摘要
研究了一类具有隔离仓室和潜伏仓室的非线性高维自治微分系统SEQIJR传染病模型,得到疾病绝灭与否的阈值——基本再生数R_0。证明了当R_0≤1时,模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的,疾病最终绝灭;当R_0>1时,模型存在两个平衡点,无病平衡点不稳定,地方病平衡点全局渐近稳定,疾病将持续。隔离措施影响着基本再生数,进而推得结论:适当地增大隔离强度,将有益于有效地控制疾病的蔓延。这就从理论上揭示了隔离对疾病控制的积极作用。
In this paper, a class of non-linear high dimensional autonomous SEQIJR epidemiology model containing quarantine is studied. The threshold, basic reproductive number, which determines whether a disease is extinct or not is obtained. The existence and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved. The conclusions indicate that a proper increasing of segregation intension benefits the efficient restraining disease spread. It is theoretically showed that the segregation has an active effect on disease controlling.
出处
《生物数学学报》
CSCD
北大核心
2009年第3期461-469,共9页
Journal of Biomathematics
关键词
传染病模型
基本再生数
全局稳定性
轨道渐近稳定
Epidemic model
Basic reproductive number
Global stability
Orbital asymptotical stability
