Song Pengfei, Xiao Yanni
Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China.
J Math Biol. 2018 Apr;76(5):1249-1267. doi: 10.1007/s00285-017-1173-y. Epub 2017 Aug 29.
We proposed a delay differential model, associated with the response time for individuals to the current infection, to examine the media impact on the transmission dynamics of infectious diseases. We investigated the global bifurcation by considering the delay as a bifurcation parameter and examined the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical studies to identify ranges of parameters for coexisting multiple periodic solutions are guided by the bifurcation analysis and the Matlab package DDE-BIFTOOL developed by Engelborghs et al. Further, we parameterized the proposed model on the basis of the 2009 A/H1N1 pandemic influenza data in Shaanxi province, China, and estimated the basic reproduction number to be 1.79 [95% CI (1.77-1.80)] and the time delay to be 2.94 days [95% CI (2.56-3.24)]. Our main results indicated that media impact with time delay significantly influenced the transmission dynamics of infectious diseases.
我们提出了一个与个体对当前感染的反应时间相关的延迟微分模型，以研究媒体对传染病传播动力学的影响。我们将延迟视为分岔参数来研究全局分岔，并研究了从一个正平衡点出发的霍普夫分岔的起始和终止。通过分岔分析以及由恩格尔博格斯等人开发的Matlab软件包DDE-BIFTOOL来指导确定共存多个周期解的参数范围的数值研究。此外，我们根据中国陕西省2009年甲型H1N1大流行性流感数据对所提出的模型进行参数化，并估计基本再生数为1.79 [95%置信区间(1.77 - 1.80)]，时间延迟为2.94天 [95%置信区间(2.56 - 3.24)]。我们的主要结果表明，具有时间延迟的媒体影响显著影响了传染病的传播动力学。
