English
Related papers

Related papers: A wolbachia infection model with free boundary

200 papers

We investigate a reaction-diffusion-advection equation of the form $u_t-u_{xx}+\beta u_x=f(u)$ $(t>0,\,0<x<h(t))$ with mixed boundary condition at $x=0$ and a free boundary condition at $x=h(t)$. Such a model may be applied to describe the…

Analysis of PDEs · Mathematics 2015-08-17 Yonggang Zhao , Mingxin Wang

Numerous studies have examined the growth dynamics of Wolbachia within populations and the resultant rate of spatial spread. This spread is typically characterised as a travelling wave with bistable local growth dynamics due to a strong…

Dynamical Systems · Mathematics 2016-06-29 Matthew H. Chan , Peter S. Kim , Robert Marangell

This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…

Analysis of PDEs · Mathematics 2025-11-21 Qian Qin , JinJing Jiao , Zhiguo Wang , Hua Nie

In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a…

Analysis of PDEs · Mathematics 2021-05-12 Lingyu Liu

This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…

Dynamical Systems · Mathematics 2019-05-24 Jia-Feng Cao , Wan-Tong Li , Jie Wang

This paper continues to study the monostable cooperative system with nonlocal diffusion and free boundary, which has recently been discussed by [Du and Ni, 2020, arXiv:2010.01244]. We here aim at the four aspects: the first is to give more…

Analysis of PDEs · Mathematics 2021-11-12 Lei Li , Xueping Li , Mingxin Wang

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and…

Analysis of PDEs · Mathematics 2019-12-06 Meng Zhao , Yang Zhang , Wan-Tong Li , Yihong Du

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…

Analysis of PDEs · Mathematics 2024-06-11 Xueping Li , Lei Li , Mingxin Wang

We study a mosquito-borne epidemic model where the vector population is distinct in aquatic and adult stages and a saturating effect of disease transmission is assumed to ocurr when the number of infectious (humans and mosquitoes) becomes…

Populations and Evolution · Quantitative Biology 2014-02-10 E. Avila-Vales , B. Buonomo , N. Chan-Chi

We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…

Pattern Formation and Solitons · Physics 2020-10-05 Ryan J Murphy , Pascal R Buenzli , Ruth E Baker , Matthew J Simpson

In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…

Analysis of PDEs · Mathematics 2017-10-27 Mingxin Wang , Qianying Zhang

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…

Analysis of PDEs · Mathematics 2024-05-08 Lei Li , Mingxin Wang

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…

Analysis of PDEs · Mathematics 2017-10-17 Zhiguo Wang , Hua Nie , Yihong Du

A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a…

Biological Physics · Physics 2014-08-26 V. M. Kenkre , S. Sugaya

The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing…

Analysis of PDEs · Mathematics 2020-02-05 Félix del Teso , Jørgen Endal , Juan Luis Vázquez

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and…

Analysis of PDEs · Mathematics 2018-12-03 Yunfeng Liu , Zhiming Guo , Mohammad El Smaily , Lin Wang

In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential…

Analysis of PDEs · Mathematics 2020-04-27 Lei Li , Siyu Liu , Mingxin Wang

The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half plane, in which reaction-diusion phenomena take place, exchanges mass with a line having a large diusion of its…

Analysis of PDEs · Mathematics 2019-03-15 Luis Caffarelli , Jean-Michel Roquejoffre

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…

Analysis of PDEs · Mathematics 2022-02-01 Hong-Ming Yin , Jun Zou

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…

Analysis of PDEs · Mathematics 2017-10-17 Yihong Du , Chang-Hong Wu