In this paper, we study a nonlocal periodic reaction–diffusion system modeling the West Nile virus transmission between mosquitoes and birds. For the subsystem of mosquito growth, we establish a global stability result on the extinction and persistence in terms of mosquito reproduction number ${\mathcal{R}}_M$, which is defined as the cone spectral radius of a monotone homogeneous map. For the full model, we introduce the basic reproduction number ${\mathcal{R}}_0$ and show that the disease transmission dynamics is determined by the sign of ${\mathcal{R}}_0-1$ under the assumption that ${\mathcal{R}}_M>1$. Moreover, we obtain the global attractivity of the positive constant steady state in the case where all the coefficients are constants. We also conduct numerical simulations to reveal the effects of diffusion, heterogeneity and periodic delay on ${\mathcal{R}}_0$.

在本文中，我们研究了一个模拟西尼罗河病毒在蚊子和鸟类之间传播的非局部周期性反应-扩散系统。对于蚊子生长子系统，我们根据蚊子繁殖数建立了灭绝和持久性的全局稳定性结果${\mathcal{R}}_{米}$, 定义为单调齐次图的锥光谱半径。对于完整型号，我们介绍了基本复制编号${\mathcal{R}}_0$并表明疾病传播动态由${\mathcal{R}}_0-1$在假设${\mathcal{R}}_{米}>1$. 此外，我们在所有系数都是常数的情况下获得了正常数稳态的全局吸引力。我们还进行了数值模拟，以揭示扩散、异质性和周期性延迟对${\mathcal{R}}_0$.