DYNAMICS OF AN INFECTIOUS DISEASES WITH MEDIA/PSYCHOLOGY INDUCED NON-SMOOTH INCIDENCE
DYNAMICS OF AN INFECTIOUS DISEASES WITH MEDIA/PSYCHOLOGY INDUCED NON-SMOOTH INCIDENCE
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媒体/心理导致的传染病的非平稳发病动态
DOI：
10.3934/mbe.2013.10.445
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发表时间：
2013-04-01
影响因子：
2.6
通讯作者：
Tang, Sanyi
中科院分区：
文献类型：
--
作者：
Xiao, Yanni;Zhao, Tingting;Tang, Sanyi
本文建立并分析了具有分段光滑传染率的、考虑媒介/心理效应的传染病系统的数学模型。所提出的模型扩展了经典模型与媒体报道，包括一个分段光滑的发病率表示，减少因子，因为媒体报道取决于案件的数量和案件数量的变化率。根据LambertW函数的性质，将隐式定义的模型转化为显式定义的分段光滑系统，并从理论上分析了系统的全局动力学行为。当某个阈值小于1时，无病平衡点是全局渐近稳定的;当阈值小于1时，地方病平衡点是全局渐近稳定的。媒体/心理影响虽然不影响流行阈值，但延迟了流行高峰，并导致爆发规模较小（或受感染个体的平衡水平）。
This paper proposes and analyzes a mathematical model on an infectious disease system with a piecewise smooth incidence rate concerning media/psychological effect. The proposed models extend the classic models with media coverage by including a piecewise smooth incidence rate to represent that the reduction factor because of media coverage depends on both the number of cases and the rate of changes in case number. On the basis of properties of Lambert W function the implicitly defined model has been converted into a piecewise smooth system with explicit definition, and the global dynamic behavior is theoretically examined. The disease-free is globally asymptotically stable when a certain threshold is less than unity, while the endemic equilibrium is globally asymptotically stable for otherwise. The media/psychological impact although does not affect the epidemic threshold, delays the epidemic peak and results in a lower size of outbreak (or equilibrium level of infected individuals).