终身免疫下包含MSM人群的梅毒模型的稳定性分析
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摘要
对终身免疫下包含MSM(男同性恋者)人群的梅毒模型进行稳定性分析,求得基本再生数后计算得到两个平衡点,并通过建立Lyapunov函数以及其他方法证明两个平衡点是全局渐近稳定的.
In this paper, the stability of a syphilis model with MSM(gay men) population under lifelong immunity is analyzed. After obtaining the basic reproduction number, two equilibrium points are calculated. By establishing Lyapunov function and other methods, it is proved that the two equilibrium points are globally asymptotically stable.
In this paper, the stability of a syphilis model with MSM(gay men) population under lifelong immunity is analyzed. After obtaining the basic reproduction number, two equilibrium points are calculated. By establishing Lyapunov function and other methods, it is proved that the two equilibrium points are globally asymptotically stable.
引文
[1] SALOJEE H,VELAPHI S,GOGA Y,et al.The prevention and management of congenital syphilis:an overview and recommendations[J].Bull World Health Organ,2004,82:424-430.
[2] PARREN T.Syphilis:a public health problem[J].Science,1938,87:147-152.
[3] HOPKINS S,LYONS F,COLEMAN C,et al.Resurgence in infectious syphilis in Ireland:an epidemiological study[J].Sexually Transmitted Dis,2014,31:317-321.
[4] SAAD ROY C M,ZHISHENG SHUAI,VAN P DEN DRIESSCHE.A mathematical model of syphilis transmission in an MSM population[J].Mathematical Biosciences,2016,277:59-70.
[5] IBOI E,OKUONGHAE D.Population dynamics of a mathematical model for syphilis[J].Applied Mathematical Modelling,2016,40:3573-3590.
[6] GARNETT G P,ARAL S O,HOYLE D V,et al.The natural history of syphilis:Implica -tions for the transition dynamics and control of infection[J].Sexually Transmitted Diseases,1997,24(4):185-200.
[7] VAN DEN DRIESSCHE P.Watmouh James.Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Mathematical Bioscien-ces,2002,180:29-48.
[8] ZHI SHENG SHUAI,VAN P DEN DRIESSCHE.Global stability of infectious disease models using Lyapunov functions[J].SIAM Journal of Applied Mathematics Math,2013,73:1513-1532.
[2] PARREN T.Syphilis:a public health problem[J].Science,1938,87:147-152.
[3] HOPKINS S,LYONS F,COLEMAN C,et al.Resurgence in infectious syphilis in Ireland:an epidemiological study[J].Sexually Transmitted Dis,2014,31:317-321.
[4] SAAD ROY C M,ZHISHENG SHUAI,VAN P DEN DRIESSCHE.A mathematical model of syphilis transmission in an MSM population[J].Mathematical Biosciences,2016,277:59-70.
[5] IBOI E,OKUONGHAE D.Population dynamics of a mathematical model for syphilis[J].Applied Mathematical Modelling,2016,40:3573-3590.
[6] GARNETT G P,ARAL S O,HOYLE D V,et al.The natural history of syphilis:Implica -tions for the transition dynamics and control of infection[J].Sexually Transmitted Diseases,1997,24(4):185-200.
[7] VAN DEN DRIESSCHE P.Watmouh James.Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Mathematical Bioscien-ces,2002,180:29-48.
[8] ZHI SHENG SHUAI,VAN P DEN DRIESSCHE.Global stability of infectious disease models using Lyapunov functions[J].SIAM Journal of Applied Mathematics Math,2013,73:1513-1532.