Groupe de Travail BioMaths Normand

Fédération Normandie-Mathématiques

LMAH (Le Havre Normandie) & LMRS (Rouen Normandie)

Le GT BioMaths normand est un groupe de travail de la Fédération Normandie Mathématiques.
Celui-ci a pour objectif de favoriser les échanges sur les mathématiques appliquées à la biologie, en particulier en Normandie.

Organisateurs:

Elisa Affili, LMRS, Université de Rouen Normandie.
Matthieu Alfaro, LMRS, Université de Rouen Normandie.
Adel Blouza, LMRS, Université de Rouen Normandie.
Arnaud Ducrot, LMAH, Université Le Havre Normandie.
Quentin Griette, LMAH, Université Le Havre Normandie.
David Manceau, LMAH, Université Le Havre Normandie.

Sessions

Session 8: Le Havre, 28/11/2024 (14h-17h30) and 29/11/2024 (10h-12h).
Jeudi 28/11, salle B201.
- 14h00-15h00: Laura Kanzler, LJLL, Sorbonne Université.
  Modelling the evolution of the size-distribution in aquatic ecosystems.
  
  Laura Kanzler (LJLL, Sorbonne Université).
  Modelling the evolution of the size-distribution in aquatic ecosystems.
  
  Trophic interactions between animals in the ocean were matter of interest since the 60', where it was quickly discovered that the individuals' body size acts as 'master trait' in food webs of animals, giving rise to emergent distributions of biomass, abundance and production of organisms. We propose and investigate a deterministic jump-growth model, which is given by a kinetic equation for coalescing particles, aiming to capture this emergence phenomenon in aquatic ecosystems. The equation of interest is derived from individual based dynamics governed by a stochastic process. Following the observation of the body mass being the crucial trait in these dynamics it is based on the assumption that binary interactions between individuals in the ecosystem take place: A predator feeding on a prey, which then results in growth of the predator with assimilating a certain (usually very small) amount of its prey's mass as well as plankton production. Analytical results in various parameter regimes are discussed and numerical simulations underlying these observations are given.
- 15h00-16h00: Léon Matar Tine, Institut Camille Jordan, Université Claude Bernard Lyon-1.
  Description et analyse d'un modèle spatial pour la propagation de la maladie d'Alzheimer.
  
  Léon Matar Tine (Institut Camille Jordan, Université Claude Bernard Lyon-1).
  Description et analyse d'un modèle spatial pour la propagation de la maladie d'Alzheimer.
  
  Dans cet exposé, on discutera des aspects de modélisation de la maladie d'Alzheimer suivant l'hypothèse de cascade amyloïdes basée sur le processus de polymérisation de la protéine \(A\beta\) d'abord sous forme de proto-oligomères puis sous forme d'oligomères.
  Un modèle spatial de propagation des protéines \(A\beta\) avec prise en compte de l'activité neuronale sera décrit et son analyse alimentera les discussions durant l'exposé. Des résultats numériques seront également présentés.
  Ce travail est le fruit d'une collaboration avec Martin Andrade-Restrepo (Los Andes University, Colombia), Paul Lemarre (Novadiscovery), Sorin Ciuperca (Lyon 1), Laurent Pujo-menjouet (Lyon 1).
- 16h30-17h30: Nessim Dhaouadi, LMRS, Université de Rouen Normandie.
  Population adaptation in shifting environments.
  
  Nessim Dhaouadi (LMRS, Université de Rouen Normandie).
  Population adaptation in shifting environments.
  
  We introduce a model to study the adaptation of a diffusing population facing two different dynamics. On one hand, the population growth is time and space dependent, thus modelling strong heterogeneities of the environment. On the other hand, the environment itself is dynamic. It can both change size and shift over time. The reasons for such moving range boundaries could be the consequences of flooding, forest fire, etc.
  We will first investigate the fixed domain case, in particular estimating the principal eigenvalue of the underlying periodic parabolic operator. This estimate is crucial to construct sub and supersolutions on the moving domain. We then address the problem of extinction vs. persistence, taking into account the interplay between the moving habitat and the selection. Finally, to explore these dynamics, we construct a stable space-time finite elements scheme using upwind test functions in order to gain some insight on the dynamics of this problem. These will unravel some significant differences with classical results on fixed domains.
Vendredi 29/11, salle A008.
- 10h00-11h00: Giulia Cavalleri, University of Pavia, Italy.
  A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage.
  
