Related papers: A host-pathogen coevolution model. Part I: Run str…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…
Animal behavior is often quantified through subjective, incomplete variables that may mask essential dynamics. Here, we develop a behavioral state space in which the full instantaneous state is smoothly unfolded as a combination of…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…
This paper investigates the coexistence of two competing species on random geometric graphs (RGGs) in continuous time. The species grow by occupying vacant sites according to Richardson's model, while simultaneously competing for occupied…
We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the…
This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…
We study some simple mathematical models designed to test the following hypothesis: can a pathogen escape the immune system only because of its high probability of mutation? We propose both spatial and non-spatial models. In all of our…
The search for traveltime parameters is a global optimization problem. Several metaheuristics have been proposed to locate the global optima to compute the least amount of their objective functions. However, the theoretical limitations…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior…
We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission and recovery are possible during…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
In one-dimensional, heterogeneous systems, the whole traffic dynamics depend strongly on the behavior of the leading vehicle. This result holds for a class of vehicular traffic models satisfying the following properties. The interactions…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
The interplay between parasites and their hosts is found in all kinds of species and plays an important role in understanding the principles of evolution and coevolution. Usually, the different genotypes of hosts and parasites oscillate in…