Related papers: Applicability of the Fisher Equation to Bacterial …
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimension subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria, for example, track in a…
An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Risk spreading in bacterial populations is generally regarded as a strategy to maximize survival. Here, we study its role during range expansion of a genetically diverse population where growth and motility are two alternative traits. We…
The effect of mechanical interactions between cells in the spreading of bacterial populations was investigated in one-dimensional space. A continuum-mechanics approach, comprising cell migration, proliferation, and exclusion processes, was…
The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…
Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is…
Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) family, influence the migration of a population of cells during wound healing. Fisher's Equation has…
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…
We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions,…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is non-local, and show that spatial structures with interesting…
Bacteria populations rely on mechanisms such as quorum sensing to coordinate complex tasks that cannot be achieved by a single bacterium. Quorum sensing is used to measure the local bacteria population density, and it controls cooperation…
In this article a kinetic model for the dynamics of myxobacteria colonies on flat surfaces is investigated. The model is based on the kinetic equation for collective bacteria dynamics introduced in arXiv:2001.02711, which is based on the…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…