  Giulia Cavalleri (University of Pavia, Italy).
  A phase field model of Cah-Hilliard type for tumour growth with mechanical effects and damage.
  
  We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn-Hilliard type equation that describes the phase separation process between healthy and tumour tissue. This equation is coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of forces, including inertial and viscous effects. The main novelty is the introduction of tissue damage, whose evolution is ruled by a parabolic differential inclusion. We prove a global-in-time existence result for weak solutions by passing to the limit in a time-discretized and regularized version of the system.
- 11h00-12h00: Mostafa Adimy, Institut Camille Jordan, Université Claude Bernard Lyon-1.
  Modeling the mechanisms of antibody mixtures in viral infections: the cases of sequential homologous and heterologous dengue infections.
  
  Mostafa Adimy (Institut Camille Jordan, Université Claude Bernard Lyon-1).
  Modeling the mechanisms of antibody mixtures in viral infections: the cases of sequential homologous and heterologous dengue infections.
  
  Antibodies play an essential role in the immune response to viral infections, vaccination, or antibody therapy. Nevertheless, they can be either protective or harmful during the immune response. Moreover, competition or cooperation between mixed antibodies can enhance or reduce this protective or harmful effect. Using the laws of chemical reactions, we propose a new approach to modeling the antigen-antibody complex activity (see, [1]). The resulting expression covers not only purely competitive or purely independent binding but also synergistic binding which, depending on the antibodies, can promote either neutralization or enhancement of viral activity. We then integrate this expression of viral activity in a within-host model and investigate the existence of steady-states and their asymptotic stability. We complete our study with numerical simulations to illustrate different scenarios: firstly, where both antibodies are neutralizing, and secondly, where one antibody is neutralizing and the other enhancing. The results indicate that efficient viral neutralization is associated with purely independent antibody binding, whereas strong viral activity enhancement is expected in the case of purely competitive antibody binding. Finally, data collected during a secondary dengue infection were used to validate the model. The data set includes sequential measurements of virus and antibody titers during viremia in patients. Data fitting shows that the two antibodies are in strong competition, as the synergistic binding is low. This contributes to the high levels of virus titers and may explain the Antibody-Dependent Enhancement phenomenon. Besides, the mortality of infected cells is almost twice as high as that of susceptible cells, and the heterogeneity of viral kinetics in patients is associated with variability in antibody responses between individuals. Other applications of the model may be considered, such as the efficacy of vaccines and antibody-based therapies.
  This work has been done in collaboration with Charlotte Dugourd-Camus (Centre Inria de Lyon) and Claudia P. Ferrreira (Institute of Biosciences, UNESP Botucatu, Brazil).
  
  [1] C. Dugourd-Camus, C.P. Ferreira, M. Adimy. Modelling the mechanisms of antibody mixtures in viral infections: the cases of sequential homologous and heterologous dengue infections. Journal of the Royal Society Interface 21 (2024).
Session 7: Rouen, 14/05/2024, Salle de séminaire du LMRS.
- 10h30-11h30: Sylvain Billiard, Université de Lille.
  Stochastic foraging paths primarily drives consumption rates variations within and across species.
  
  Sylvain Billiard (Université de Lille).
  Stochastic foraging paths primarily drives consumption rates variations within and across species.
  
  The speed of interactions between individuals, typically between a predator and its prey, is at the core of most ecological theories and models. Generally, the consumption rate of prey by a single predator is supposed density-dependent, and variou functional forms have been proposed, the so-called "functional responses". The variability within and between species in consumption rates is often attributed to between-individuals variability, environmental heterogeneity or measurements errors. However, the process of interaction itself is stochastic, primarily because foraging in an unknown and unpredictable environment is random. Hence, the observed variability in consumption rates can stem from intrinsic stochasticity, rather than solely from extrinsic variabilities. In this study, our objective was to estimate the expected variability of prey consumption rates due to intrinsic stochasticity alone, using a simple random walk process. We demonstrate that depending on the dimensionality of the environment, intrinsic variability can be of a similar order of magnitude as the mean. We then compare observed fluctuations across hundreds of experiments and find that the observed variability is quantitatively compatible with our model's predictions. We conclude that the observed variability is primarily attributable to the stochasticity of foraging paths.
- 11h30-12h30: Michèle Romanos, Institut Camille Jordan.
  Mathematical modeling, analysis and simulation of crowd dynamics in Myxococcus xanthus bacteria.
  
