measurements of spatial distributions [7].

  References

  [1] N. Marilleau, C. Lang, and P. Giraudoux. Coupling agent-based with equation-based models to study spatially explicit megapopulation dynamics. Ecological Modelling, 384:34–42, 2018.

  [2] C. Donadello, T. N. T. Nguyen, and U. Razafison. On the mathematical modeling of vole populations spatial dynamics via transport equations on a graph. Applied Mathematics and Computation, 396:125885, 2021.

  [3] G. M. Coclite, C. Donadello, and T. N. T. Nguyen. A PDE model for the spatial dynamics of a vole population structured by age. Nonlinear Analysis, 196:111805, 2020.

  [4] G. M. Coclite, C. Donadello, and T. N. T. Nguyen. A hyperbolic–parabolic predator–prey model involving a vole population structured by age. Journal of Mathematical Analysis and Applications, 502:125232, 2021.

  [5] S. Bernard, F. Crauste, O. Gandrillon, C. Knibbe, and D. Parsons. Simuscale: A Modular Framework for Multiscale Single-Cell Modelling. Technical Report RT-0520, Inria Lyon, January 2024.

  [6] T. N. T. Nguyen, M. Martin, C. Arpin, S. Bernard, O. Gandrillon, and F. Crauste. In silico modelling of CD8 T cell immune response links genetic regulation to population dynamics. ImmunoInformatics, 15:100043, 2024.

  [7] T. N. T. Nguyen, C. Koering, E. Vallin, S. Gonin-Giraud, L. Broutier, S. Bernard, F. Crauste, and O. Gandrillon. Multiscale modeling of the spatial structure of stem cells in neuroblastoma patient-derived tumoroids reveals a critical role for a short-range diffusive process. PLoS Computational Biology.



• January 15 2026, 02:00 pm Maxime Estavoyer, Marseille University.
  
  Title: Mathematical modeling of dermal competence and cellular aggregation effects on feather follicle emergence speed.
  Abstract: We study a reaction–diffusion–chemotaxis system motivated by feather follicle morphogenesis, focusing on the interaction between a propagating competence front and a pattern-forming aggregation mechanism. The model exhibits two distinct propagation phenomena: a traveling wave associated with tissue competence acquisition and a secondary instability leading to spatial aggregation. We compute the speed of the competence wave and perform a weakly nonlinear analysis to estimate the aggregation-driven emergence speed within the competent domain. Numerical simulations demonstrate a speed-selection mechanism: when the spatial pattern propagates faster than the competence front, the resulting pattern synchronizes with the competence wave, while the competence wave remains dynamically independent.


• January 8 2026, 02:00 pm Kamal Khalil, Le Havre.
  
  Title: Invariant sets under semiflows via a Lie--Trotter product formula for semilinear evolution equations
  Abstract: Using a Lie--Trotter product formula for local semiflows, we derive sufficient conditions for the invariance of closed convex sets for a class of semilinear parabolic evolution equations in Banach spaces. As an application, we study a coupled diffusion--advection--reaction system and provide concrete assumptions on the initial data ensuring the invariance of prescribed convex regions. In particular, the obtained criteria guarantee positivity and uniform bounds for solutions within this class.


• December 18 2025, 02:00 pm Charlotte Dugourd-Camus, INRIA, Lyon.
  
  Title: Multi-serotype nested immuno-epidemiological model for dengue hemorrhagic fever involving backward bifurcation and serotype invasion
  Abstract: Reinfection with the same dengue serotype is generally benign, as individuals develop protective immunity. On the other hand, in the case of reinfection with a different serotype, pre-existing antibodies can increase the risk of developing Dengue Hemorrhagic Fever (DHF), by inducing Antibody-Dependent Enhancement (ADE). To model this dynamic, we introduce a multi-scale immuno-epidemiological system. The immunological part is described by a system of ODEs representing the interaction between two antibodies (from previous and current infection) and the virus. The epidemiological part is represented by an infection-age structured SIRS system (for both the primary and secondary infections) and a recovery-age structured equation (for the first infection). We provide results on the equilibrium points of the multi-scale reinfection model, including disease-free, mono-endemic and bi-endemic states. We derive an expression for the invasion reproduction number, which shows that the second serotype can invade the population after a mono-endemic first serotype. We also investigate the dependence of the basic and invasion reproduction numbers on the immunological parameters of the first and second infections. This gives us a better understanding of the relationship between DHF and ADE during secondary infection.


• November 27 2025, 03:00 pm Louis Fostier, INRAE Tours.
  
  Title: Analyse et calibration de modèles de dynamique de populations structurées : application à des populations cellulaires
  Abstract: Ces travaux portent sur l’étude de modèles de dynamiques de populations structurées en taille, s’écrivant sous la forme d’une EDP de transport, avec des termes non locaux sur la condition au bord (recrutement de nouvelles cellules), la vitesse de transport (croissance cellulaire) et le terme source (mort cellulaire). Sous une hypothèse de séparabilité sur le taux de croissance, on se ramène à l’étude de problèmes de Cauchy semilinéaires abstraits, pour lesquels on peut déterminer la stabilité locale des solutions stationnaires, et l'existence de solutions périodiques. Ces résultats sont appliqués à : (i) la dynamique des cellules germinales femelles (ovogenèse) chez les poissons, et (ii) la dynamique des cellules adipeuses. On présente ensuite une méthode d’inférence non paramétrique des taux de recrutement, vitesse et mort basée sur les Physics-Informed Neural Networks (PINNs), illustrée sur des données expérimentales relatives à la dynamique des cellules germinales femelles.


• November 20 2025, 02:00 pm Nathanaë l Boutillon, University of Vienna, Austria.
  
  Title: Qualitative properties of the spreading speed of a population structured in space and in phenotype
  Abstract: We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of an individual may depend on its spatial position and on its phenotype. The population spreads at some finite speed given by a Freidlin-Gärtner formula. We study the behaviour of the spreading speed in different scaling limits: small and large period, small and large mutation coefficient. This amounts to studying the behaviour of the principal eigenvalue of an elliptic operator in which the second-order term is very small in one direction. We deal with the interaction between the slow and fast scales by using a probabilistic interpretation of the principal eigenfunction as a quasi-stationary distribution of some killed process, along with techniques from Hamilton-Jacobi equations.


• November 6 2025, 02:00 pm Sergei Trofimchuk, University of Talca, Chili.
  
