Related papers: Traveling Wave Solutions in a Reaction-Diffusion M…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…
This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We…
We develop and analyze mathematical models for residential burglary that incorporates police deployment through a delayed feedback mechanism. Motivated by empirical observations from publicly available crime and policing data, we extend a…
In this paper, the existence of a non-trivial, positive and bounded critical traveling wave solution of a diffusive disease model, whose reaction system has infinity many equilibria, is obtained for the first time. This gives an affirmative…
In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its…
This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
We study the existence of traveling wave solutions for a diffusive predator-prey system. The system considered in this paper is governed by a Sigmoidal response function which is more general than those studied previously. Our method is an…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Containing the spreading of crime in urban societies remains a major challenge. Empirical evidence suggests that, left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult,…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established.…
We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equals a certain number, and below which there is no…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
We introduce a novel approach of epidemic modeling by combining age-structured models with damped wave equations. This transforms the parabolic-type reaction-diffusion model into a hyperbolic system that shares many properties with a wave…
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…