相关论文: On a reaction-diffusion virus model with general b…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…
An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…
The flux of visitors through popular places undoubtedly influences viral spreading -- from H1N1 and Zika viruses spreading through physical spaces such as airports, to rumors and ideas spreading though online spaces such as chatrooms and…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
The time-global unique solvability on the reaction diffusion equations for prey-predator models with density-dependent inhibitor and dormancy on predators is established. The crucial step of the proof is to construct time-local non-negative…
West Nile virus (WNV) is a climate-sensitive mosquito-borne arbovirus circulating between mosquitoes of the genus Culex and birds, with a potential spillover to humans and other mammals. Recent trends in climatic change, characterized by…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous…
Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the world. The Zika virus has been known since 1947 and invaded South America in 2013. It can be transmitted not only by…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
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 treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…