  Title: The peak-end rule and differential equations with maxima: a view on the unpredictability of happiness
  Abstract: In the 1990s, after a series of experiments, the behavioural psychologist and economist Daniel Kahneman and his colleagues formulated the following peak-end evaluation rule: the remembered utility of pleasant or unpleasant episodes is accurately predicted by averaging the peak (most intense value) of instant utility (or disutility) recorded during an episode and the instant utility recorded near the end of the experience (Kahneman et al 1997 Q. J. Econ. 112 375–405). Based on this rule, we propose a mathematical model for the time evolution of the experienced utility function u(t) given by the scalar differential equation \[u'(t)=a u(t) + b \max \limits_{s\in [t-h,t]}u(s) +f(t) \ (*), \] where f represents exogenous stimuli, h is the maximal duration of the experience, a and b are some averaging weights. In this work, we study equation and show that, for a range of parameters and a periodic sine-like term f, the dynamics of can be completely described in terms of an associated one-dimensional dynamical system generated by a piece-wise continuous map from a finite interval into itself. We illustrate our approach with two representative examples. In particular, we show that the utility u(t) (e.g. ‘happiness’, interpreted as hedonic utility) can exhibit chaotic behaviour. References: Nonlinearity, doi:10.1088/1361-6544/aca50d


• June 5 2025, 03:00 pm H. Rezaei, INRAE
  
  Title: Intrinsic Dynamics and Deterministic Diversification Drive a New Model of Prion Replication and Dissemination
  Abstract: Prion diseases, or transmissible spongiform encephalopathies (TSEs), are fatal neurodegenerative disorders caused by the accumulation of misfolded conformers (PrP^Sc ) of the cellular prion protein (PrP^C ). These pathogenic assemblies propagate through a self-templating process, resulting in strain- specific patterns of neurodegeneration, yet the mechanisms underlying their tissue tropism and dissemination remain incompletely understood. Using advanced physico-chemical approaches, we revealed that PrP Sc assemblies exhibit an intrinsic capacity for structural diversification and material exchange, independently of templated replication. These findings challenge traditional paradigms by suggesting that prion replication is not solely governed by templating kinetics, but also shaped by inherent assembly dynamics. Building on this foundation, we incorporated these experimental observations into a stochastic reaction-diffusion model—parametrized with the Gillespie algorithm—that accounts for nonlinear tissue responses, particularly the unfolded protein response (UPR), and strain-specific replication kinetics. This integrated framework demonstrates that the interplay between the intrinsic dynamics of prion assemblies and tissue feedback mechanisms can lead to diverse replication regimes, including oscillatory, transient, and abortive behaviors. Notably, the model reveals that structural subpopulations such as PrP^Sc A and PrP^Sc B_i can be differentially selected depending on tissue environment and strain properties. Furthermore, strain co-propagation and dominance interference are emergent behaviors resulting from shared substrate competition and UPR coupling, independent of direct kinetic interaction. By simulating prion dissemination across neural networks, the model also underscores the role of the brain’s connectome—not as a passive conduit, but as an active modulator of propagation dynamics through axon-guided diffusion and local replication. Together, these insights offer a comprehensive and mechanistically rich model of prion replication and neuroinvasion, with broader implications for other protein misfolding diseases characterized by strain diversity and tissue tropism.


• April 29 2025, 03:00 pm Loïc MICHEL, Nantes University and Centrale School of Nantes
  
  Title: A Connectome-Based Inference of Dynamical Neural Wiring: A Control Approach
  Abstract: This work aims to build a growing neural network in order to explore the concept of learning through a closed-loop control algorithm and additionally propagate statistic information from the synaptic weights. To emphasize the interactions between the connections and the neurons, the connections are activated randomly, like into a « connectome », for which the neurons can be used simultaneously to learn and store several type of information from the learning process and the wiring statistics, depending on the configuration of the connections. The preliminary results highlight the feasibility of the proposed learning concept considering few neurons, for which stabilization of the trained synaptic weights is a priori observed. Joint work with Jean-Pierre BARBOT from Cergy-Pontoise University. Video


• April 17 2025, 03:00 pm A. Thorel, Le Havre Normandie University
  
  Title: Exemples concrets.
  Abstract: TBA


• April 10 2025, 03:00 pm A. Thorel, Le Havre Normandie University
  
  Title: Introduction à la théorie des sommes d'opérateurs linéaires.
  Abstract: TBA


• April 3 2025, 03:00 pm A. Thorel, Le Havre Normandie University
  
  Title: Fermabilité et fermeture d'opérateurs linéaires non bornés dans les espaces de Banach.
  Abstract: TBA


• March 27 2025, 03:00 pm Zhenkun Wang, University of Science and Technology of China
  
  Title: Threshold Dynamics of an Impulsive PDE Model with Habitat Shift Driven by Climate Change
  Abstract: Persistence or extinction of moving animal species is a fundamental question in spatial ecology. This paper focuses on the impact of habitat shift driven by climate change on the persistence and propagation of a population with birth pulse. We first present a class of impulsive reaction-diffusion models with heterogeneous nonlinear reaction in high-dimensional space and study their threshold dynamics. We provide the persistence criterion of the system in bounded domains, and prove the existence, uniqueness and global attraction of a positive steady state. Then we extend the results from bounded domains to the whole space. Our results indicate how the speed of the shifting habitat edge and impulsive reproduction (or harvesting) rate determine the persistence and extinction of the population. Numerical simulations are presented to illustrate the theoretical results.


• March 7 2025, 03:30 pm Sapna Ratan Shah,Jawaharlal Nehru University, New Delhi, India
  
  Title: Computational and Mathematical Modeling of Biological Systems in Biomechanics
  Abstract: This talk deals with several contributions on mathematical models of bio-fluids with practical medical applications.


• February 27 2025, 03:30 pm Todd L. Parsons, CNRS and Sorbonne University
  
  Title: Puzzles in the Persistence of Pathogens
  Abstract: If a new pathogen causes a large epidemic then it might "burn out" before causing a second epidemic. The burnout probability can be estimated from large numbers of computationally intensive simulations, but an easily computable formula for the burnout probability has never been found. Using a conceptually simple approach, we have derived an accurate and easily computable formula for the burnout probability for the stochastic SIR epidemic model with vital dynamics (host births and deaths). With this formula, we have recently shown (https://www.pnas.org/doi/10.1073/pnas.2313708120) that the burnout probability is always smaller for diseases with longer infectious periods, but is bimodal with respect to transmissibility (the basic reproduction number). Our analysis has shown further that the persistence of typical human infectious diseases cannot be explained by births of new susceptibles alone. However, in current work applying our analytical approach to models that include more biological details, we are able to make precise comments on the roles of other mechanisms, substantially improving our understanding of disease persistence. Joint work with Ben Bolker, Jonathan Dushoff, and David Earn (McMaster University).

Seminars LMAH 2024

• October 24 2024, 04:00 pm Achraf Zinihi, Meknes University, Morroco
  
  Title: Mathematical Analysis in Epidemiology: Evolution, Modeling, and Control Strategies
  Abstract: The talk's primary goal is to make an analysis and study a reaction-diffusion SIR epidemic mathematical model expressed as a parabolic system of partial differential equations using the p-Laplacian operator. Immunity is compelled through vaccination distribution, which is seen as a control variable. Our main goal is to define an optimal control, which reduces the spread of infection and the cost of vaccination over a limited period of time and space. Existence and uniqueness of a positive solution and existence of an optimal control for the proposed model are proved. Then a description and characterization of the optimal control is provided in terms of state and adjoint functions. Optimality system is numerically resolved by a discrete iterative scheme pertaining to the forward-backward algorithm. Furthermore, using various p-values for the p-Laplacian operator, numerical results demonstrate the effectiveness of the suggested control strategy, which yields meaningful outcomes.


