陕西师范大学学报(自然科学版)
陝西師範大學學報(自然科學版)
협서사범대학학보(자연과학판)
JOURNAL OF SHAANXI NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2014年
5期
6-11
,共6页
基本再生数%时滞%稳定性%Hopf分支%周期解
基本再生數%時滯%穩定性%Hopf分支%週期解
기본재생수%시체%은정성%Hopf분지%주기해
basic reproduction number%time delay%stability%Hopf bifurcation%periodic solution
研究了具有不同潜伏阶段和时滞的艾滋病模型。在模型中,一些感染个体可以通过治疗从有症状阶段转移到无症状阶段。得到模型的基本再生数R0,当R0<1时,在一定条件下无病平衡点E0是局部渐近稳定的;当R0>1时,给出疾病平衡点E*局部稳定的充分条件;时滞影响疾病平衡点E*的稳定性,并产生 Hopf分支现象。用分支理论研究 Hopf分支周期解的稳定性,数值模拟验证了结论的正确性。
研究瞭具有不同潛伏階段和時滯的艾滋病模型。在模型中,一些感染箇體可以通過治療從有癥狀階段轉移到無癥狀階段。得到模型的基本再生數R0,噹R0<1時,在一定條件下無病平衡點E0是跼部漸近穩定的;噹R0>1時,給齣疾病平衡點E*跼部穩定的充分條件;時滯影響疾病平衡點E*的穩定性,併產生 Hopf分支現象。用分支理論研究 Hopf分支週期解的穩定性,數值模擬驗證瞭結論的正確性。
연구료구유불동잠복계단화시체적애자병모형。재모형중,일사감염개체가이통과치료종유증상계단전이도무증상계단。득도모형적기본재생수R0,당R0<1시,재일정조건하무병평형점E0시국부점근은정적;당R0>1시,급출질병평형점E*국부은정적충분조건;시체영향질병평형점E*적은정성,병산생 Hopf분지현상。용분지이론연구 Hopf분지주기해적은정성,수치모의험증료결론적정학성。
An acquired immune deficiency syndrome(AIDS)model with different latent stages and time delay is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. The basic reproduction number R0 is defined.When R0 < 1 , the disease-free equilibrium E0 is locally asymptotically stability in a special case.When R0>1 ,the sufficient conditions for the local stability of the infected equilibrium E* are obtained.The time delay can change the stability of the infected equilibrium E* and lead to the existence of Hopf bifurcation. The stability of bifurcating periodic solutions is also studied by the theory of Hopf bifurcation. Numerical simulations check out the obtained theory.