一类自调节免疫的时滞病毒感染模型分析  

The Analysis of a Delay Virus Infection Model with Self-Adjusting Immune

作　　者：韩云丽[1] 刘茂省[1] 李有文[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2015年第1期317-324,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10901145);山西省自然科学基金(2012011002-1)

摘　　要：针对病毒在感染宿主的过程中,细胞免疫的时间滞后、非线性发生率、自调节免疫等因素往往同时出现的问题,建立了具有饱和发生率和自调节免疫的时滞病毒感染模型,证明了当R_0≤1,τ为任意值时,无病平衡点局部渐近稳定,当R_0>1时,存在唯一正平衡点,且在一定的条件下,存在-σ_0>0,当τ<τ_0时,正平衡点局部渐近稳定;当τ>τ_0时,正平衡点不稳定.最后,通过数值模拟验证了理论结果的正确性.In this paper, there exists some factors at the same time such as delay, nonlinear incidence and self regulating immune when virus infects host cell, a virus infection model with saturated incidence rate and immune regulation delay is set up. We prove that if R0≤1, T is arbitrary value, then the disease-free equilibrium is locally asymptotically stable. When R0 〉 1, we prove that there exists a unique endemic equilibrium,and under certain conditions, there is a τ0 〉 0, when τ 〈 τ0,the endemic equilibrium is locally asymptotically stable. While τ 〉 τ0, it is unstable. In the end, Numerical simulations are carried out to explain the mathematical conclusions .

关 键 词：基本再生数 局部渐近稳定 饱和发生率 Routh.Hurwitz判据 时滞 自调节免疫 

分 类 号：O175[理学—数学]