Department of Mathematical Sciences, Florida Atlantic University, Science Building, Room 234 777 Glades Road, Boca Raton, FL, 33431, USA.
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL, 32611, USA.
Bull Math Biol. 2018 Aug;80(8):2209-2241. doi: 10.1007/s11538-018-0453-z. Epub 2018 Jun 13.
The Zika virus (ZIKV) epidemic has caused an ongoing threat to global health security and spurred new investigations of the virus. Use of epidemiological models for arbovirus diseases can be a powerful tool to assist in prevention and control of the emerging disease. In this article, we introduce six models of ZIKV, beginning with a general vector-borne model and gradually including different transmission routes of ZIKV. These epidemiological models use various combinations of disease transmission (vector and direct) and infectious classes (asymptomatic and pregnant), with addition to loss of immunity being included. The disease-induced death rate is omitted from the models. We test the structural and practical identifiability of the models to find whether unknown model parameters can uniquely be determined. The models were fit to obtain time-series data of cumulative incidences and pregnant infections from the Florida Department of Health Daily Zika Update Reports. The average relative estimation errors (AREs) were computed from the Monte Carlo simulations to further analyze the identifiability of the models. We show that direct transmission rates are not practically identifiable; however, fixed recovery rates improve identifiability overall. We found ARE is low for each model (only slightly higher for those that account for a pregnant class) and help to confirm a reproduction number greater than one at the start of the Florida epidemic. Basic reproduction number, [Formula: see text], is an epidemiologically important threshold value which gives the number of secondary cases generated by one infected individual in a totally susceptible population in duration of infectiousness. Elasticity of the reproduction numbers suggests that the mosquito-to-human ratio, mosquito life span and biting rate have the greatest potential for reducing the reproduction number of Zika, and therefore, corresponding control measures need to be focused on.
寨卡病毒（ZIKV）疫情持续对全球卫生安全构成威胁，促使人们对该病毒展开新的研究。利用虫媒病毒病的流行病学模型可以成为协助防控新发疾病的有力工具。在本文中，我们介绍了六种 ZIKV 模型，从一般的虫媒传播模型开始，逐渐涵盖 ZIKV 的不同传播途径。这些流行病学模型使用疾病传播（媒介和直接）和感染类别（无症状和孕妇）的各种组合，此外还包括免疫丧失。模型中忽略了疾病引起的死亡率。我们测试了模型的结构和实际可识别性，以确定未知模型参数是否可以唯一确定。我们使用时间序列数据对模型进行拟合，该数据来自佛罗里达州卫生部门每日寨卡病毒更新报告中的累积发病率和孕妇感染情况。我们从蒙特卡罗模拟中计算平均相对估计误差（ARE），以进一步分析模型的可识别性。我们表明，直接传播率实际上是不可识别的；然而，固定的恢复率总体上提高了可识别性。我们发现，每个模型的平均相对估计误差（ARE）都较低（仅那些考虑孕妇类别的模型略高），有助于确认佛罗里达州疫情开始时的繁殖数大于 1。基本繁殖数，[Formula: see text]，是一个流行病学上重要的阈值，它表示在具有传染性的时间内，一个受感染者在完全易感人群中产生的次生病例数。繁殖数的弹性表明，蚊子与人的比例、蚊子寿命和叮咬率对降低寨卡病毒的繁殖数潜力最大，因此，相应的控制措施需要集中在这些方面。
