洛阳师范学院学报
洛暘師範學院學報
락양사범학원학보
Journal of Luoyang Teachers College
2012年
8期
5~9
,共null页
肖雪霞 郭玉玲 刘璐菊
肖雪霞 郭玉玲 劉璐菊
초설하 곽옥령 류로국
病例失踪的结核病模型 平衡点 基本再生数 Lyapunov函数 全局渐近稳定
病例失蹤的結覈病模型 平衡點 基本再生數 Lyapunov函數 全跼漸近穩定
병례실종적결핵병모형 평형점 기본재생수 Lyapunov함수 전국점근은정
TB model with defaulters; equilibrium; the basic reproduction number; Laypunov functions; globally asymptotically stable
建立了一类具有病例失踪的结核病数学模型，定义了模型的基本再生数R0，通过构造适当的Lyapunov函数证明了模型解的渐近性态．证明了当基本再生数小于1时，无病平衡点是全局渐近稳定的；当基本再生数大于1时，唯一的地方病平衡点是全局渐近稳定的．
建立瞭一類具有病例失蹤的結覈病數學模型，定義瞭模型的基本再生數R0，通過構造適噹的Lyapunov函數證明瞭模型解的漸近性態．證明瞭噹基本再生數小于1時，無病平衡點是全跼漸近穩定的；噹基本再生數大于1時，唯一的地方病平衡點是全跼漸近穩定的．
건립료일류구유병례실종적결핵병수학모형，정의료모형적기본재생수R0，통과구조괄당적Lyapunov함수증명료모형해적점근성태．증명료당기본재생수소우1시，무병평형점시전국점근은정적；당기본재생수대우1시，유일적지방병평형점시전국점근은정적．
A class of TB mathematical model with defaulters was formulated in this paper. The basic reproduc- tion number Ro was defined and the asymptotic behavior of the solutions of the TB model was studied by constructing the proper Lyapunov functions. The result shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one- and the unique endemic equilibrium is globally asymptotically sta- ble if the basic reproduction number is greater than one.
