Asymptotic Behavior of the Basic Reproduction Ratio for Periodic Reaction-Diffusion Systems
Asymptotic Behavior of the Basic Reproduction Ratio for Periodic Reaction-Diffusion Systems
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DOI：
10.1137/20m1366344
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Lei Zhang;Xiao-Qiang Zhao
中科院分区：
文献类型：
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作者：
Lei Zhang;Xiao-Qiang Zhao
研究了周期反应扩散系统在小扩散系数和大扩散系数情况下基本再生比的渐近性态。我们首先建立了基本再生比关于参数的连续性，通过发展预解式正算子的理论。然后，我们研究了大扩散系数的相关周期特征值问题的主特征值的极限轮廓。然后，我们得到的基本再生比的渐近行为的扩散系数分别为零和无穷大。当扩散系数足够大时，我们还研究了具有Neumann边界条件的周期反应扩散系统和合作反应扩散系统的正周期解的极限行为.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.