報告題目：Global threshold dynamics and finite-time contraction stability for age-structured HIV models with delay

報告人：張啟敏

報告時間：2022年12月12日20：30-22：30

騰訊會議ID：994-465-977

報告摘要：Considering age of infected cells and intracellular delay in both virus-to-cell and cell-to-cell transmissions, we develop an age-structured HIV model with delay to investigate the global threshold dynamics, which show the uninfected and infected steady states of the model. Using the Lyapunov function and LaSalle's invariance principle, we show that the global threshold dynamics of the model can be determined by utilizing basic reproduction number. Moreover, given that sudden environmental changes can lead to uncertainty in parameters of the model, a stochastic age-structured HIV model with Markovian switching is developed to study the finite-time contraction stability, which characterizes transmission properties of virus over a finite time. The sufficient conditions of the finite-time contraction stability are obtained by employing the Lyapunov function and stochastic comparison theorem. Numerical examples are presented to illustrate the theoretical results, and numerical results show that different noise intensity and delay affect stability of the HIV models.

報告人簡介：寧夏大學(xué)數(shù)學(xué)統(tǒng)計學(xué)院二級教授，博士研究生導(dǎo)師,，寧夏自治區(qū)313人才,。中國生物數(shù)學(xué)學(xué)會常務(wù)理事,，中國人口學(xué)會理事和寧夏統(tǒng)計學(xué)會理事,。長期以來一直從事隨機種群模型,、流行病模型及生態(tài)模型動力學(xué),、最優(yōu)控制及數(shù)值計算理論研究工作,。主持國家自然基金4項,、國家社科基金1項,、寧夏自然基金目4項及寧夏重點研發(fā)項目1項。在科學(xué)出版社出版學(xué)術(shù)專著3部,，發(fā)表論文100余篇,。