• October 10 2024, 04:00 pm Ali Moussaoui, Tlemcen, University, Algeria
  
  Title: Mathématiques des épidémies
  Abstract: Avec l'apparition de la pandémie de coronavirus en 2020, la modélisation mathématique est devenue un outil incontournable pour anticiper l'évolution de la maladie et évaluer les effets des différentes interventions. Dans la premi&eagrave;re partie de cet exposé, je vais aborder les premiers mod&eagrave;les mathématiques développés pour étudier les maladies infectieuses. Dans la deuxième partie, nous étudierons un systéme d'équations de réaction-diffusion non local qui modélise la répartition des virus en fonction de leurs génotypes et leur interaction avec la réponse immunitaire.


• October 3 2024, 04:00 pm Cherifa Guezzen, Tlemcen University, Algeria
  
  Title: The Impact of Imperfect Quarantine on the Control of Infectious Diseases in a General Diffusive Epidemic Model.
  Abstract: In this work, we investigate a general class of susceptible, infected, quarantine, recovered (SIQR) epidemic models with spatial heterogeneity and imperfect quarantine, focusing on the role of quarantines in controlling infectious diseases. We first determine the expression of the basic reproduction number for two infected classes and allowing the transmission between them. For $R_0 \leq 1$, the disease will die out, which is guaranteed by the global asymptotic stability of the disease-free steady state, and for $R_0 > 1$, the disease will persist. Moreover, we analyze the impact of small/large diffusion rates of susceptible and infected individuals depending on the quarantine rates. Finally, based on the numerical results we deduce that for suitable values of quarantine and relapse rates, infectious disease can be contained for a varying total population.


• May 2 2024, 04:30 pm Mattia Sensi, Politecnico di Torino
  
  Title: Various approaches to the mathematical modelling of epidemics
  Abstract: In this talk, we present various papers sharing the overarching theme of mathematical models of infectious disease spreading. The first part of the talk will be devoted to instances of ODE models exhibiting a separation of timescales. In such models, some of the processes evolve at a much slower rate than other (e.g. demography and infectivity windows), and we exploit this separation to reduce the dimensionality of the systems and to focus on the geometry of some special manifolds. This allows, moreover, to split numerically stiff systems into multiple, smaller non-stiff ones. After, we briefly present more classical ODE models, as well as PDE, DDE and mean field approximation of epidemics on networks. In particular, we focus on multiple approaches to the inclusion of information and opinion spreading in a population, simultaneously to the spread of a communicable disease.
• March 28 2024, 02:00 pm Mingmin Zhang, Toulouse University
  
  Title: The logarithmic correction for Fisher-KPP equations on the lattice Z.
  Abstract: In this talk, I will present the logarithmic Bramson correction for Fisher-KPP equations on the lattice Z. The level sets of solutions with step-like initial conditions are located at position ct -(3/2λ*) ln t + O(1) as t → +∞ for some explicit positive constants c* and λ*. This extends a well-known result of Bramson in the continuous setting to the discrete case using only PDE arguments.


• February 22 2024, 02:00 pm Renaud Raquépas, Courant Institute of Mathematical Sciences, NYU
  
  Title: La production d’entropie dans le cadre des diffusions non dégénérées: temps longs et bruit disparaissante.
  Abstract: La production d'entropie (PE) est une quantité issue de la thermodynamique qui mesure l'irréversibilité des évolutions temporelles. Je commencerai par une introduction générale aux différentes approches permettant de définir la PE. Ensuite, je me concentrerai sur le cadre des diffusions non dégénérées et je décrirai les propriétés des grandes déviations de la PE lorsque le temps tend vers l'infini. Enfin, je discuterai du comportement de la fonction de taux du principe de grandes déviations lorsque l'intensité du bruit tend ensuite vers zéro.


• February 8 2024, 02:30 pm Pierre Roux, Institut Camille Jordan, école centrale de Lyon,
  
  Title: Modélisation des cellules de grille par une équation de Fokker-Planck non-linéaire et non-locale.
  Abstract: Depuis leur découverte en 2005 par Moser, Moser et leurs collègues, les cellules de grilles - des neurones spécifique du cortex entorhinal qui jouent un rôle crucial dans la navigation spatiale des mammifères - ont été l’objet de nombreuses études. Un point clef de leur fonctionnement est qu’elles constituent des modules dont l’activité électrique se stabilise en un motif hexagonal (qui constitue une sorte de grille). Dans cet exposé, je présenterai un modèle aux dérivées partielles de type Fokker-Planck non-linéaire, développé par Carrillo, Clini, Holden et Solem, visant à comprendre l'apparition du motif hexagonal et à étudier sa robustesse au bruit. À travers un mélange de résultats théoriques (existence locale et globale, convergence en entropie relative, bifurcations entraînées par le bruit) et d'explorations numériques, José Antonio Carrillo, Susanne Solem et moi-même avons œuvré à améliorer la compréhension du modèle et du phénomène sous-jacent. video


• (Friday) February 2 2024, 02:30 pm Ayman Moussa, Jacques-Louis Lions Lab, Sorbonne University
  
  Title: Estimée de stabilité locale et dérivation du système SKT.
  Abstract: Nous commencerons par rappeler l'origine du système de réaction-diffusion " SKT " et les défis à ce jour non résolus concernant celui-ci. L'exposé abordera ensuite un schéma d'approxipation proposé en 2019 par Daus, Desvillettes et Dietert pour construire des solutions. Nous expliquerons comment ce schéma peut, à l'aide d'une estimation de stabilité locale sur le système, conduire à un résultat partiel de dérivation reliant le système SKT à une famille de marches aléatoires répulsives sur un réseau discret. Il s'agit d'un travail en collaboration avec Vincent Bansaye et Felipe Muñoz-Hernández. Coming soon.


• January 11 2024, 02:30 pm Fatima Bouyghf, LMNO, Université de Caen Normandie
  
  Title: A unified approach to Krylov subspace methods for solving linear systems.
  Abstract: To solve large linear systems, iterative methods and projection meth-ods are commonly employed. Among these methods, the Krylov subspace methods are widely utilized. The primary principle of these methods is based on the Petrov-Galerkin condition. Krylov methods involve com puting an approximation of the solution to a linear system within the Krylov subspace, with the requirement that the residual is orthogonal to another subspace known as the left subspace. The choice of the left sub- space leads to dierent variants of Krylov methods, which vary in terms of execution time, memory usage, and computational accuracy. Therefore, our research focuses on analyzing the convergence of these methods. We have contributed to this eld by proposing a unied approach and a general framework to simplify the study of these methods using left inverses of the Krylov matrix. This approach is based on the fact that all Krylov methods compute the coecients of the minimal polynomial of the system matrix for an initial residual. By leveraging mathematical tools and the properties of orthogonal projectors, we have enhanced the computational accuracy of most of these methods while preserving the same storage and execution time. Furthermore, our approach has facilitated the development of new implementations that exhibit interesting computational performance for selected methods. We have also investigated the block case of these methods in our studies. The eectiveness and the accuracy of all proposed algorithms are illustrated by some numerical experiments.



