Zhao Hongyong, Wang Liping, Oliva Sergio Muniz, Zhu Huaiping
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People's Republic of China.
Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP, CEP 05508-090, Brazil.
Bull Math Biol. 2020 Jul 23;82(8):99. doi: 10.1007/s11538-020-00776-1.
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.
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，例如喷洒杀虫剂、研发疫苗和药物。然而，由于该国医疗资源有限，并非每个感染寨卡病毒的患者都能及时得到治疗。我们旨在通过引入分段光滑的治疗恢复率来建立一个确定性的寨卡模型，以研究医疗资源有限对寨卡病毒传播和控制的影响。对于未进行治疗的模型，我们分析了平衡点的全局稳定性。对于进行治疗的模型，该模型表现出复杂的动力学特性。我们证明进行治疗的模型会经历反向分岔、霍普夫分岔和余维2的博格达诺夫 - 塔克恩斯分岔。这意味着存在医疗资源有限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。我们还应用该模型，利用2016年3月25日至2018年4月14日巴西每周报告的累计寨卡病例数据，估计寨卡病毒传播的基本繁殖数和控制繁殖数。
