scholarly journals An almost periodic epidemic model in a patchy environment

2015 ◽  
Vol 21 (1) ◽  
pp. 271-289 ◽  
Author(s):  
Bin-Guo Wang ◽  
Wan-Tong Li ◽  
Lizhong Qiang
Keyword(s):  
Epidemic Model ◽  
Patchy Environment ◽  
Almost Periodic

A reaction–diffusion epidemic model with incubation period in almost periodic environments

2020 ◽  
pp. 1-24
Author(s):  
LIZHONG QIANG ◽  
BIN-GUO WANG ◽  
ZHI-CHENG WANG
Keyword(s):  
Time Delay ◽  
Spatial Heterogeneity ◽  
Incubation Period ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Fixed Time ◽  
Reaction Diffusion Equations ◽  
Threshold Dynamics ◽  
Almost Periodic ◽  
Periodic Reaction

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent $${\lambda ^*}$$ for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of $${\lambda ^*}$$ . It is shown that the disease-free almost periodic solution is globally attractive if $${\lambda ^*} < 0$$ , while the disease is persistent if $${\lambda ^*} < 0$$ . By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

Dynamical Behaviors of a Pest Epidemic Model with Impulsive Control Over a Patchy Environment

2018 ◽  
Vol 28 (14) ◽  
pp. 1850173 ◽  
Author(s):  
Zhichun Yang ◽  
Cheng Chen ◽  
Lanzhu Zhang ◽  
Tingwen Huang
Keyword(s):  
Epidemic Model ◽  
Impulsive Control ◽  
Threshold Value ◽  
Impulsive System ◽  
Asymptotically Stable ◽  
Patchy Environment ◽  
Globally Asymptotically Stable ◽  
Dynamical Behaviors ◽  
Persistence Theory ◽  
Chaotic Characteristic

An epidemic model for pest management with impulsive control over a patchy environment is proposed in this paper. We investigate the dynamical behaviors on extinction and permanence and obtain the threshold value [Formula: see text] of dynamics for the impulsive system by utilizing a small amplitude perturbation method, matrix spectral analysis and persistence theory. We prove that the periodic pest-eradication solution of the system is globally asymptotically stable if [Formula: see text], while the system is persistent if [Formula: see text]. Furthermore, by discussion on the two-patch case, we analyze the effects of the dispersal and impulsive control on dynamical behaviors of the system. Some numerical examples are given to illustrate the effectiveness of the obtained results and to demonstrate the complexity such as chaotic characteristic of the system.

An epidemic model in a patchy environment

2004 ◽  
Vol 190 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Wendi Wang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Epidemic Model ◽  
Patchy Environment
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