Seminars LMAH 2023

• November 16 2023, 03:30 pm Shigui Ruan, Department of Mathematics, University of Miami, USA
  
  Title: Spatiotemporal Dynamics in Epidemic Models with Levy Flights: A Fractional Diffusion Approach.
  Abstract: Recent field and experimental studies show that mobility patterns for humans exhibit scale-free nonlocal dynamics with heavy-tailed distributions characterized by Levy flights. To study the long-range geographical spread of infectious diseases, in this paper we propose a susceptible-infectious-susceptible epidemic model with Levy flights in which the dispersal of susceptible and infectious individuals follows a heavy-tailed jump distribution. Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. The primary focuses are on the existence and stability of disease-free and endemic equilibria and the impact of dispersal rate and fractional power on spatial profiles of these equilibria. A variational characterization of the basic reproduction number R0 is obtained and its dependence on the dispersal rate and fractional power is also examined. Then R0 is utilized to investigate the effects of spatial heterogeneity on the transmission dynamics. It is shown that R0 serves as a threshold for determining the existence and nonexistence of an epidemic equilibrium as well as the stabilities of the disease-free and endemic equilibria. In particular, for low-risk regions, both the dispersal rate and fractional power play a critical role and are capable of altering the threshold value. Numerical simulations were performed to illustrate the theoretical results.


• November 16 2023, 02:30 pm Romain Ducasse, Jacques-Louis Lions Lab, University of Paris
  
  Title: Quelques résultats sur des modèles d'EDP en épidémiologie.
  Abstract: Nous présenterons dans cet exposé quelques résultats récents sur des modèles d'épidémiologie. Nous nous intéresserons à des modèles déterministes qui prennent la forme de systèmes d'équations de réaction-diffusion (équations paraboliques non-linéaires). Le plus célèbre de ces modèles est sans doute le système SIR (Sains-Susceptibles-Remis, introduit par Kermack et McKendrick en 1937), mais de multiples variantes ont été introduites depuis. Nous établirons quelques résultats sur certains de ces modèles, en particulier sur des modèles hétérogènes.Nous nous intéresserons à comprendre le comportement qualitatif des solutions de ces modèles : stabilité, convergence, vitesses de propagations.


• October 26 2023, 02:30 pm Irmand Mikiela, Le Havre Normandie University
  
  Title: Modélisation et analyse de systèmes dynamiques inspirés de l'épidémiologie mathématique et déployés sur réseaux complexes.
  Abstract: Ma thèse explore divers modèles à compartiments et des problèmes mathématiques associés. J'aborde dans cet exposé un modèle réaction-diffusion à compartiments avec des coefficients de diffusion non locaux, explorant les implications de cette non-localité. Je propose ensuite une approche relativement nouvelle pour modéliser les couplages des équations aux dérivées partielles (EDP), intégrant des probabilités de déplacement tout en veillant à respecter le principe de conservation du flux. Je propose des résultats théoriques pour les cas avec couplage linéaire des systèmes à compartiments avec contrôle de masse. Ces travaux participent à la compréhension des systèmes dynamiques sur réseaux complexes, leur modélisation et analyse. Si le temps le permet, je parlerai d'une application basé sur un modèle EDO à compartiments inspiré de l'épidémiologie mathématique, ciblant les comportements humains en situation de catastrophe, pour lequel je donnerai des résultats sur le contrôle optimal.


• October 5 2023, 02:30 pm Ahmed Bendjeddou, Setif, Algeria
  
  Title: Integration method for a planar polynomial differential system
  Abstract: In many problems appearing in applied mathematics, nonlinear differential systems are present, as in physics, chemistry, economics, etc. If we have a differential system in the plane and having a first integral, then its phase portrait is completely determined. It is therefore important to know the first integral for a differential system, but the question arises: given a differential system, how do we know if it has a first integral? This presentation aims to study how to find, under certain conditions, a first integral for certain classes of polynomial differential systems.


• June 8- July 5 2023, 04:00 pm, BDD2023 (Bio Dynamics Days)


• March 2 2023, 03:30 pm Aymen Balti, Paris Est University, France
  
  Title: L'approche mécaniste en pharmacologie préclinique pour optimiser les thérapies anticancéreuses innovantes.
  Abstract: Le cancer est une maladie de nature volutive. Or, les outils théoriques de systèmes dynamiques et/ou mathématiques pour prédire et controler les systèmes évolutifs issus des modèles biologiques sont encore souvent absents de la pratique clinique. Dans ce travail, nous faisons appel aux outils des systèmes dynamiques non-linéaires comme l'analyse de bifurcation et la théorie de contrôle pour quantifier des études cliniques. Ainsi, l'approche mécanistique basée sur des syst`emes quantitatifs s'est confirmée etre un outil puissant pour clarifier la complexité physio-pathologique sous-jacente qui est amplifiée par la variabilité physiologique et par le niveau de sophistication des schémas thérapeutiques. La combinaison de l'immunothérapie avec des traitements classiques, y com- pris la chimiothérapie et la radiothérapie, sont de plus en plus utilisées. Ces combinaisons servent à augmenter la réponse immunitaire contre les cellules tumorales. Afin d'obtenir les meilleures performances de ces approches combinatoires et d'en déduire des stratégies thérapeutiques plus efficaces, une meilleure compréhension de la dynamique d'interaction entre la tumeur et le système immunitaire est nécessaire. L'objectif de ce travail est d'apporter de nouvelles connaissances sur l'évolution tumorale versus la réponse immunitaire en présence de traitement immuno oncologique et d'énoncer des nouvelles stratégies thérapeutiques. Comme étude de cas, nous utiliserons un modèle QSP récent de Kosinsky et al. [J. Immunautre. Cancer 6, 17 (2018)] qui visait à reproduire la dynamique d'interaction entre la tumeur et le système immunitaire lors de l'administration de la radiothérapie et de l'immunothérapie.
  Abstract with references
  
• February 23 2023, 03:00 pm M. Kostic, University of Novi Sad, Serbia
  
  Title: Selected Topics in Almost Periodicity
  Abstract: The class of almost periodic functions was introduced by H. Bohr, the younger brother of the Nobel Prize-winning physicist N. Bohr, around 1925 and later generalized by many other authors. The almost periodic functions play a significant role in the qualitative theory of differential equations, physics, mathematical biology, control theory and technical sciences. In this talk, we will present the main results about almost periodic functions in complex Banach Spaces. Abstract (pdf) . Video
  
  
• February 16 2023, 03:00 pm Danièle Fournier, INSA Toulouse
  
  Title: Modélisation de l'évolution de 2 ou 3 espèces interagissant entre elles à partir de récurrences de dimension 2 ou 3. Prise en compte de l'effet Allee.
  Abstract: L'objectif de cette conférence est de présenter différents types de modèles non linéaires en dynamique des populations via des récurrences de dimension 2 ou 3. Dans une première partie, trois types d'interactions sont considérés : symbiose, proie-prédateur et compétition. Dans une seconde partie, nous nous intéressons plus particulièrement à l'effet Allee. Dans les deux parties, l'étude analytico-numérique des bifurcations permet de mettre en évidence des propriétés de stabilité, des comportements chaotiques et des phénomènes d'extinction des espèces. Video
  
  
• January 25 2023, 03:00 pm Evariste Sanchez-Palencia, CNRS and French Academy of Sciences.
  
