具有双线性发生率的SIR模型的研究
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摘要
针对双线性发生率的的SIR传染病模型,利用微分不等式和比较原理对该SIR传染病模型进行研究,得知在R_0> 1时,该模型存在唯一一个地方病平衡点,并得到了地方病平衡点全局稳定的充分条件。
An SIR epidemic model with bilinear incidence was considered and studied. By virtue of differential inequalities and comparison principle,we exploit the SIR model under the basic reproductive number R_0> 1 to get the uniqueness and global stability of the endemic equilibrium.
An SIR epidemic model with bilinear incidence was considered and studied. By virtue of differential inequalities and comparison principle,we exploit the SIR model under the basic reproductive number R_0> 1 to get the uniqueness and global stability of the endemic equilibrium.
引文
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[6]陆征一,周义仓.数学生物学进展[M].北京:科学出版社,2006.
[7]沃松林,许波.人口增长的具有暂时免疫的流行病模型(SIRS模型)[J].常州大学学报(自然科学版),2002,14(2):54-56.
[8]RUAN S,WANG W.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].J Differ Equ,2003,188:135-163.
[9]GUO H,LI M Y,SHUAI Z.Global stability of the endemic equilibrium of multigroup SIR epidemic models[J].Can Appl Math,2009,3:268-288.
[10]GUO H,LI M Y.Global dynamics of a staged progression model for infectious diseases[J].J Biol Dyn,2006,3(3):513-525.
[2]WEBB G F.Theory of Nonlinear Age-dependent Population Dynamics[M].New York:Springer-Verlag,1987.
[3]ANDERSON R M,MAY R M.Infections Diseases of Humans:Dynamics and control[M].Oxford:Oxford University Press,1991.
[4]刘应麟.传染病学[M].北京:人民卫生出版社,1997.
[5]马知恩,周义仓,王稳地,等.传染病动力学的数学建模与研究[M].北京:科学出版社,2004.
[6]陆征一,周义仓.数学生物学进展[M].北京:科学出版社,2006.
[7]沃松林,许波.人口增长的具有暂时免疫的流行病模型(SIRS模型)[J].常州大学学报(自然科学版),2002,14(2):54-56.
[8]RUAN S,WANG W.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].J Differ Equ,2003,188:135-163.
[9]GUO H,LI M Y,SHUAI Z.Global stability of the endemic equilibrium of multigroup SIR epidemic models[J].Can Appl Math,2009,3:268-288.
[10]GUO H,LI M Y.Global dynamics of a staged progression model for infectious diseases[J].J Biol Dyn,2006,3(3):513-525.