  Michèle Romanos (Institut Camille Jordan).
  Mathematical modeling, analysis and simulation of crowd dynamics in Myxococcus xanthus bacteria.
- 14h15-15h15: Sophie Hecht, Sorbonne Université.
  On the early morphogenesis of bacteria micro-colony: microscopic and macroscopic modelling.
  
  Sophie Hecht (Sorbonne Université).
  On the early morphogenesis of bacteria micro-colony: microscopic and macroscopic modelling.
- 15h15-16h15: Cécile Carrère, Université d'Orléans.
  Recovery of maladapted traits in an experiment of biphasic bacteria.
  
  Cécile Carrère (Université d'Orléans).
  Recovery of maladapted traits in an experiment of biphasic bacteria.
  
  We present a model of bacteria that can live in two environments, namely inside worms and on the soil. The bacteria population is structured in phenotype, and different environments favor different phenotypes. In the experiment presented here, to mimic the life cycle of these bacteria, worms are periodically moved to fresh soil without bacteria. We will show through numerical simulations that in this situation, even if traits adapted to the worms should disappear from the final population, we recover them when a reset is applied.
Session 6: Rouen, 21/11/2023, Salle de séminaire du LMRS.
- 10h30-11h30: Nicolas Loeuille, Sorbonne Université.
  Dynamiques éco-évolutives sous changements globaux, conséquences pour le maintien de la diversité et la structure des réseaux écologiques.
  
  Nicolas Loeuille (Sorbonne Université).
  Dynamiques éco-évolutives sous changements globaux, conséquences pour le maintien de la diversité et la structure des réseaux écologiques.
- 11h30-12h30: Nastassia Pouradier Duteil, Sorbonne Université, INRIA.
  Graph Limit for Interacting Particle Systems on Weighted Random Graphs.
  
  Nastassia Pouradier Duteil (Sorbonne Université, INRIA).
  Graph Limit for Interacting Particle Systems on Weighted Random Graphs.
  
  We study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of graphons. We prove that as the number of particles tends to infinity, the finite-dimensional particle system converges in probability to the solution of a deterministic graph-limit equation, in which the graphon prescribing the interaction is given by the first moment of the weighted random graph law.
- 14h15-15h15: Bastien Polizzi, Université de Franche-Comté.
  (Epi)mutation rates and the evolution of composite trait architectures.
  
  Bastien Polizzi (Université de Franche-Comté).
  (Epi)mutation rates and the evolution of composite trait architectures.
  
  Mutation rates vary widely along genomes and across inheritance systems. This suggests that complex traits - resulting from the contributions of multiple determinants - might be composite in terms of the underlying mutation rates. Here we investigate through mathematical modeling whether such heterogeneity may drive changes in traits' architectures, especially in fluctuating environments where phenotypic instability can be beneficial. We first identify a convexity principle, relating to the shape of the trait's fitness functions, setting conditions under which composite architectures should be adaptive or, conversely and more commonly, should be selected against. Simulations reveal, however, that applying this principle to realistic evolving populations requires taking into account pervasive epistatic interactions that take place in the system. Indeed, the fate of a mutation affecting the architecture depends on the (epi)genetic background, itself depending upon the current architecture in the population. We tackle this problem by borrowing the adaptive dynamics framework from evolutionary ecology - where it is routinely used to deal with such resident/mutant dependencies - and find that the principle excluding composite architectures generally prevails. Yet, the predicted evolutionary trajectories will typically depend on the initial architecture, possibly resulting in historical contingencies. Finally, by relaxing the large population size assumption, we unexpectedly find that not only the strength of selection on a trait's architecture, but also its direction, depend on population size, revealing a new occurrence of the recently coined phenomenon of 'sign inversion'. This work is a collaboration with Vincent Calvez, Étienne Rajon, and Sylvain Charlat.
- 15h15-16h15: Alessandro Zilio, Université Paris Cité, campus Grands Moulins.
  Profils asymptotiques pour des systèmes de compétition-diffusion : spirales.
  
  Alessandro Zilio (Université Paris Cité, campus Grands Moulins).
  Profils asymptotiques pour des systèmes de compétition-diffusion : spirales.
  