  Title: Dialectique dans les sciences et systèmes dynamiques
  
  Abstract: Ce livre est le fruit d’une réflexion sur un certain nombre de problèmes de systèmes dynamiques (notamment en dynamique écologique) développés ou revisités dans le but de comprendre les éléments de l’évolution biologique qui sortent de l’élémentaire survivance des plus aptes, et plus précisément qui engendrent des structures nouvelles, souvent dynamiques, que certains appellent émergentes. Cela permet d’expliquer comment des mécanismes naturels sans le moindre finalisme conduisent à la formation de configurations stables de nature variée, constante ou pulsante, mettant en œuvre une diversité d’espèces en interaction. Le rôle de la stabilité est présent partout, et conduit à des phénomènes remarquables, comme les synchronisations spontanées, les communautés d’espèces purement dynamiques (sans point d’équilibre, stable ou pas) et bien de comportements qui apparaissent comme paradoxaux du point de vue de l’optimisation (dont le rôle est restreint en théorie des systèmes dynamiques). Cela conduit naturellement à une réflexion synthétique de nature épistémologique pour dégager des idées générales permettant de mieux appréhender la causalité mise en œuvre dans l’évolution biologique.
  Video , Presentation (pdf)
  
• January 12 2023, 03:00 pm Stan Mintchev, The Cooper Union, New York, USA.
  
  Title: Examples of oscillation transmission and transmutation in chains of certain idealized neurons.
  
  Abstract: The study of voltage oscillations — their emergence, persistence, and proliferation in neural tissues — represents a central focus of mathematical neuroscience. Neuronal model reduction to phase dynamics, based on dynamical systems and geometry theory from the 1960s and 70s, has been a standard albeit overly simplistic tool for developing insights into this area. Based on various strong assumptions regarding hyperbolicity and structural stability of periodic orbits in the (full) phase space, such reductions culminate in the mathematical analysis of phase-oscillator ensembles; a wealth of results follow based on the specific context / original model. Some of these will be reviewed briefly in the first part of this talk. The hyperbolicity theory leading to model phase reduction is not directly applicable in the regime prior to rhythmic depolarization, when a neuron is excitable but its full dynamics are not fully captured by a compact 1-dimensional phase space. Our talk will present findings in another idealized setting, that of a feed-forward chain of Dirac-kick-coupled FitzHugh-Nagumo neurons, where we observe both analogies to the simpler phase oscillator counterpart as well as characteristically distinct oscillation propagation and signal filtration phenomenology. We find that, unlike in the simpler phase oscillator model, stimulus frequency (and size) plays a pronounced role in determining whether the oscillation propagation is like a traveling wave (analogy to prior work) or significantly more complex, due to a mixed-mode oscillation mechanism embedded within the FitzHugh-Nagumo model.
  Video
  
  

  Seminars LMAH 2022

• December 13 2022, 03:30 pm Tewfik Mahdjoub, Tlemcen University, Algeria.
  
  Title: Some approaches of modeling geographical Chagas disease expansion’s by applying orthogonal polynomials, integrodifference equations and agent-based simulations.
  
  Abstract: Chagas disease is a potentially fatal disease that affects 10 to 12 million people worldwide and is responsible for about 50 000 deaths per year. It is caused by a flagellated parasite called Tripanosoma Cruzi (T.Cruzi). The main transmission mode of the disease is based on the biological system: parasite (T.Cruzi)-vector (triatominae)-host (mammals). This complex system is considered as: (1) an epidemiological one if the interest is on the absence or presence of T.Cruzi; (2) a population’s ecology system if the study is on population dynamics of vectors; (3) or both types at the same time. In addition, if the spatial dispersal of the parasite encompasses an area of human habitation, the transmission is said to be domestic. Otherwise, it is sylvatic (transmission in a domain like the forest). These different approaches allow the application of various mathematical tools. In the case of sylvatic transmission, we present, a first model, via the ecology of populations, by application of orthogonal polynomials , then an epidemiological one by application of integrodifference equations and a third one by application of agent-based simulations. Abstract with references
  
  
• November 16, 17 2022, GT BIOMATHS Normand More details Here



• November 17 2022, 15:00 (France Time), Sylvain Mangiarotti, Institut de Recherche pour le Développement, Centre d’Etudes Spatiales de la Biosphère, Toulouse, France
  
  Title: La théorie du chaos appliquée à la modélisation de l’environnement à partir de données observées en conditions réelles
  
  Abstract: L’objectif de cette présentation est de montrer le potentiel applicatif de la théorie du chaos. A cette fin, je rappellerai d’abord brièvement quelques éléments de bases de cette théorie et je montrerai la puissance qu’elle offre, que ce soit pour retrouver des jeux d’équations originaux ou pour détecter des couplages, directement à partir de séries temporelles. La seconde partie sera entièrement dédiée aux applications, partant de données issues du monde réel: Différents systèmes environnementaux seront considérés avant de se focaliser plus spécifiquement sur des problèmes d’épidémiologie et d’éco-épidémiologie.
  Video
  
  
• July 7 2022, 17:00 (France Time), C. Hameni, Univesity of Douala, Cameroon
  
  Title: Mathematical modeling of COVID-19 pandemic in the context of sub-Saharan Africa: a short term forecasting in Cameroon and Gabon
  
  Abstract: In this paper, we propose and analyze a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematicalmodel for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number ℛ₀ when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that ℛ₀ ≈ 1.8377 in Cameroon, while ℛ₀ ≈ 1.0379 in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new vague of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals ℛ_0h and from the SARS-CoV-2 in the environment ℛ_0v has been done in Cameroon and Gabon. The results help us to understand why the lockdown was not the solution to cope with the pandemic in Cameroon but, was the solution to cope with it in Gabon and also why the disinfection and decontamination of infected places and strict compliance to hygiene rules are a solution to cope the COVID-19 pandemic in Cameroon. However, long term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program, detection process and the eradication of the pandemic is highly dependent on the control measures taken by each government. Keywords: COVID-19; Mathematical model; Basic reproduction number; EnKf; Forecasts.
  Video
  
  
• June 22 2022, 11:00 am (NY Time)/17:00 (France Time), J. Epstein, New York Univesity, New York, USA
  
  Title: Triple Contagion: Toward Cognitive Epidemiology,
  
  Abstract: Epstein will present differential equation and agent-based models in which contagious disease transmission is affected by contagious fear of the disease and contagious fear of the control, in this case vaccine. The three contagions—one viral-particulate and two cognitive--are coupled. The two fears evolve and interact in ways that shape distancing behavior, vaccine uptake, and their relaxation. These behavioral dynamics in turn can amplify or suppress disease transmission, revealing several coupled contagion mechanisms for multiple pandemic waves, including cases where waves increase in amplitude. Methodologically, the coupled contagion approach advances infectious disease modeling by including human behavioral adaptations, grounded in the cognitive neuroscience of fear learning, extinction, and transmission.
  Video Part 1, Video Part 2
  
• June 7 2022, 04:00 pm, Stan Mintchev, The Cooper Union, New York, USA
  
  Title: An introduction to some basic principles from geometric singular perturbation theory, with applications to the FitzHugh-Nagumo model for neuronal dynamics.
  
