Wang Aili, Xiao Yanni, Smith Robert
School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, People's Republic of China.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China.
Theory Biosci. 2020 Feb;139(1):47-65. doi: 10.1007/s12064-019-00297-z. Epub 2019 Aug 7.
A non-smooth epidemic model with piecewise incidence rate dependent on the derivative of the case number is proposed for the transmission dynamics of an infectious disease with media coverage, enhanced vaccination and treatment policy. This is an implicitly defined system, which is converted into an explicit system with three thresholds by employing the properties of the Lambert W function. We first analyze the dynamics of the proposed model for the limiting case, which induces two non-smooth but continuous models. The dynamic analysis of the model demonstrates that either one of the two generalized equilibria or the pseudo-equilibrium is globally asymptotically stable if the disease does not die out. This suggests that the case number can be contained either at an a priori level or at a high/low level, depending on the threshold, which governs whether the enhanced vaccination and treatment policies are implemented. Media coverage cannot help eradicate the disease, but it significantly delays the epidemic peak and lowers the peak case number. Hence, a good threshold policy and continuously updating the awareness of case numbers are required to combat the disease successfully.
针对具有媒体报道、强化疫苗接种和治疗策略的传染病传播动力学，提出了一种具有依赖病例数导数的分段发病率的非光滑流行病模型。这是一个隐式定义的系统，通过利用兰伯特W函数的性质将其转化为具有三个阈值的显式系统。我们首先分析所提出模型在极限情况下的动力学，这产生了两个非光滑但连续的模型。模型的动力学分析表明，如果疾病不灭绝，两个广义平衡点之一或伪平衡点是全局渐近稳定的。这表明病例数可以在先验水平或高/低水平得到控制，这取决于阈值，该阈值决定是否实施强化疫苗接种和治疗策略。媒体报道无助于根除疾病，但它会显著延迟疫情高峰并降低峰值病例数。因此，需要一个良好的阈值策略并持续更新病例数意识，以成功抗击该疾病。
