新疆大学数学与系统科学学院
纸质出版:2024
移动端阅览
[1]罗颜涛,陆腾腾,杨谨鸿.一类具有媒体报道和环境传播的SEVIQBR传染病模型的动力学分析[J].新疆大学学报(自然科学版)(中英文),2024,41(02):188-195.
[1]罗颜涛,陆腾腾,杨谨鸿.一类具有媒体报道和环境传播的SEVIQBR传染病模型的动力学分析[J].新疆大学学报(自然科学版)(中英文),2024,41(02):188-195. DOI: 10.13568/j.cnki.651094.651316.2023.05.31.0003.
DOI:10.13568/j.cnki.651094.651316.2023.05.31.0003.
考虑媒体报道以及环境传播对疾病传播的影响
建立了一类受媒体报道和环境传播影响的SEVIQBR传染病模型.首先
通过下一代矩阵的方法得到了模型的基本再生数R0
基于基本再生数讨论模型无病平衡点以及地方病平衡点的存在性.接着
借助Hurwitz判据研究了无病平衡点的局部稳定性
并构造适当的Lyapunov函数证明无病平衡点的全局渐近稳定性.结果表明:当基本再生数R0<1时
模型的无病平衡点是全局渐近稳定的
当R0满足一定条件时
模型的地方病平衡点是存在的.最后
通过数值模拟验证了理论结果.
Considering the influence of media reports and environmental transmission on disease transmission
a SEVIQBR infectious disease model is established. Firstly
the basic reproduction number R0of the model is obtained by the next generation matrix method. Based on the basic reproduction number
the existence of disease-free equilibrium and endemic equilibrium of the model is discussed. Then
the local stability of disease-free equilibrium is studied by means of Hurwitz criterion
and the global asymptotic stability of disease-free equilibrium is studied by constructing an appropriate Lyapunov function. The results show that when the basic reproduction number R0< 1
the disease-free equilibrium of the model is globally asymptotically stable. When R0satisfies certain conditions
the endemic equilibrium of the model exists. Finally
we give some numerical simulations to explain the theoretical results.
LUO Y T,ZHANG L,TENG Z D,et al.Analysis of a general multi-group reaction-diffusion epidemic model with nonlinear incidence and temporary acquired immunity[J].Mathematics and Computers in Simulation,2021,182:428-455.
KHARAZIAN N A,MAGPANTAY F M G.The honeymoon period after mass vaccination[J].Mathematical Biosciences and Engineering,2020,18(1):354-372.
李学志,党艳霞.一类具有接种疫苗时滞的两菌株传染病模型的Hopf分支[J].应用泛函分析学报,2017,19(1):60-70.LI X Z,DANG Y X.Hopf bifuraction of a two-strain epidemic models with vaccination delay[J].Acta Analysis Functionalis Applicata,2017,19(1):60-70.(in Chinese)
桑瑞,张龙,吴浩.媒体诱导迁移率变化的双斑块SIRS传染病模型研究[J].新疆大学学报(自然科学版)(中英文),2023,40(1):49-56+60.SANG R,ZHANG L,WU H.Media-induced migration changes in a two-patch SIRS epidemic model[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2023,40(1):49-56+60.(in Chinese)
郭婷,滕志东.一类与环境有关的传染病模型的稳定性分析[J].新疆大学学报(自然科学版),2013,30(4):401-407.GUO T,TENG Z D.Stability analysis of an SIQR epidemic model with environmental component[J].Journal of Xinjiang University(Natural Science Edition),2013,30(4):401-407.(in Chinese)
张钰倩,张太雷,侯雯珊,等.一类具有媒体效应和追踪隔离的SIQR时滞传染病模型[J].浙江大学学报(理学版),2022,49(2):159-169.ZHANG Y Q,ZHANG T L,HOU W S,et al.A delayed SIQR epidemic model with media effect and tracking quarantine[J].Journal of Zhejiang University(Science Edition),2022,49(2):159-169.(in Chinese)
王荣年.反应扩散系统的比较原理和动力学性态[D].合肥:中国科学技术大学,2006.WANG R N.Comparative principles and dynamical properties of reaction-diffusion systems[D].Hefei:University of Science and Technology of China,2006.(in Chinese)
DIEKMANN O,HEESTERBEEK J A P,METZ J A J.On the definition and the computation of the basic reproduction ratio R0in models for infectious diseases in heterogeneous populations[J].Journal of Mathematical Biology,1990,28(4):365-382.
李从清.系统稳定性的劳斯判据与赫尔维茨判据的等价性论证[J].天津城市建设学院学报,2009,15(3):207-210.LI C Q.Equivalence demonstration of Routh criterion and Hurwitz criterion for system stability[J].Journal of Tianjin Institute of Urban Construction,2009,15(3):207-210.(in Chinese)
赵爱民,任晓晓,刘桂荣.考虑环境传播的肺结核模型的定性分析[J].山西大学学报(自然科学版),2021,44(1):20-26.ZHAO A M,REN X X,LIU G R.Qualitative analysis of environmentally transmitted tuberculosis model[J].Journal of Shanxi University(Natural Science Edition),2021,44(1):20-26.(in Chinese)
DING C X,QIU Z P,ZHU H P.Multi-host transmission dynamics of schistosomiasis and its optimal control[J].Mathematical Biosciences and Engineering,2015,12(5):983-1006.
徐润.关于李雅普诺夫稳定性理论若干定理的推广[J].沈阳师范大学学报(自然科学版),2003,21(2):87-90.XU R.The generalization of certain theorems on Liapunov stability theory of difference equation groop[J].Journal of Shenyang Normal University(Natural Science Edition),2003,21(2):87-90.(in Chinese)
0
浏览量
355
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构
京公网安备11010802024621