  Abstract: For the first half of this talk, we review some definitions surrounding the notion of timescale separation as well as the preliminary theory of slow-fast systems that arises from appropriate concatenations of reduced and layer dynamics in this setting. We also give an overview of how this theoretical foundation applies to the example of a FitzHugh-Nagumo neuronal model in its various parameter regimes. In the second half of our talk, we discuss the consequences of this structure at the cell level for network dynamics, specifically, in a feedforward architecture that involves instantaneous Dirac spike contributions to a receiving cell’s dynamics. We finish with an overview of results in this setting that distinguish between low and high stimulus-frequency response, a consequence of the nuances associated with the slow-fast structure at the cellular level.
  
  
• May 25 2022, 02:00 pm, GT BIOMATHS Normand More details Here



• May 18 2022, 02:00 pm, Emmanuelle Augeraud-Veron, University of Bordeaux
  
  Title: Prevention and Mitigation of Epidemics: Biodiversity Conservation and Confinment Policies,
  
  Abstract: The relation between biodiversity loss and frequency of zoonose pandemic risk is well documented in the literature. In this article we present a rst model to integrate this phenomenon in the context of a general equilibrium dynamic economic set-up. The occurrence of pandemic episodes is modeled as Poissonian leaps in stochastic economic variables. The planner can intervene in two ways: first (prevention), by preserving a greater quantity of biodiversity, and second (mitigation), through a partial blockage of economic activity. The policy is evaluated using a social welfare function which takes into account risk aversion, fluctuation aversion, altruism towards future generations and discount of future utility. Biodiversity conservation is shown to be more relevant for more "forward looking" societies and societies with a high degree of altruism towards future generations. Societies accepting a large welfare loss to mitigate the pandemics are also societies doing a more prevention, not to have to incur the loss too often. After calibrating the model with COVID-19 pandemic data we compare the mitigation efforts predicted by the model with those of the recent literature and we study the optimal prevention-mitigation policy mix.
  
  
• March 3 2022, 03:00 pm Rachid MCHICH, Ecole Nationale de Commerce et de Gestion, Université Abdelmalek Essaâdi, Tanger, Maroc.
  
  Title: Systèmes dynamiques en gestion des pêcheries marocaines : agrégation, contrôle et prix variable.
  
  Abstract: Les systèmes dynamiques font intervenir, en général, des équations non linéaires, et peuvent contenir un grand nombre de variables. Ces dernières sont liées à la population étudiée, à l'hétérogénéité du milieu d'évolution et aux différentes activités des espèces considérées. Aussi, une étude analytique directe peut-elle s'avérer très difficile. Les simulations numériques, quant à elles, peuvent donner des informations précises, encore faudrait-il que les paramètres exogènes soient fiables pour une description détaillée de la dynamique du système complet. En fait, dans ce genre de modèles, sur toutes les variables des équations du système étudié, seules quelques-unes présentent, en général, un intérê t particulier dans la dynamique globale. Ces variables sont appelées des variables globales. Ensuite, les espèces considérées peuvent ê tre d'â ges différents, ou situées différemment dans l’espace ou dans le temps. D'où la possibilité de les subdiviser en sous-populations évoluant dans des sous-milieux. Ces sous-populations correspondent chacune à un âge précis, à une position précise dans l’espace ou dans le temps, ou à une activité particulière. D'où l'importance d'une structuration hiérarchique en rapport avec l'hétérogénéité du milieu. De même, une espèce peut être étudiée différemment, selon qu'on la considère au niveau de l'individu, de la sous-population, de la communauté ou de l'écosystème. Dans ce travail, concernant l’étude de systèmes dynamiques concernant la gestion de pê cheries au Maroc, nous tenons compte de l’existence de ces deux échelles de temps, pour mettre le système sous une "forme adaptée" et considérer des hypothèses adéquates. Nous considérons aussi le cas où le prix est une variable dépendant du temps. Tout ceci nous permet de réduire le nombre d'équations et de variables du système, et de faire émerger ce qui est communément appelé: un système agrégé, dont l’étude permet l’émergence de nouvelles situations intéressantes pour la gestion de telles pêcheries.Résumé avec références
  
  
• February 9 2022, 03:00 pm Fatima Zahra Lahbiri, Ibn Zohr University, Agadir, Morocco and Le Havre Normandie University
  
  Title: Analysis and Control of Stochastic Evolution Equations in Infinite Dimensions.
  
  Abstract: In this work, we study infinite dimensional stochastic systems having both unbounded control and observation operators. It is in fact a stochastic version of known linear Salamon-Weiss systems. First of all, using a semigroup approach, we give another take of the well-posedness of stochastic control systems. On the other hand, we study the observed stochastic systems, then we propose a new variation of constants formula for mild solutions of perturbed abstract stochastic Cauchy problems using the concept of Yosida extensions of admissible operators. Then, we study exact observability for semilinear stochastic systems. Finally, we apply the results to a general class of stochastic systems with delays in state, control and observation parts.
  Keywords: Stochastic well-posed systems, admissible operators, semigroup theory, Yosida extensions, observability of semilinear stochastic systems, stochastic delay systems.
  Video
  
• February 3 2022, 03:00 pm Israël Tankam, INRIA Sophia Antipolis and Yaoundé University
  
  Title: Multi-seasonal modelling and optimal management of a banana soilborne pest
  
  Abstract: We propose on the one hand a framework for mathematical analysis and simulation of the burrowing nematode Radopholus similis dynamic interaction with banana or plantain roots, and on the other hand we identify the best control method to optimize the economical yield of banana and plantain crops. In the first step, we study the infestation dynamics of banana or plantain plants by R. similis. Two control strategies are analyzed: pesticides, which are still widely used, and fallow deployment, which is more environmentally friendly. We propose two semi-discrete models to represent the host-parasite interactions and we derive conditions on the pesticide load or the fallow to ensure the stability of the pest-free equilibrium. In a second step, we propose an eco-friendly optimization of banana or plantain yield by a control of the burrowing nematode which relies on fallow deployment. The aim is to find the best way, in terms of profit, to allocate the durations of fallow periods between the cropping seasons over a fixed time horizon spanning several seasons. We prove the existence of an optimal allocation and we propose an adaptive random search algorithm to solve the optimization problem. For a relatively long time horizon, deploying one season less than the maximum possible number of cropping seasons allows us to increase the fallow period durations and results in a better multi-seasonal profit.
  Key words: epidemiological modelling, pest management, yield optimization, burrowing nematode, banana (Musa spp.)
  Video
  
  
• January 19 2022 (Wednesday), 03:30 pm Mathieu Desroches, INRIA Sophia Antipolis
  
  Title: Slow-fast analysis of neural bursters: old and new
  
  Abstract: In this talk, I will present recent work on multiple-timescale dynamical systems displaying complex oscillations with both slow and fast components. After a brief review of bursting oscillations and the role of so-called spike-adding transitions in square-wave bursters, I will introduce a four-dimensional extension of this scenario which creates small-amplitude slow (sub-threshold) oscillations in between bursts, mediated by so-called canard solutions. In the second half of the talk, I will revisit another type of four-dimensional bursting scenario with two slow variables, namely parabolic bursting, and provide explanations on how the spike-adding mechanism in such bursters is also organised by canards but of a different type than before. This will be showcased on several examples of parabolic bursters, both biophysical ones like the Plant model, and simplified ones like theta models. Finally, I will show how the burst-excitable structure of networks of theta model may persist across scales up to some mean-field limit. [This is based on joint papers with D Avitabile (Amsterdam), GB Ermentrout (Pittsburgh), TJ Kaper (Boston), M Krupa (Nice) and S Rodrigues (Bilbao)]
  Video
  
  
• December 9 2021, 03:00 pm Zhucheng Jin, Le Havre Normandie University
  
  Title: Propagation phenomena in non-autonomous Fisher-KPP equations with nonlocal diffusion.
  
