摘要
为分析传染病的传播与控制,研究了一类疾病发生率与潜伏期人群移出率受信息因素影响的SEIR传染病模型,利用下一代矩阵法得到了模型的基本再生数通过数学分析得到了模型平衡点的存在性.应用Lyapunov函数与Hurwitz判据证明了当基本再生数小于1时,无病平衡点是全局稳定的;当基本再生数大于1时,地方病平衡点是局部渐进稳定的.最后用计算机模拟进一步验证了理论分析的结果,并发现加强对传染病信息的实时共享、对染病者的及时隔离及严格的出行管控都有助于疫情防控.
In order to analyze the spread and control of the epidemic,an SEIR epidemic model was established in which the disease incidence rate and the removal rate of the latency were affected by information factors.The basic reproduction number is obtained by the method of the next-generation matrix.Analyzing mathematically,the existence of equilibria is obtained.Conclusions are deduced by applying the Lyapunov function and Hurwitz criterion that the disease-free equilibrium point is globally stable if the basic reproduction number is less than 1 and the endemic disease equilibrium point is locally progressively stable if the basic reproduction number is greater than 1.Finally,theoretical results were further verified by computer simulations.It was also found that strengthening the timely sharing of disease information,the timely isolation of infected persons and the strict travel management all can contribute to the prevention and control of an epidemic.
作者
张杰豪
陈永雪
申佳瑜
张慧
温永仙
ZHANG Jie-hao;CHEN Yong-xue;SHEN Jia-yu;ZHANG Hui;WEN Yong-xian(College of Computer and Information,Fujian Agriculture and Forestry University,Fuzhou 350002,China;Institute of Applied Statistics,Fujian Agriculture and Forestry University,Fuzhou 350002,China)
出处
《数学的实践与认识》
2021年第11期316-323,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(32071892)。
关键词
信息因素
SEIR模型
基本再生数
计算机模拟
information factor
SEIR model
basic reproduction number
computer simulation
