论文标题
西尼罗河病毒的几乎周期性反应扩散系统的空间和时间动力学
Spatial and temporal dynamics of an almost periodic reaction-diffusion system for West Nile virus
论文作者
论文摘要
在目前的论文中，我们在空间异质和几乎是周期性的环境中提出了一个针对西尼罗河病毒的反应扩散系统，并具有自由界限，以研究栖息地差异的影响和季节性变化对西尼罗河病毒传播的影响。给出了该疾病模型的全球解决方案的存在，独特性和规律性估计。专注于空间异质性和时间几乎是周期性的效果，我们将主要的Lyapunov指数$λ（t）$与时间$ t $一起应用于使最初的感染域阈值$ l^*$来分析该解决方案的长期动力学行为，以使这种几乎是周期性的西尼罗河病毒模型和散布散布的dichotismismemime dichotime dichotime dichotime dichotime dichotime dichotime dichotime dichotime dichotime dicemimes fige dichotime dicemimessime。尤其是，我们证明，这种西尼罗河病毒模型的解决方案在$ \ \ m rathbb r $中的$ x $中几乎是周期性的功能，当时传播发生时，这是由空间差异和季节性复发驱动的。此外，最初的疾病感染域和前扩展率对流行病的永久性和灭绝有重大影响。最终，数值模拟确定了我们的理论结果。
In current paper, we put forward a reaction-diffusion system for West Nile virus in spatial heterogeneous and time almost periodic environment with free boundaries to investigate the influences of the habitat differences and seasonal variations on the propagation of West Nile virus. The existence, uniqueness and regularity estimates of the global solution for this disease model are given. Focused on the effects of spatial heterogeneity and time almost periodicity, we apply the principal Lyapunov exponent $λ(t)$ with time $t$ to get the initial infected domain threshold $L^*$ to analyze the long-time dynamical behaviors of the solution for this almost periodic West Nile virus model and give the spreading-vanishing dichotomy regimes of the disease. Especially, we prove that the solution for this West Nile virus model converges to a time almost periodic function locally uniformly for $x$ in $\mathbb R$ when the spreading occurs, which is driven by spatial differences and seasonal recurrence. Moreover, the initial disease infected domain and the front expanding rate have momentous impacts on the permanence and extinction of the epidemic disease. Eventually, numerical simulations identify our theoretical results.
