论文标题
通过对流建模西尼罗河病毒的反应扩散系统的动力和扩散速度
Dynamics and Spreading Speed of a Reaction-Diffusion System with Advection Modeling West Nile Virus
论文作者
论文摘要
本文旨在通过具有自由界限的反应 - 侵蚀 - 扩散系统探索西尼罗河病毒的时间空间扩散和渐近行为，尤其是考虑到对流术语对西尼罗河病毒的灭绝和持久性的影响。我们以对流率和一般的基本疾病复制数字$ r^d_0 $来定义空间 - 周期性风险指数$ r^{f} _ {0}（t）$，以获得西尼罗尔病毒的消失二分法。我们表明，存在阈值的阈值$μ^{*} $，并获得其阈值结果。从长远来看，当扩散发生时，我们研究了溶液的渐近动力学行为，并首先给出一个更尖锐的估计，即左前方的渐近扩散速度小于右前方的渐进速度，价格为$ 0 <μ<μ^*$。最后，我们给出了一些数值模拟，以确定对流的显着影响。
This paper aims to explore the temporal-spatial spreading and asymptotic behaviors of West Nile virus by a reaction-advection-diffusion system with free boundaries, especially considering the impact of advection term on the extinction and persistence of West Nile virus. We define the spatial-temporal risk index $R^{F}_{0}(t)$ with the advection rate and the general basic disease reproduction number $R^D_0$ to get the vanishing-spreading dichotomy regimes of West Nile virus. We show that there exists a threshold value $μ^{*}$ of the advection rate, and obtain the threshold results of it. When the spreading occurs, we investigate the asymptotic dynamical behaviors of the solution in the long run and first give a sharper estimate that the asymptotic spreading speed of the leftward front is less than the rightward front for $0<μ<μ^*$. At last, we give some numerical simulations to identify the significant effects of the advection.
