Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model
Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model
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DOI：
10.3934/dcdsb.2016.21.1297
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发表时间：
2016-03
影响因子：
1.2
通讯作者：
K. Yamazaki;Xueying Wang
中科院分区：
文献类型：
--
作者：
K. Yamazaki;Xueying Wang
本文研究了文献[38]中发展的一类霍乱动力学的反应-对流-扩散传染病模型--易感-感染-恢复-易感-细菌（SIRS-B）传染病PDE模型的初边值问题.首先，依赖于合作动力学系统的理论，得到了一个局部适定性结果。通过利用系统的特殊结构和局部理论论证的继续，我们证明了该问题实际上是全局适定的。其次，我们基于与该模型相关的基本再生数分析了解的局部渐近稳定性。
In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the special structure of the system and continuation of local theory argument, we show that in fact this problem is globally well-posed. Secondly, we analyze the local asymptotic stability of the solutions based on the basic reproduction number associated with this model.