scholarly journals Threshold dynamics of a time periodic reaction–diffusion epidemic model with latent period

2015 ◽  
Vol 258 (9) ◽  
pp. 3011-3036 ◽  
Author(s):  
Liang Zhang ◽  
Zhi-Cheng Wang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Latent Period ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Periodic Reaction ◽  
Time 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.

scholarly journals Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jinliang Wang ◽  
Hongquan Sun
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Heterogeneous Environment ◽  
Threshold Parameter ◽  
Simulation Results ◽  
Heroin Model

This paper is concerned with a reaction-diffusion heroin model in a bound domain. The objective of this paper is to explore the threshold dynamics based on threshold parameter and basic reproduction number (BRN) ℜ0, and it is proved that if ℜ0<1, heroin spread will be extinct, while if ℜ0>1, heroin spread is uniformly persistent and there exists a positive heroin-spread steady state. We also obtain that the explicit formula of ℜ0 and global attractiveness of constant positive steady state (PSS) when all parameters are positive constants. Our simulation results reveal that compared to the homogeneous setting, the spatial heterogeneity has essential impacts on increasing the risk of heroin spread.

Sign in / Sign up

Export Citation Format

Share Document