一类具有预防接种的SEIRS_vI_v媒介传染病模型
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摘要
建立了一类具有预防接种的SEIRS_vI_v媒介传染病模型,得到了基本再生数R_0的表达式,证明了以下结论:当R_0<1时,模型的无病平衡点是全局渐近稳定的;当R_0>1时,唯一地方病平衡点是局部渐近稳定的。通过数值模拟验证了结论的正确性。
A SEIRS_vI_v vector-borne epidemic model with vaccination was built.The reproduction number was obtained,and the following conclusions were drawn:if R_0<1,the disease-free equilibriumof the model was globally asymptotically stable;if R_0>1,the model had a unique endemic equilibrium and was locally asymptotically stable.The numerical simulation was given to validate the conclusion.
A SEIRS_vI_v vector-borne epidemic model with vaccination was built.The reproduction number was obtained,and the following conclusions were drawn:if R_0<1,the disease-free equilibriumof the model was globally asymptotically stable;if R_0>1,the model had a unique endemic equilibrium and was locally asymptotically stable.The numerical simulation was given to validate the conclusion.
引文
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[2]DRIESSCHE P,WATMOUGH J.Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Mathematical biosciences,2002,180:29-48.
[3]LASHARI A A,OZAIRL M,ZAMAN G,et al.Global analysis of a Host-Vector model with infectious force in latent and infected period[J].Acta analysis functionalis applicata,2012,14(4):321-329.
[4]CHITNIS N,CUSHING J M,HYMAN J M.Bifurcation analysis of a mathematical model for malaria transmission[J].SIAM Journal on applied mathematics,2006,67(1):24-25.
[5]康彩丽,张志纯.一类媒介传染病模型动力学性态分析[J].高师理科学刊,2015,35(3):1-6.
[6]张秋娟.虫媒传染病模型的稳定性分析[D].大连:大连交通大学,2012.
[7]邱光明.两类疟疾传播模型的稳定性[D].兰州:兰州理工大学,2014.
[8]肖亚男,薛亚奎.一类具有标准发生率的媒介传染病模型的稳定性[J].高师理科学刊,2015,35(3):11-14.
[9]马知恩,周义仓,王稳地.传染病动力学的数学建模与研究[M].北京:科学出版社,2004:1-59.
[10]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001:24-47.