Zika virus, a reemerging mosquito-borne flavivirus, posed a global public health emergency in 2016. Brazil is the most seriously affected country. Some measures have been implemented to control the Zika transmission, such as spraying mosquitoes, developing vaccines and drugs. However, because of the limited medical resources (LMRs) in the country, not every infected patient can be treated in time when infected with Zika virus. We aim to build a deterministic Zika model by introducing a piecewise smooth treatment recovery rate to research the effect of LMRs on the transmission and control of Zika. For the model without treatment, we analyze the global stability of equilibria. For the model with treatment, the model exhibits complex dynamics. We prove that the model with treatment undergoes backward bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation of codimension 2. It means that the model with LMRs is sensitive to parameters and initial conditions, which has important significance for control of Zika. We also apply the model to estimate the basic and control reproduction numbers for the Zika transmission by using the data on weekly reported accumulated Zika cases from March 25, 2016, to April 14, 2018, in Brazil.

中文翻译：

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医疗资源有限的寨卡病毒传播建模与动力学分析

寨卡病毒是一种重新出现的蚊媒黄病毒，在 2016 年引发了全球公共卫生紧急事件。巴西是受影响最严重的国家。已经采取了一些措施来控制寨卡病毒的传播，例如喷洒蚊子、开发疫苗和药物。但是，由于该国的医疗资源（LMR）有限，并非每个感染者在感染寨卡病毒时都能得到及时治疗。我们旨在通过引入分段平滑治疗恢复率来构建确定性寨卡病毒模型，以研究 LMR 对寨卡病毒传播和控制的影响。对于未经处理的模型，我们分析了均衡的全局稳定性。对于有治疗的模型，模型表现出复杂的动态。我们证明了经过处理的模型经历了向后分叉，Hopf 分岔和 Codimension 2 的 Bogdanov-Takens 分岔。这意味着具有 LMR 的模型对参数和初始条件敏感，这对寨卡病毒的控制具有重要意义。我们还利用巴西 2016 年 3 月 25 日至 2018 年 4 月 14 日每周报告的累积寨卡病例数据，应用该模型来估计寨卡病毒传播的基本和控制传播数量。