

浏览全部资源
扫码关注微信
重庆交通大学数学与统计学院
Published:2024
移动端阅览
[1]沈鑫,刘子建.一类具有预防意识的多斑块SEIQR传染病模型的阈值动力学研究[J].新疆大学学报(自然科学版)(中英文),2024,41(02):145-156.
[1]沈鑫,刘子建.一类具有预防意识的多斑块SEIQR传染病模型的阈值动力学研究[J].新疆大学学报(自然科学版)(中英文),2024,41(02):145-156. DOI: 10.13568/j.cnki.651094.651316.2023.08.29.0004.
DOI:10.13568/j.cnki.651094.651316.2023.08.29.0004.
结合一般传染病病毒传播的特点,提出了一类具有预防意识和斑块间流动感染的SEIQR传染病传播动力学模型.根据下一代矩阵法算出了单斑块下疾病传播的阈值Ra和两斑块下疾病传播的阈值Ra~φ,得到当Ra≤1时单斑块下无病平衡点全局渐近稳定和Ra~φ≤1时两斑块下无病平衡点局部稳定的结论,数值模拟证实了理论结果.敏感性分析说明了参数对基本再生数的影响,结果表明增加人群预防意识能够抑制病毒在斑块间的传播,但群体在斑块间流动时发生感染会加剧病毒的传播.
We consider the characteristics of viral transmission of common infectious diseases
multi-patch SEIQR infectious disease transmission dynamic model with prevention awareness was proposed and studied. According to the next generation matrix method
the disease transmission threshold Rain a single patch and the disease transmission threshold Ra~φ in the two patches were calculated. The theoretical results show that the disease free equilibrium in a single patch is globally asymptotically stable if Ra≤ 1 and the disease free equilibrium in two patches are locally stable if Ra~φ≤ 1. Numerical simulations confirm the theoretical results
sensitivity analysis discusses the effects of parameters to the basic regeneration number
which shows that increasing the awareness of prevention could inhibit the spread of the virus between patches
but infection during transportation can increase it.
NEUMANN G,NODA T,KAWAOKA Y.Emergence and pandemic potential of swine-origin H1N1 influenza virus[J].Nature,2009,459:931-939.
FINEBERG H V.Pandemic preparedness and response:Lessons from the H1N1 influenza of 2009[J].The New England Journal of Medicine,2014,370(14):1335-1342.
SATTENSPIEL L,DIETZ K.A structured epidemic model incorporating geographic mobility among regions[J].Mathematical Biosciences,1995,128(1/2):71-91.
MISHRA A,GAKKHAR S.Non-linear dynamics of two-patch model incorporating secondary dengue infection[J].International Journal of Applied and Computational Mathematics,2018,4(1):1-22.
LIU J L,JIA Y,ZHANG T L.Analysis of a rabies transmission model with population dispersal[J].Nonlinear Analysis:Real World Applications,2017,35:229-249.
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 epidemicmodel[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2023,40(1):49-56+60.(in Chinese)
朱紫睿,陈丽娟.非线性出生率对双斑块模型动力学行为的影响[J].福州大学学报(自然科学版),2023,51(3):301-306.ZHU Z R,CHEN L J.Influence of nonlinear birth rate on dynamic behavior of a two-patch model[J].Journal of Fuzhou University(Natural Science Edition),2023,51(3):301-306.(in Chinese)
散雪峰.斑块环境下传染病模型的传播动力学[D].兰州:兰州大学,2022.SAN X F.Propagation dynamics of epidemic models in patchy environments[D].Lanzhou:Lanzhou University,2022.(in Chinese)
SAMANTA S,RANA S,SHARMA A,et al.Effect of awareness programs by media on the epidemic outbreaks:A mathematical model[J].Applied Mathematics and Computation,2013,219(12):6965-6977.
SAHU G P,DHAR J.Dynamics of an SEQIHRS epidemic model with media coverage,quarantine and isolation in a community with pre-existing immunity[J].Journal of Mathematical Analysis and Applications,2015,421(2):1651-1672.
YANG C Y,WANG X Y,GAO D Z,et al.Impact of awareness programs on cholera dynamics:Two modeling approaches[J].Bulletin of Mathematical Biology,2017,79(9):2109-2131.
MISRA A K,SHARMA A,SHUKLA J B.Stability analysis and optimal control of an epidemic model with awareness programs by media[J].Bio Systems,2015,138:53-62.
常星花.疾病信息与传染病共演化动力学性态分析与研究[D].太原:中北大学,2022.CHANG X H.Analysis and research on the coevolution dynamics of disease information and infectious diseases[D].Taiyuan:North University of China,2022.(in Chinese)
DENPHEDTNONG A,CHINVIRIYASIT S,CHINVIRIYASIT W.On the dynamics of SEIRS epidemic model with transportrelated infection[J].Mathematical Biosciences,2013,245(2):188-205.
KUMAR K A,VENKATESH A.Mathematical analysis of SEITR model for influenza dynamics[J].Journal of Computational Analysis&Applications,2023,31(1):281-293.
UMAPATHY K,PALANIVELU B,JAYARAJ R,et al.On the decomposition and analysis of novel simultaneous SEIQR epidemic model[J].AIMS Mathematics,2022,8(3):5918-5933.
陈伟,张龙.具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学[J].新疆大学学报(自然科学版)(中英文),2022,39(4):401-411+420.CHEN W,ZHANG L.Threshold dynamics in two-strain delayed HIV infection model with saturated incidence[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2022,39(4):401-411+420.(in Chinese)
RIFHAT R,WANG K,WANG L,et al.Global stability of multi-group SEIQR epidemic models with stochastic perturbation in computer network[J].Electronic Research Archive,2023,31(7):4155-4184.
VAN DEN DRIESSCHE P,WATMOUGH J.Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Mathematical Biosciences,2002,180:29-48.
CHEN Y,YAN M,XIANG Z Y.Transmission dynamics of a two-city SIR epidemic model with transport-related infections[J].Journal of Applied Mathematics,2014,2014:1-12.
0
Views
307
下载量
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution
京公网安备11010802024621