  Dans cet exposé, je présenterai un travail de recherche développé avec Susanna Terracini (Università di Torino) et Gianmaria Verzini (Politecnico di Milano). Nous étudions la structure de l'ensemble nodal des solutions de systèmes de réaction-diffusion (cas planaire et stationnaire) avec des interactions entre composantes de type Lotka-Volterra fortement compétitives, lorsque la matrice des coefficients de compétition interspécifique est asymétrique et que le paramètre de compétition tend vers l'infini. Contrairement au cas symétrique, où l'on sait que l'ensemble nodal consiste en une collection localement finie de courbes se rencontrant avec des angles égaux en un nombre localement fini de points singuliers, le cas asymétrique montre l'émergence de courbes nodales en spirale, se rencontrant toujours en des points localement isolés avec un ordre de fuite fini. Je présenterai ensuite un article avec Ariel Sarlot (Universidad de Buenos Aires) dans lequel nous construisons des solutions au système parabolique correspondant. Plus précisément, nous construisons des solutions en forme de spirale tournante éternelle.
Session 5: Le Havre, 24/05/2023, Salle du PRSH.
- 14h00-15h00: Romain Ducasse, Laboratoire Jacques-Louis Lions (LJLL), Université Paris Cité.
  Propagation properties for a multi-species SIR reaction-diffusion system.
  
  Romain Ducasse (LJLL, Université Paris Cité).
  Propagation properties for a multi-species SIR reaction-diffusion system.
  
  The SIR system is a reaction-diffusion model that describes the spread of diseases in a population. In this talk, we present a multi-species version of this model, describing the interactions between the propagation of different strains of a disease. The model takes the form of a system of reaction-diffusion PDEs. We shall study the long-time behavior of solutions (convergence to equilibria, speed of convergence...) and prove that there is a "selection via propagation" phenomenon.
- 15h-15h15: pause café.
- 15h15-16h15: Christophe Minier, SEBIO, Université Le Havre Normandie.
  Les perturbateurs endocriniens: impacts et significations toxicologiques.
  
  Christophe Minier (SEBIO, Université Le Havre Normandie).
  Les perturbateurs endocriniens: impacts et significations toxicologiques.
  
  Les toxiques de l'environnement comportent de nombreuses familles de composés chimiques. La dernière identifiée correspond aux "perturbateurs endocriniens". Ces derniers correspondent aux substances chimiques qui interfèrent avec le système hormonal des êtres vivants. L'étude de ces composés a rapidement mis en évidence qu'ils étaient susceptibles d'avoir des impacts très significatifs sur la santé. Ils interfèrent ainsi avec le développement, la reproduction, le comportement et le métabolisme des organismes vivants touchant des physiologies et mécanismes très essentiels. Au-delà de leurs effets délétères, leurs mécanismes d'action et leurs spécificités interrogent les concepts de la toxicologie classique et révèlent des défis importants pour la recherche et pour la protection de la santé des êtres vivants.
- 16h15-17h15: Irmand Mikiela, LMAH, Université Le Havre Normandie.
  Couplage non-local d'équations de réaction-diffusion sur des domaines disjoints.
  
  Irmand Mikiela (LMAH, Université Le Havre Normandie).
  Couplage non-local d'équations de réaction-diffusion sur des domaines disjoints.
  
  Dans cet exposé, nous proposons une méthode de couplage non-local d'EDPs en dynamique de populations et épidémiologie. La méthode que nous proposons permet de coupler des EDPs, en garantissant la bonne définition du modèle couplé obtenu et la vérification du principe de conservation du flux. De plus, cette méthode permet de se défaire de l'hypothèse selon laquelle "tous les domaines du réseau sont identiques" qu'on retrouve dans plusieurs travaux en littérature et elle permet aussi d'analyser le modèle indépendamment de la topologie du réseau.
Session 4: Rouen,16/11/2022 et 17/11/2022,
Mercredi 16/11, Amphi B.
- 14h00-14h50: Samuel Alizon, CIRB, Collège de France.
  Utilisation des infections multiples pour inférer réseaux de contacts et patrons d'immunité croisée.
  
  Samuel Alizon (CIRB, Collège de France).
  Utilisation des infections multiples pour inférer réseaux de contacts et patrons d'immunité croisée.
- 14h50-15h20: pause café.
- 15h20-16h10: Frédéric Hamelin, L'Institut Agro, Rennes.
  Host Diversification May Split Epidemic Spread into Two Successive Fronts Advancing at Different Speeds.
  
