Related papers: Establishing Traveling Wave in Bistable Reaction-D…
A deterministic nonlinear ordinary differential equation model for mosquito dynamics in which the mosquitoes can quest for blood either within a human population or within non-human/vertebrate populations is derived and studied. The model…
Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the…
Local climate conditions play a major role in the development of the mosquito population responsible for transmitting Dengue Fever. Since the {\em Aedes Aegypti} mosquito is also a primary vector for the recent Zika and Chikungunya…
Genetically engineered bacteria to increase the tumbling frequency of the run-and-tumble motion for the higher local bacterial density form visible stripe pattern composed of successive high and low density regions on an agar plate. We…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering the underlying diffusion mechanisms, which is…
We present an analysis of an epidemic spreading process on the Apollonian network that can describe an epidemic spreading in a non-sedentary population. The modified diffusive epidemic process was employed in this analysis in a…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…
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…
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
Vector-borne diseases arise from the coupled dynamics of human mobility and mosquito ecology, producing outbreaks shaped by both spatial distributions and temporal patterns of movement. Here we develop a coarse-grained hub--leaf reduction…
Seasonality frequently occurs in population models, and the corresponding seasonal patterns have been of great interest to scientists. This paper is concerned with traveling waves to a time-periodic bistable Lotka-Volterra competition…
Bacteria can spontaneously develop collective motions by aligning their motions in dense systems. Here, we show that bacteria can also respond collectively to an alternating electrical field and form dynamic clusters oscillating at the same…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
Feedback control schemes are a promising way to manipulate transport properties of driven colloidal suspensions. In the present article we suggest a feedback scheme to enhance the collective transport of colloidal particles with repulsive…
We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of…
We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated…
A new experimental colonial pattern and pattern transition observed in E. coli MG1655 swarming cells grown on semi-solid agar are described. We present a reaction-diffusion model that, taking into account the slime generated by these cells…
Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all…