scholarly journals Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment

2020 ◽  
Vol 25 (1) ◽  
pp. 81-98
Author(s):  
Chengxia Lei ◽  
◽  
Jie Xiong ◽  
Xinhui Zhou
Keyword(s):  
Qualitative Analysis ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Mass Action ◽  
Heterogeneous Environment ◽  
Infection Mechanism ◽  
Reaction Diffusion Model ◽  
Sis Epidemic ◽  
Spontaneous Infection

scholarly journals Hopf Bifurcation in an Oscillatory-Excitable Reaction–Diffusion Model with Spatial Heterogeneity

2017 ◽  
Vol 27 (05) ◽  
pp. 1750065
Author(s):  
Benjamin Ambrosio
Keyword(s):  
Hopf Bifurcation ◽  
Qualitative Analysis ◽  
Spatial Heterogeneity ◽  
Numerical Simulations ◽  
Diffusion Model ◽  
Center Manifold ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model

We focus on the qualitative analysis of a reaction–diffusion model with spatial heterogeneity. The system is a generalization of the well-known FitzHugh–Nagumo system, in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of a Hopf bifurcation and determine an equation of the center-manifold in which the solution asymptotically evolves. Numerical simulations illustrate the phenomenon.

scholarly journals Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model

2008 ◽  
Vol 21 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Linda J. S. Allen ◽  
◽  
B. M. Bolker ◽  
Yuan Lou ◽  
A. L. Nevai ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Steady States ◽  
Reaction Diffusion Model ◽  
Sis Epidemic

scholarly journals Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chengxia Lei ◽  
Xinhui Zhou
Keyword(s):  
Infectious Disease ◽  
Reaction Diffusion ◽  
Endemic Equilibrium ◽  
Heterogeneous Environment ◽  
Small Diffusion ◽  
Susceptible Population ◽  
Asymptotic Behaviors ◽  
Sis Epidemic Model ◽  
Sis Epidemic ◽  
Spontaneous Infection

<p style='text-indent:20px;'>In this paper, we investigate the effect of spontaneous infection and advection for a susceptible-infected-susceptible epidemic reaction-diffusion-advection model in a heterogeneous environment. The existence of the endemic equilibrium is proved, and the asymptotic behaviors of the endemic equilibrium in three cases (large advection; small diffusion of the susceptible population; small diffusion of the infected population) are established. Our results suggest that the advection can cause the concentration of the susceptible and infected populations at the downstream, and the spontaneous infection can enhance the persistence of infectious disease in the entire habitat.</p>

scholarly journals Tropical tree cover in a heterogeneous environment: A reaction-diffusion model

PLoS ONE ◽  
2019 ◽  
Vol 14 (6) ◽  
pp. e0218151 ◽  
Author(s):  
Bert Wuyts ◽  
Alan R. Champneys ◽  
Nicolas Verschueren ◽  
Jo I. House
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Tropical Tree ◽  
Tree Cover ◽  
Heterogeneous Environment ◽  
Reaction Diffusion Model
Sign in / Sign up

Export Citation Format

Share Document