  Frédéric Hamelin (L'Institut Agro, Rennes)
  Host Diversification May Split Epidemic Spread into Two Successive Fronts Advancing at Different Speeds
- 16h10-17h00: Florian Lavigne, LMRS, Université de Rouen Normandie.
  Sélection/Mutations: Quelques généralisations de l'équation replicator-mutator.
  
  Florian Lavigne (LMRS, Université de Rouen Normandie).
  Sélection/Mutations: Quelques généralisations de l'équation replicator-mutator.
Jeudi 17/11, Amphi S ESITECH.
- 09h30-10h20: Magali Ribot, Institut Denis Poisson, Université d'Orléans.
  Modèles de mélange pour la croissance de biofilms.
  
  Magali Ribot (Institut Denis Poisson, Université d'Orléans).
  Modèles de mélange pour la croissance de biofilms.
- 10h20-11h10: Quentin Richard, IMAG, Université de Montpellier.
  Un modèle épidémiologique structuré sur la transmission du paludisme.
  
  Quentin Richard (IMAG, Université de Montpellier)
  Un modèle épidémiologique structuré sur la transmission du paludisme.
- 11h10-11h30: Mini Break.
- 11h30-12h20: Quentin Griette, LMAH, Université Le Havre Normandie.
  Long-time dynamics of a competition-selection model in the space of measures: persistence and concentration.
  
  Quentin Griette (LMAH, Université Le Havre Normandie).
  Long-time dynamics of a competition-selection model in the space of measures: persistence and concentration.

Session 3: Le Havre, 24/05/2022, Amphi Lesueur,UFR ST.
(Les exposés avaient aussi lieu en ligne)
- 14h00-15h00: Jean Baptiste Burie, Université de Bordeaux et Institut Mathématiques de Bordeaux (UMR CNRS 5251).
  Des modèles pour la propagation de maladies de la vigne.
  
  Jean Baptiste Burie (IMB, Université de Bordeaux).
  Des modèles pour la propagation de maladies de la vigne.
  
  Dans cet exposé, nous présenterons des modèles de maladies fongiques de plantes cultivées. En particulier, nous nous intéressons à l'oïdium de la vigne et au mildiou. Ces modèles ont été élaborés dans le cadre de collaborations avec l'INRAE de Bordeaux (UMR SAVE). Un premier modèle basé sur un système d'équations différentielles décrit la propagation de la maladie à l'échelle d'une seule plante. Il permet d'étudier comment la croissance de la vigne agit sur la maladie. Ce modèle est ensuite étendu à l'échelle d'une parcelle en utilisant un système d'équations aux dérivées partielles (réaction-diffusion) décrivant la dispersion des spores dans l'environnement. L'INRAE développe des variétés résistantes aux maladies. La modélisation donne des indications sur la façon dont ces variétés doivent être déployées dans la parcelle pour avoir un maximum d'efficacité contre la maladie. Enfin, en introduisant une variable supplémentaire décrivant le trait phénotypique du pathogène, on peut étudier sa capacité évolutive à s'adapter à son hôte. Le but est ici de retarder le plus possible cette adaptation qui permet au pathogène de contourner totalement la résistance après quelques années. L'analyse de ces modèles se fait soit par des simulations numériques directes, soit par l'analyse mathématique (détermination du nombre de reproduction de base R_0, existence et description de fronts épidémiques).
- 15h-15h15: pause café.
- 15h15-16h15: Romain Coulaud, SEBIO, Université Le Havre Normandie.
  Modélisation et changement d'échelles pour la biosurveillance des milieux aquatiques.
  
  Romain Coulaud (SEBIO, Université Le Havre Normandie).
  Modélisation et changement d'échelles pour la biosurveillance des milieux aquatiques.
- 16h15-17h15: Samuel Tréton, LMRS, Université de Rouen Normandie.
  The field-road diffusion model: fundamental solution and asymptotic behavior.
  
  Samuel Tréton (LMRS, Université de Rouen Normandie).
  The field-road diffusion model: fundamental solution and asymptotic behavior.
  
  We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. Despite the complex geometry of the problem and the exchange condition, we provide the first explicit expression of its fundamental solution and of the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. Furthermore, we estimate the rate of decay of the \(L^\infty\) norm of the solution.