  Abstract: In this talk, we aim to understand and to describe the propagation phenomena generating from Fisher-KPP equations with nonlocal diffusion in time heterogeneous media. The propagation phenomena can be mathematically quantified by two notions: travelling waves and spreading speeds. Firstly, we study generalized travelling waves for equations with general time heterogeneities both for the dispersal kernel and the reaction term. We investigate the existence and nonexistence of generalized travelling waves for such a problem. Under certain assumptions, we derive a sharp estimate for the average speed functions of generalized travelling waves. Then, we show some spreading speeds properties for the nonlocal diffusion Fisher-KPP equation equipped with compactly supported and exponentially decaying initial data respectively, and with time uniquely ergodic coefficients in reaction term. This talk is based on joint works with Prof. Arnaud Ducrot

Seminars LMAH 2021

• November 25 2021, 03:00 pm Lois Naudin, Le Havre Normandie University
  
  Title: Modélisation mathématique du neurone au réseau : le cas Caenorhabditis elegans
  
  Abstract: : Le but des neurosciences computationnelles est d'expliquer comment les systèmes nerveux fonctionnent pour produire un comportement. Le système nerveux du nématode Caenorhabditis elegans (C. elegans) fournit une sérieuse opportunité pour y parvenir de par sa relative simplicité et la connaissance complète de son connectome. Dans cette présentation, nous développerons dans un premier temps des modèles à base de conductance (MBC) qui reproduisent le comportement de trois neurones de C. elegans représentatifs de sa diversité neuronale actuelle non-spiking. Nous questionnerons dans un second temps la capacité de généralisation de ce type de modèle (définie comme la capacité du modèle à prédire des nouveaux comportements neuronaux associés à des stimuli non considérés dans la construction même du modèle), et nous proposerons une méthode pour les doter de façon systématique de cette capacité. Une troisième partie consistera à proposer et à étudier un MBC générique pour les neurones de C. elegans, dans le sens ou ce modèle permettra la génération d'un grand nombre de modèles adaptés à l'électrophysiologie de ses neurones. Enfin, les MBCs ayant certaines limitations intrinsèques à leur complexité que nous exposerons, nous construirons un modèle phénoménologique simple capable de reproduire les comportements des neurones non-spikings. Ce modèle sera testé sur un ensemble de neurones non-spikings de C. elegans. Une ouverture sur l'étude des réseaux neuronaux de C. elegans sera alors présentée.
  
  
• November 18 2021, 04:00 pm Megan Morrison, Courant Institute of Mathematical Science, New York University
  
  Title: Nonlinear control in the nematode C. elegans
  
  Abstract: Whole-brain calcium imaging of the nematode C. elegans shows that the neural activity associated with behavior is dominated by dynamics on a low-dimensional manifold that can be clustered according to behavioral states. I will review previous models of C. elegans neural activity which include linear switching models and Markov-switching models. I will then present a global, nonlinear control model which is minimally parameterized and captures the state transitions described by Markov-switching models with a single dynamical system. This model is constructed in PCA space and characterizes control in the neuron population dynamics in C. elegans which governs behavior.
  Video
  
  
• October 28 2021, 03:00 pm Djamila Boukehil, Université de Rouen Normandie
  
  Title: Estimation d'une matrice de précision sous mélange de lois de Wishart
  
  Abstract: Dans ce travail, nous nous intéressons à l’estimation de la matrice de précision Σ^-1 d’un modèle de mélange de lois de Wishart. Abstract pdf
  
  
• May-July 2021, BDD2021
  
  See details here
  
  
• June 2 2021, 04:00 pm Jacques Bélair, Université de Montreal
  
  Title: Modélisation d’infections virales: quelques approches récentes
  
  Abstract: La pandémie actuelle a motivé un nombre considérable de travaux sur la modélisation plus ou moins proches des données épidémiologiques recueillies essentiellement en temps réel. Nous présenterons des modèles de type SEIAR élaborés pour représenter d’abord l’épidémie à Wuhan et le rôle des hôpitaux de campagne dans le contrôle de la propagation, puis les stratégies de confinement déployées dans la ville de Toronto. Nous présenterons finalement, dans une perspective un peu différente, des résultats théoriques sur le rôle de l’immunité décroissante dans la coinfection par souches du virus de la Dengue.
  Video
  
• April 30 2021, 02:00 pm Luc Pellerin, Université de Poititers
  
  Title: Transporteurs aux monocarboxylates cérébraux : régulations d’expression et rôles dans l’apprentissage et la mémoire
  
  Abstract: Les mécanismes régissant l’approvisionnement énergétique cérébral ont connu un regain d’intérêt récemment. En effet, des hypométabolismes cérébraux localisés ont été détectés dans un grand nombre de pathologies cérébrales sans que l’on connaisse leur origine ni leurs conséquences. Alors que le glucose demeure le substrat énergétique privilégié du système nerveux central, son utilisation directe par les neurones ou sa transformation en lactate par les astrocytes avant de servir de substrat pour les neurones ont fait l’objet d’un immense débat. En appui d’un rôle important du lactate astrocytaire en neuroénergétique, nos travaux ont révélé que les transporteurs aux monocarboxylates (qui permettent les échanges de lactate) sont sujet à des régulations d’expression aussi bien chez les astrocytes que chez les neurones. De plus, nous avons montré récemment leur implication essentielle dans la réalisation de tâches d’apprentissage et de mémoire. Il devient donc important de tenir compte de ces nouveaux acteurs dans l’interprétation des altérations métaboliques observés et des conséquences sur le comportement.
  Video
  
  
• April 8 2021, 02:00 pm : Kamal Khalil, Le Havre Normandie University
  
  Title: On the almost periodicity of nonautonomous evolution equations and application to Lotka-Volterra systems
  
  Abstract: Consider the nonautonomous semilinear evolution equation of type: $(\star) \; u'(t)=A(t)u(t)+f(t,u(t)), \; t \in \mathbb{R},$ where $ A(t), \, t\in \mathbb{R} $ is a family of closed linear operators in a Banach space $X$, the nonlinear term $f$, acting on some real interpolation spaces, is assumed to be almost periodic only in a weak sense (i.e. in Stepanov sense) with respect to $t$ and Lipschitzian in bounded sets with respect to the second variable. We prove the existence and uniqueness of almost periodic solutions in the strong sense (Bohr sense) for equation $ (\star) $ using the exponential dichotomy approach. Then, we establish a new composition result of Stepanov almost periodic functions by assuming just the continuity of $f$ in the second variable. Moreover, we provide an application to a nonautonomous system of reaction-diffusion equations describing a Lotka--Volterra predator--prey model with diffusion and time-dependent parameters in a generalized almost periodic environment.
  
