吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
JOURNAL OF JILIN UNIVERSITY(SCIENCE EDITION)
2009年
6期
1165-1171
,共7页
Logistic死亡率%脉冲免疫接种%全局渐近稳定性%持久性%周期解
Logistic死亡率%脈遲免疫接種%全跼漸近穩定性%持久性%週期解
Logistic사망솔%맥충면역접충%전국점근은정성%지구성%주기해
Logistic death rate%impulsive vaccination%global asymptotic stability%permanence%periodic solution
建立了一类具有一般Logistic死亡率和标准传染率的SIRS传染病模型, 在脉冲免疫接种条件下, 利用离散动力系统的频闪映射方法, 得到了系统的无病周期解. 运用Floquet乘子理论和脉冲微分方程比较定理, 证明了该周期解的全局渐近稳定性, 并获得了系统一致持续生存的条件. 结果表明, 为了阻止疾病流行, 需要选择恰当的脉冲接种率和脉冲免疫接种周期.
建立瞭一類具有一般Logistic死亡率和標準傳染率的SIRS傳染病模型, 在脈遲免疫接種條件下, 利用離散動力繫統的頻閃映射方法, 得到瞭繫統的無病週期解. 運用Floquet乘子理論和脈遲微分方程比較定理, 證明瞭該週期解的全跼漸近穩定性, 併穫得瞭繫統一緻持續生存的條件. 結果錶明, 為瞭阻止疾病流行, 需要選擇恰噹的脈遲接種率和脈遲免疫接種週期.
건립료일류구유일반Logistic사망솔화표준전염솔적SIRS전염병모형, 재맥충면역접충조건하, 이용리산동력계통적빈섬영사방법, 득도료계통적무병주기해. 운용Floquet승자이론화맥충미분방정비교정리, 증명료해주기해적전국점근은정성, 병획득료계통일치지속생존적조건. 결과표명, 위료조지질병류행, 수요선택흡당적맥충접충솔화맥충면역접충주기.
An SIRS epidemic model with generalized Logistic death rate and standard incidence was formulated. By use of the discrete dynamical system determined by the stroboscopic map, an "infection-free" periodic solution of the model under impulsive vaccination was obtained. Based on Floquet theory and the comparison theorem of impulsive differential equation, the analysis of global asymptotic stability of the "infection-free" periodic solution was given. And the sufficient condition for the permanence of the system was obtained. The results show that in order to prevent the epidemic disease from generating an endemic, an appropriate vaccination rate and an appropriate vaccination period can be chosen.
