具有隔离仓室流行病传播数学模型的全局稳定性

Global Stability for the Model with Quarantine in Epidemiology

研究了一类具有隔离仓室的非线性高维自治微分系统SEIQR流行病传播数学模型,得到疾病绝灭与否的阈值———基本再生数R0,证明了无病平衡点和地方病平衡点的存在性及全局渐近稳定性,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.

A kind of non-linear high dimensional autonomous system, SEIQR 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.