论文标题
定期反应扩散系统基本繁殖比的渐近行为
Asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems
论文作者
论文摘要
本文致力于在大小扩散系数的情况下研究周期性反应扩散系统基本繁殖比的渐近行为。我们首先通过发展分解阳性运算符理论来建立基本繁殖比率相对于参数的连续性。然后，我们研究了针对大扩散系数的相关周期特征值问题的主要特征值的限制曲线。然后，随着扩散系数分别为零和无穷大，我们获得了基本繁殖比的渐近行为。当扩散系数足够大时，我们还研究了带有Neumann边界条件的周期性和合作反应扩散系统的阳性周期性解决方案的限制行为。最后，我们将这些结果应用于寨卡病毒传播的反应扩散模型。
This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic reproduction ratio with respect to parameters by developing the theory of resolvent positive operators. Then we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem for large diffusion coefficients. We then obtain the asymptotic behavior of the basic reproduction ratio as the diffusion coefficients go to zero and infinity, respectively. We also investigate the limiting behavior of positive periodic solution for periodic and cooperative reaction-diffusion systems with the Neumann boundary condition when the diffusion coefficients are large enough. Finally, we apply these results to a reaction-diffusion model of Zika virus transmission.
