一个带有隔离和扰动的SIQ模型的动力学分析  

Analysis of a SIQ epidemic model with isolation and perturbation

作　　者：丁金梅 

机构地区：[1]宁夏大学人事处,宁夏银川750021

出　　处：《宁夏工程技术》2017年第4期327-330,共4页Ningxia Engineering Technology

基　　金：宁夏重点研发计划(软科学)项目(NZY201604);宁夏教育厅优秀青年基金项目(NGY2016073);宁夏留学回国人员创新团队建设项目(20150102)

摘　　要：对包含隔离策略的传染病模型,通过修改传染率形式、加入随机扰动项等方面的改进建立了更加合理、更广泛适用的随机传染病模型。首先,利用It?公式、大数定律等结论证明了该随机模型正解的几乎必然全局存在性;其次利用It?公式、局部鞅不等式、Hasminskii定理等通过构造二阶连续可微函数得到了疾病指数灭绝的充分条件;最后利用Matlab软件给出仿真结果验证了所得结论。A more reasonable and widely applicable model is obtained by introducing the stochastic perturbations and general nonlinear incidence rate into a epidemic model containing vaccination. Firstly,we show that the solution with initial positive value exists globally almost surely. Secondly, the conditions of extinction are obtained by applying the Ito ＇s formula,local martingale inequality and Hasminskii theory respectively. At last, the simulation using Matlab verifies the analytic results in the paper.

关 键 词：传染病模型 隔离 随机扰动 灭绝性 

分 类 号：O175.13[理学—数学]