河北工业科技2017，Vol.34Issue(6)：402-407,6.DOI:10.7535/hbgykj.2017yx06003
具有时滞和治疗的丙肝模型分析
Analysis of Hepatitis C Virus model with time delay and treatment
摘要
Abstract
In order to further study the mechanism of Hepatitis C Virus(HCV)transmission and effective methods for its treatment,aiming at the characteristics that the latent period of HCV is quite long and HCV is an infectious virus throughout the whole disease period,based on the existing model,the time delay is used to reflect the existence of the latent period of HCV.In order to study the effect of the time delay and the medical treatment on HCV,a model with the constant input and the time delay is established.The existence of equilibria is evaluated using the qualitative theory of ordinary differential equation, the global stability of the disease-free equilibrium is got by constructing the suitable Liapunov function,and the influence of the time delay on the system is also discussed.The analysis results show that if the time delay is greater than zero and the repro-duction number is less than 1 ,the system is globally asymptotically stable at the disease-free equilibrium;the stable and unsta-ble conditions of the endemic equilibrium are given,respectively,and the system can generate a Hopf bifurcation under the con-dition.Finally,the measures to control HCV are put forward by analyzing the threshold.The numerical simulation verifies the corresponding results.Therefore,it is significant to study the HCV model with the time delay and the medical treatment,and it can provide new ideas for reducing the prevalence of Hepatitis C.关键词
稳定性理论/丙肝/时滞/治疗/Hopf分支Key words
theory of stability/Hepatitis C Virus/time delay/treatment/Hopf bifurcation分类
数理科学引用本文复制引用
张丽婷,冯飞,董亚丽,乔志琴..具有时滞和治疗的丙肝模型分析[J].河北工业科技,2017,34(6):402-407,6.基金项目
国家自然科学基金(11401541) （11401541）
博士学科点专项科研基金(20111420120006) （20111420120006）
