【作者】 石秀厂；

【导师】 薛亚奎；

【作者基本信息】 中北大学 ， 应用数学， 2008， 硕士

【摘要】 在传统的结核病模型中,一般把人群分成四种类型:易感者,潜伏者,染病者,治愈者.随着结核病的发展和人们对结核病的进一步了解,结核病出现了最新的几个特点:二次感染,未治愈比率和抗药菌珠的出现,潜伏者也能传染等情况.本文在传统的结核病模型的基础上,结合结核病的最新的特点,主要研究了新特点下的结核病的两个传染模型;同时,结合结核病的最新的特点,给出了单、双菌珠下的结核病的传染模型.在第二章中考虑了二次感染,未治愈比率和部分免疫在结核病的传播中起到的重要作用,建立了具有二次传染的未治愈的结核病模型.通过具有二次传染的未治愈的结核病模型的研究,得到了在基本再生数R0 ,并且在R0 < 1,系统存在多地方病平衡点。同时,通过分析表明,未治愈率可能是现今结核病不绝灭的一个很重要的原因.在第三章中在结核病传播的数学模型的动力学系统基础上,利用Hurwitz判据和复合矩阵理论,讨论了具有常数移入的结核病传播的数学模型的动力学性质,研究了具有常数移入的结核病模型的地方病平衡点的局部和全局渐近稳定性,得到了具有常数移入的结核病模型的地方病平衡点是局部和全局渐近稳定的充分条件.在第四章中结合结核病的最新的特点,建立了单、双菌珠下的结核病的传染模型.更多还原

【Abstract】 In traditional Tuberculosis models,the host population is divided into the following four classes: susceptible, exposed, infectious and treated individuals.With Tuberculosis developing and being known about deeply, Tuberculosis has some following new characteristics: the appearing of reinfection, untreaed rate and drug-resistant strains ,and that exposed individuals can also be infectious.Combining with these new characteristics,the paper mainly proposes two Tuberculosis models on the basis of traditional Tuberculosis models.Meanwhile, combined with these new characteristics, Tuberculosis models of one-strain and two-strains are developed.In chapter 2,with the imoportant influence of reinfection, untreaed rate,and partle immuned rate ,an untread Tuberculosis model with reinfection is developed.By proposing this model,the basic reproductive number R0 is obtained,and when R0 < 1,the multipie endemic equilibria may exists in the system.Meanwhile,untreaed rate is an important factor for today Tuberculosis prevalence.In chapter 3,on the basis of the dynamical system on a Tuberculosis spread model, the paper mainly discusses the dynamical behavior of a Tuberculosis spread model with constant immigration.The local and global asymptotically stability of the endemic equilibrium on this model is studied. It is proved by using the hurwitz criterion and the compound matrix theory. Sufficient conditions for the local and global asymptotically stability of the endemic equilibrium on this model are obtained.In chapter 4, combined with these new characteristics, Tuberculosis models of one-strain and two-strains are developed.更多还原