新疆大学学报（自然科学版）
新疆大學學報（自然科學版）
신강대학학보（자연과학판）
XINJIANG UNIVERSITY JOURNAL(NATURAL SCIENCE EDITION)
2014年
3期
273-279
,共7页
离散SIRS传染病模型%无病平衡点%地方病平衡点%全局稳定性%Lyapunov函数
離散SIRS傳染病模型%無病平衡點%地方病平衡點%全跼穩定性%Lyapunov函數
리산SIRS전염병모형%무병평형점%지방병평형점%전국은정성%Lyapunov함수
Discrete SIRS epidemic model%Disease-free equilibrium%Endemic equilibrium%Global stability%Lyapunov function
研究了两类离散SIRS 传染病动力学模型。得到了无病平衡点和地方病平衡点的全局稳定性。通过归纳法得到了解的正性与有界性，并构造适当的离散的Lyapunov 函数，得到无病平衡点和地方病平衡点的全局渐近稳定性的判别准则，且平衡点的全局稳定性由阈值来完全决定。
研究瞭兩類離散SIRS 傳染病動力學模型。得到瞭無病平衡點和地方病平衡點的全跼穩定性。通過歸納法得到瞭解的正性與有界性，併構造適噹的離散的Lyapunov 函數，得到無病平衡點和地方病平衡點的全跼漸近穩定性的判彆準則，且平衡點的全跼穩定性由閾值來完全決定。
연구료량류리산SIRS 전염병동역학모형。득도료무병평형점화지방병평형점적전국은정성。통과귀납법득도료해적정성여유계성，병구조괄당적리산적Lyapunov 함수，득도무병평형점화지방병평형점적전국점근은정성적판별준칙，차평형점적전국은정성유역치래완전결정。
In this paper, we investigate two classes of discrete SIRS epidemic models. By inductive method ,the positive and the boundedness of the solution are obtained. By constructing new Lyapunov functions, the criterion of the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium for these epidemic models is obtained.It is showed that the global dynamics of each discrete SIRS epidemic model is fully determined by a threshold R0, then endemic equilibrium is globally asymptotically stable.
