南京师大学报（自然科学版）
南京師大學報（自然科學版）
남경사대학보（자연과학판）
JOURNAL OF NANJING NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2013年
2期
20-26
,共7页
SEIRS模型%全局渐近稳定%数值模拟%传染病
SEIRS模型%全跼漸近穩定%數值模擬%傳染病
SEIRS모형%전국점근은정%수치모의%전염병
SEIRS model%globally asymptotical stability%numerical simulation%epidemic
研究具有一般Logistic死亡率和标准传染率的SEIRS传染病模型的动力学行为。利用Floquet乘子理论和脉冲微分系统比较定理,证明了无病周期解的存在性和全局渐近稳定性,获得临界值τ0,θ0；并通过Matlab数值模拟的方法发现当τ>τ0或θ<θ0时会形成地方病。
研究具有一般Logistic死亡率和標準傳染率的SEIRS傳染病模型的動力學行為。利用Floquet乘子理論和脈遲微分繫統比較定理,證明瞭無病週期解的存在性和全跼漸近穩定性,穫得臨界值τ0,θ0；併通過Matlab數值模擬的方法髮現噹τ>τ0或θ<θ0時會形成地方病。
연구구유일반Logistic사망솔화표준전염솔적SEIRS전염병모형적동역학행위。이용Floquet승자이론화맥충미분계통비교정리,증명료무병주기해적존재성화전국점근은정성,획득림계치τ0,θ0；병통과Matlab수치모의적방법발현당τ>τ0혹θ<θ0시회형성지방병。
The dynamical behavior of SEIRS epidemic model with generalized Logistic death and standard contact rate is investigated in this paper. Based on Floquet theory and comparison theorem of impulsive differential equation, the existence and globally asymptotical stability of infection free periodic solution are examined,then the critical valueτ0 ,θ0 are obtained. Finally,numerical simulation reveals that the disease will become endemic whenτ>τ0 ,θ<θ0 .
