Padmanabhan P, Seshaiyer P
Foxcroft School, Middleburg, VA, USA.
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA.
Comput Math Methods Med. 2017;2017:4290825. doi: 10.1155/2017/4290825. Epub 2017 Aug 15.
We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.
我们提出了新的数学模型，这些模型包含了使用选定的预防措施（如经杀虫剂处理的蚊帐）对控制或缓解寨卡病毒传播的影响。对于这些模型，我们推导出了基本再生数以及关于最终规模关系的精确估计。我们首先提出一个单阶段模型，该模型随后被扩展为一个新的寨卡多阶段模型，该模型纳入了人类和病媒更现实的潜伏期。对于这些模型中的每一个，我们都推导出一个基本再生数和一个最终规模关系估计。我们观察到，多阶段模型的基本再生数收敛到宿主和病媒潜伏期固定的标准寨卡流行模型的预期值。最后，我们还进行了几个计算实验，以验证这项工作中获得的理论结果，并研究各种参数对模型的影响。
