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This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as -coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number of active lineages were obtained by the author in a previous work. Analogous results for the number of active mutation-free lineages and the combined lineage lengths are derived using the same martingale-based technique. They are given in terms of convergence in...
In this note, we consider a nonlinear diffusion equation with a bistable reaction term
arising in population dynamics. Given a rather general initial data, we investigate its
behavior for small times as the reaction coefficient tends to infinity: we prove a
generation of interface property.
The authors consider the nonlinear difference equation
with . They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model
consists of a system of nonlinear partial differential equations for the spatial population
density of a species and the spatial concentration of a chemoattractant in n-dimensional
space. We prove the existence of solutions, which exist globally, and are L∞-bounded on
finite time intervals. The hypotheses require nonlocal conditions on the species-induced
production of the chemoattractant.
This paper is devoted to the study of global existence of periodic solutions of a delayed
tumor-immune competition model. Also some numerical simulations are given to illustrate
the theoretical results
This paper is concerned with a delayed single population model with hereditary effect. Under appropriate conditions, we employ a novel argument to establish a criterion of the global exponential stability of positive almost periodic solutions of the model. Moreover, an example and its numerical simulation are given to illustrate the main result.
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
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