  
• March 25 2021, 02:00 pm : Arnaud Ducrot, Le Havre Normandie University
  
  Title: Quelques résultats pour un modèle d’épidémiologie évolutive des plantes
  
  Abstract: Dans cet exposé, nous présentons un modèle de type intégro-différentiel pour décrire l'adaptation d'un pathogène producteur de spores à son environnent. On se focalisera ici sur un environnement homogène composé d'un ou de deux types d'hôte.Dans le cas d'un seul type d'hôte, On décrira précisément la dynamique du système ainsi que des effets de concentration des solutions, typiquement sur un unique trait phénotypique, en fonction d'un petit paramètre de mutation. Pour un environnement avec deux types d'hôte, les états stationnaires du système sont typiquement concentrés autour d'un trait ou de deux traits phénotypiques (équilibres monomorphes ou dimorphes) en fonction de certaines propriétés des fonctions de fitness.
  Video
  
  
• March 4 2021, 02:00 pm : Hao Kang, Le Havre Normandie University
  
  Title: Age-structured Models with Nonlocal Diffusion: Principal Spectral Theory, Limiting Properties and Global Dynamics
  
  Abstract: Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse and interact nonlocally and the age structure of individuals matters. In this paper we study the principal spectral theory of age-structured models with nonlocal diffusion. First, we provide a criterion on existence of the principal eigenvalue by using the theory of resolvent positive operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal spectrum point. Next we establish the strong maximum principle for age-structured nonlocal diffusion operators. Finally we study the effects of the principal eigenvalue on the global dynamics and show that the principal eigenvalue being zero is critical.
  Slides
  
  
• February 25 2021, 02:00 pm : Jacques Demongeot, University of Grenoble-Alpes
  
  Title: Covid-19: phenomenological and theoretical approaches of the outbreak dynamics
  
  Abstract:
  Slides Video
  
• January 21 2021, 02:00 pm : Toni Guillamon, Polytechnic University, Barcelon, Spain
  
  Title: Extended response curves for oscillatory and damped systems
  
  Abstract: We will review the mathematical grounds to extend the concept of phase response to transient regimes, its implications and recent applications. In particular, we will show how the extension implies the concept of amplitude response, both for oscillatory and damped systems, what additional information the extended response functions carry on and how they help exerting control on the dynamics. The examples will emphasize on the applications to neuroscience.
  Video

Seminars LMAH 2020

• December 10 2020, 02:00 pm : Lara Abi Rizk, Institut de Mathématiques de Bordeaux
  
  Title: Ondes progressives et propriétés de propagation pour un problème d'épidémiologie évolutive non-local
  
  Abstract: Dans cet exposé nous étudions l'existence d'une onde progressive pour un système d'équations intégro-différentiels provenant de l'épidémiologie évolutive. Nous utilisons des idées issues de la théorie des systèmes dynamiques couplées à des estimations sur le comportement asymptotique des profils. Nous prouvons que les ondes progressives ont une structure assez simple découplant les variables de propagation spatio-temporelle des variables de trait phénotypique. Cette analyse nous permet de réduire le système d'équations des profils d'ondes progressives à dimension infinie à un système d'ODE à quatre dimensions. Nous prouvons l'existence d'ondes progressives pour toute vitesse d'onde supérieure à une vitesse minimale $c_\star$, pourvu que le seuil épidémique $\mathcal{R}_0$, qui s'exprime en fonction de la valeur propre principale d'un certain opérateur intégral, soit strictement supérieur à 1. Cette même condition de seuil est également utilisée pour démontrer que toute onde progressive relie deux états stationnaires déterminés.\\ Dans une deuxième partie, nous étudions les propriétés de propagation des solutions pour le même système d'équations spatialement distribué, avec une densité initiale de plantes infectées à support compact spatialement en $x$. Lorsque $\mathcal{R}_0>1$, nous prouvons que la propagation se produit avec une vitesse de propagation qui coïncide avec la vitesse minimale $c_\star$ des ondes progressives étudiées dans la première partie. De plus, la solution du problème de Cauchy converge asymptotiquement vers une fonction spécifique pour laquelle la variable $x$ du repère mobile et celle du phénotype $y$ sont séparées.
  
  
• November 5 2020, 02:00 pm :Horacio G. Rostein New Jersey Institute of Technology, Rutgers University, USA
  
  Title: Resonance-based mechanisms of generation of oscillations in networks of non-oscillatory neurons
  
  Abstract: everal neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations, and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonator’s resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).
  
  
• July 2 2020, 05:00 pm: Jacques Demongeot, University of Grenoble-Alpes
  
  Title: Modeling epidemics: from Bernoulli-d'Alembert model to modern approaches. Example of the Covid-19 outbreak modelling dynamics
  
  Abstract: Since the first epidemic modelling by D. Bernoulli for smallpox disease (criticized and improved by J. d'Alembert) some improvements have been done by R. Ross for malaria modelling, then by his coworker J. McKendrick, who combined BDP (Birth and Death process) and ODE (Ordinary Differential Equation) approaches. Present approaches use both continuous PDE (Partial Differential Equation) models and discrete tools on the frontiers between IBM (Individual Based Modelling), ARIMA (Autoregressive Integrated Moving Average) and BDP models. We give as application example some results concerning the present Covid-19 outbreak modelling.
  Slides
  
  
• July 2 2020, 04:00 pm: Alain Miranville, University of Poitiers
  
  Title: Mathematical models for brain lactate kinetics
  
  Abstract: Our aim in this talk is to discuss mathematical models for the kinetics of lactactes in glial cells. We will also give numerical simulations and comparisons with real data.
  Slides
• June 25 2020, 05:00 pm: Vitaly Volpert, CNRS, Institut Camille Jordan, Lyon
  
  Title: Nonlocal and delay reaction-diffusion equations in mathematical immunology
  
  Abstract: Conventional models in mathematical immunology consist of ordinary or delay differential equations for the concentrations of different cells participating in the immune response and for the concentration of pathogen. Their spatial distribution in the tissue or cell culture, or their dependence on the genotype is described by reaction-diffusion equations with time delay characterizing clonal expansion of lymphocytes and with nonlocal terms taking into account cross reaction in the immune response. In this presentation we will study some mathematical properties of such models and their biomedical applications.
  
  Slides
• June 25 2020, 04:00 pm: Y. Bakhtin, New York University, USA
  
  Title: Universal statistics of incubation times and other applications of simple diffusion models.
  
  Abstract: When available, the data on incubation periods, i.e., times between the exposure to an infection and the onset of symptoms, exhibit striking universal features over a range of diseases and associated time scales. In this talk, I will show how these features such as right-skewness and more detailed distributional properties can be explained with the help of models based on diffusion processes. I will also have time to talk about applications of similar models to reaction/decision times in psychology, about limitations of such modeling, and about the problem of universality of stopping/halting times in decision making /computing in general.