一类SIS流行病传播数学模型全局渐近稳定性

Globally Asymptotic Stability of a Kind of SIS Mathematical Model for the Spread of Epidemic

研究一类SIS流行病传播数学模型,得到决定疾病灭绝和持续生存的阈值———基本再生数.当基本再生数小于等于1时,仅存在无病平衡点;当基本再生数大于1时,除存在无病平衡点外,还存在惟一的地方病平衡点.证明了各个平衡点的全局渐近稳定性,减弱了文献(一类具有非线性接触率的种群力学流行病模型分析[J].四川师范大学学报(自然科学版),2002,25(3):261～263.)平衡点全局渐近稳定的条件,该文献的结论可作为本文的推论;计算机数值模拟了临界情形无病平衡点可能的稳定性.

A kind of SIS mathematical model for the spread of epidemic is considered. We find the basic reproductive number, determining the persistence of the infective disease. When the basic reproductive number is not larger than 1, there only exists disease free equilibrium, otherwise, two equilibria, the endemic equilibrium and the disease free equilibrium exist. The globally asymptotic stabilities of the endemic equilibrium and the disease free equilibrium are proved, and the conditions in the paper (Analysis on a species mechanics epidemical model with nonlinear in cidence rate[J]. J Sichuan Normal University (Natural Science),2002,25(3):261～263.) are reduced. The conclusion of the paper can be considered as a corollary of this paper. When the basic reproductive number equals 1, the computer numerical value simulation implies the disease free equilibrium is possibly stable.