scholarly journals Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment

2018 ◽  
Vol 15 (6) ◽  
pp. 1479-1494 ◽  
Author(s):  
Abdelrazig K. Tarboush ◽  
◽  
Jing Ge ◽  
Zhigui Lin ◽  
◽  
...  
Keyword(s):  
West Nile Virus ◽  
West Nile ◽  
Virus Model

Traveling Waves and Spread Rates for a West Nile Virus Model

2006 ◽  
Vol 68 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Mark Lewis ◽  
Joanna Rencławowicz ◽  
P. van den Driessche
Keyword(s):  
West Nile Virus ◽  
Traveling Waves ◽  
West Nile ◽  
Virus Model

Asymptotic periodicity in a diffusive West Nile virus model in a heterogeneous environment

2017 ◽  
Vol 10 (08) ◽  
pp. 1750110 ◽  
Author(s):  
Abdelrazig K. Tarboush ◽  
Jing Ge ◽  
Zhigui Lin
Keyword(s):  
Periodic Solution ◽  
West Nile Virus ◽  
Homogeneous Model ◽  
Heterogeneous Environment ◽  
West Nile ◽  
True Solution ◽  
Monotone Iterative ◽  
Number Formula ◽  
Virus Model ◽  
Asymptotic Periodicity

This paper is concerned with a diffusive West Nile virus model (WNv) in a heterogeneous environment. The basic reproduction number [Formula: see text] for spatially homogeneous model is first introduced. We then define a threshold parameter [Formula: see text] for the corresponding diffusive WNv model in a heterogeneous environment. It is shown that if [Formula: see text], the model admits at least one nontrivial T-periodic solution, whereas if [Formula: see text], the model has no nontrivial T-periodic solution. By means of monotone iterative schemes, the true solution can be obtained and the asymptotic behavior of periodic solutions is presented. The paper is closed with some numerical simulations to illustrate our theoretical results.

Global dynamics of a West Nile virus model in a spatially variable habitat

2018 ◽  
Vol 41 ◽  
pp. 313-333 ◽  
Author(s):  
Yu-Chiau Shyu ◽  
Rong-Nan Chien ◽  
Feng-Bin Wang
Keyword(s):  
West Nile Virus ◽  
Global Dynamics ◽  
West Nile ◽  
Virus Model

A West Nile Virus Model with Vertical Transmission and Periodic Time Delays

2019 ◽  
Vol 30 (1) ◽  
pp. 449-486 ◽  
Author(s):  
Fuxiang Li ◽  
Junli Liu ◽  
Xiao-Qiang Zhao
Keyword(s):  
West Nile Virus ◽  
Vertical Transmission ◽  
Time Delays ◽  
West Nile ◽  
Virus Model

scholarly journals Threshold dynamics of a West Nile virus model with impulsive culling and incubation period

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yaxin Han ◽  
Zhenguo Bai
Keyword(s):  
West Nile Virus ◽  
Incubation Period ◽  
Threshold Dynamics ◽  
Recent Theory ◽  
West Nile ◽  
Biting Rate ◽  
Virus Model ◽  
Risk Of Disease ◽  
Globally Attractive ◽  
Impulsive Culling

<p style='text-indent:20px;'>In this paper, we propose a time-delayed West Nile virus (WNv) model with impulsive culling of mosquitoes. The mathematical difficulty lies in how to choose a suitable phase space and deal with the interaction of delay and impulse. By the recent theory developed in [<xref ref-type="bibr" rid="b3">3</xref>], we define the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal {R}_0 $\end{document}</tex-math></inline-formula> as the spectral radius of a linear integraloperator and show that <inline-formula><tex-math id="M2">\begin{document}$ \mathcal {R}_0 $\end{document}</tex-math></inline-formula> acts as a threshold parameter determining the persistence of the model. More precisely, it is proved that if <inline-formula><tex-math id="M3">\begin{document}$ \mathcal {R}_0&lt;1 $\end{document}</tex-math></inline-formula>, then the disease-free periodic solution is globally attractive, while if <inline-formula><tex-math id="M4">\begin{document}$ \mathcal {R}_0&gt;1 $\end{document}</tex-math></inline-formula>, then the disease is uniformly persistent.Numerical simulations suggest that culling frequency and culling rate are strongly influenced by the biting rate. We also find that prolonging the length of the incubation period in mosquitoes can reduce the risk of disease spreading.</p>

Monotone dynamics and global behaviors of a West Nile virus model with mosquito demographics

2019 ◽  
Vol 80 (3) ◽  
pp. 809-834
Author(s):  
Zhipeng Qiu ◽  
Xuerui Wei ◽  
Chunhua Shan ◽  
Huaiping Zhu
Keyword(s):  
West Nile Virus ◽  
West Nile ◽  
Virus Model

scholarly journals Spreading and vanishing in a West Nile virus model with expanding fronts

2017 ◽  
Vol 60 (5) ◽  
pp. 841-860 ◽  
Author(s):  
Abdelrazig K. Tarboush ◽  
ZhiGui Lin ◽  
MengYun Zhang
Keyword(s):  
West Nile Virus ◽  
West Nile ◽  
Spreading And Vanishing ◽  
Virus Model
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