摘要
本文建立了一个具有时滞的SI S模型,研究了旅途过程中疾病的传染.得到了基本再生数.通过线性化方法和比较原理,证明了当基本再生数小于1时无病平衡点是全局渐近稳定的,疾病绝灭.当基本再生数大于1时,系统存在唯一的全局吸引的地方病平衡点,且疾病持续生存.数值模拟验证了扩散率对疾病传播的影响.分析了基本再生数对扩散率的依赖性.
We formulate a delayed SIS model to describe the effect of transport-related infection.The basic reproduction number is obtained.By the linearization methodand comparison principle,it is proved that the disease-free equilibrium is globallyasymptotically stable and the disease always dies out if the basic reproductionnumber is less than unity.While there exists a unique endemic equilibrium whichis globally attractive and the disease persists if the basic reproduction number isgreater than unity.The simulation results show the influence of travel rates on thedisease spread.The dependence of the basic reproduction number on the travelrates during travel is also analyzed.
作者
刘俊利
贾滢
张太雷
LIU Jun-li;JIA Ying;ZHANG Tai-lei(School of Science, Xi'an Polytechnic University, Xi'an 710048;School of Science, Chang'an University, Xi'an 710064)
出处
《工程数学学报》
CSCD
北大核心
2017年第4期409-423,共15页
Chinese Journal of Engineering Mathematics
基金
The National Natural Science Foundation of China(11101323)
the Fundamental Research Funds for the Central Universities(310812152002)
the Natural Science Foundation of Shaanxi Province(11101323)
the Natural Science Basic Research Plan in Shaanxi Province(2014JQ1038
2014JQ1018)
the Scientific Research Program Funded by Shaanxi Provincial Education Department(16JK1331)
关键词
旅途过程中的传染
基本再生数
一直持续
全局动力学
时滞
transport-related infection
basic reproduction number
uniform persistence
global dynamics
time delay
