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.

中文翻译：

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具有垂直传播和周期性时滞的西尼罗河病毒模型

季节变化在西尼罗河病毒传播的演变动力学中起着关键作用。在本文中，我们建立并分析了一种新型的时滞微分方程模型，该模型包括季节性，病毒的垂直传播，与温度有关的成熟延迟和与温度有关的外在蚊子的潜伏期。我们首先介绍该模型的基本繁殖率\（R_0 \），然后证明如果\（R_0> 1 \）该病是一致持续的。还表明如果\（R_0 <1 \）无病周期解是有吸引力的，前提是只有很小的入侵。在所有系数均为常数且疾病引起的禽类死亡率为零的情况下，我们以\（R_0 \）表示全局吸引力的阈值结果。在数值上，我们研究了美国加利福尼亚州奥兰治县的西尼罗河病毒传播。