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A West Nile Virus Model with Vertical Transmission and Periodic Time Delays
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A West Nile Virus Model with Vertical Transmission and Periodic Time Delays
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Journal Article
A West Nile Virus Model with Vertical Transmission and Periodic Time Delays
2020
Overview
Seasonal change has played a critical role in the evolution dynamics of West Nile virus transmission. In this paper, we formulate and analyze a novel delay differential equation model, which incorporates seasonality, the vertical transmission of the virus, the temperature-dependent maturation delay and the temperature-dependent extrinsic incubation period in mosquitoes. We first introduce the basic reproduction ratio
R
0
for this model and then show that the disease is uniformly persistent if
R
0
>
1
. It is also shown that the disease-free periodic solution is attractive if
R
0
<
1
, provided that there is only a small invasion. In the case where all coefficients are constants and the disease-induced death rate of birds is zero, we establish a threshold result on the global attractivity in terms of
R
0
. Numerically, we study the West Nile virus transmission in Orange County, California, USA.
Publisher
Springer US,Springer Nature B.V