Session 2: Rouen, 21/10/2021
- 14h30-15h30: Gaël Raoul, CMAP, École Polytechnique.
  Évolution de résistance aux antibiotiques dans un environnement hétérogène.
  
  Gaël Raoul (CMAP, École polytechnique).
  Évolution de résistance aux antibiotiques dans un environnement hétérogène.
  
  Nous nous intéressons à une population de pathogène structurée en trois types distincts: deux types "spécialistes", résistant respectivement à l'antibiotique A et à l'antibiotique B, ainsi qu'un type multirésistant. La multi-résistance de ce dernier type est associée à une vitesse de reproduction plus faible, ce qui est désigné comme coût de la multirésistance. Cette population vit dans un environnement de dimension 1, où les antibiotiques A et B sont appliqués de façon périodique: le traitement A sur [0,L/2), le traitement B sur [L/2,L), etc. Nous avons pu décrire la vitesse de propagation des pathogènes dans ce type d'environnement, et cette description nous a permis de mieux comprendre l'émergence des types multirésistants. Nous montrons notamment que les phases de propagation des pathogènes favorisent l'émergence de cette multirésistance. Ce travail a été réalisé en collaboration avec Matthieu Alfaro, Sylvain Gandon et Quentin Griette.
- 16h-17h: Hao Kang, LMAH, Université Le Havre Normandie.
  Age-structured Models with Nonlocal Diffusion: Principal Spectral Theory, Limiting Properties and Global Dynamics.
  
  Hao Kang (LMAH, Université Le Havre Normandie).
  Age-structured Models with Nonlocal Diffusion: Principal Spectral Theory, Limiting Properties and Global Dynamics.
  
  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.

Session 1: Le Havre, 25/06/2021 (exposés en ligne dû à la crise sanitaire)
- 15h-16h: Ramsès Djidjou-Demasse, IRD, Lab MIVEGEC.
  Mathematical models of Antimicrobial Resistance: from qualitative to quantitative resistance.
  
  Ramsès Djidjou-Demasse (IRD, Lab MIVEGEC).
  Mathematical models of Antimicrobial Resistance: from qualitative to quantitative resistance.
  
  Antimicrobial efficacy is traditionally described by a single value, the minimal inhibitory concentration (MIC), which is the lowest concentration that prevents visible growth of the bacterial population. As a consequence, bacteria are classically qualitatively categorized as resistant if therapeutic concentrations are below MIC and susceptible otherwise. However, there is continuity in the space of the bacterial resistance levels. Here, we introduce a model of within-host evolution of resistance under treatment that considers resistance as a continuous quantitative trait, describing the level of resistance of the bacterial population. The use of integro-differential equations allows to simultaneously track the dynamics of the bacterial population size and the evolution of its level of resistance.
- 16h-17h: Shigui Ruan, University of Miami, Department of Mathematics.
  Modeling the Growth, Invasion and Competition of Aedes Mosquitoes in Florida.
  
  Shigui Ruan (University of Miami, Department of Mathematics).
  Modeling the Growth, Invasion and Competition of Aedes Mosquitoes in Florida.
  
  The Aedes mosquitoes, in particular Aedes aegypti and Aedes albopictus, are the primary vectors that transmit several arboviral diseases, including chikungunya fever, dengue fever, yellow fever, and Zika. Recently, the world has been experiencing a series of major outbreaks of these vector-borne diseases (for example, the 2016 Zika outbreak in Florida, etc.). In order to study the transmission dynamics of these vector-borne diseases, it is very important and necessary to understand the population dynamics, current distributions and movements of Aedes mosquitoes for successful surveillance and control programs. In this talk, we will introduce some of our recent studies on modeling the population dynamics of Aedes mosquitoes, the invasion of Aedes albopictus mosquitoes, and the competition between Aedes aegypti and Aedes Albopictus mosquitoes in Florida, the United States. In particular, we propose a competition model with road-field diffusion in which the invasive population not only disperses in the interior of the spatial domain but also moves faster on the boundary of the domain. Both strong-weak and weak-weak competitions are discussed. It is shown that the asymptotic spreading speed of the wave fronts is increasing only if the road diffusion rate is greater than the field diffusion rate. Numerical simulations are presented to illustrate our analytical results and to explain the current estimated distributions of these two mosquito species in Florida.