一类患病阶段服从非指数分布的SEITR传染病模型的潜在假设和稳定性分析  

Underlying Assumptions and Stability Analysis of an SEITR Epidemic Model with Non-exponential Distributed Diseased Stages

作　　者：王晓静[1] 史洋洋[1] 张蒙[1] 王丹[1] 

机构地区：[1]北京建筑大学理学院,北京100044

出　　处：《数学的实践与认识》2017年第16期257-266,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11371048);北京建筑大学研究生创新项目:北京建筑大学2017年研究生教学质量提升项目(常微分方程定性理论优质课程建设)

摘　　要：建立了一类SEITR传染病模型,推导出模型潜在的假设条件,并得到了一般分布下相应的积分微分方程.进而,通过在疾病传播的特定阶段引入Gamma分布和指数分布将积分微分方程化简成了ODE方程,证明了服从指数分布的ODE方程的无病平衡点的局部和全局稳定性.对两类模型的控制再生数进行敏感度分析的结果表明传染率β是影响疾病传播的最重要因素.In this paper, we develop an SEITR epidemic model and derive its underlying assumptions, and then we obtain the corresponding integ0-differential equation with general distribution assumption. Furthermore, we reduce the intego-differential equation to ODE models by introducing Gamma distribution and exponential distribution during the duration of disease stages. On the other hand, both the local and global stability of the disease-free equilibrium of the ODE model with exponential distribution have been proved. The control reproduction numbers for two models are presented, and the examined results for their sensitives show that the infection rate/3 is the most sensitive.

关 键 词：GAMMA分布 指数分布 平衡点 稳定性 灵敏度分析 

分 类 号：O175[理学—数学]