Local existence for a general model of size-dependent population dynamics.
Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models
Logistic equation on measure chains
Logistic equation with the -Laplacian and constant yield harvesting.
Long range diffusion reaction model on population dynamics.
Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource
In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.
Lotka-Volterra type predator-prey models: Comparison of hidden and explicit resources with a transmissible disease in the predator species
The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.
Macroscopic models of collective motion and self-organization
In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...
Markov operators: applications to diffusion processes and population dynamics
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
Matematica ed Ecologia: un’interazione feconda
Mathematical model of dengue disease transmission with severe DHF compartment.
Mathematical Modeling Describing the Effect of Fishing and Dispersion on Hermaphrodite Population Dynamics
In order to study the impact of fishing on a grouper population, we propose in this paper to model the dynamics of a grouper population in a fishing territory by using structured models. For that purpose, we have integrated the natural population growth, the fishing, the competition for shelter and the dispersion. The dispersion was considered as a consequence of the competition. First we prove, that the grouper stocks may be less sensitive to the...
Mathematical modeling of antigenicity for HIV dynamics
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...
Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics
The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts....
Mean fixation time estimates in constant size populations.
Media/psychological impact on multiple outbreaks of emerging infectious diseases.
Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study
Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour...
Mesure invariante pour le système d'équations stochastiques du modèle de proie-prédateur avec diffusion spatiale
Metastable aggregation within a discrete-time model.
Methane hydrate formation and decomposition.