報(bào)告題目：Global threshold dynamics and finite-time contraction stability for age-structured HIV models with delay

報(bào)告人：張啟敏

報(bào)告時(shí)間：2022年12月12日20：30-22：30

騰訊會(huì)議ID：994-465-977

報(bào)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(bào)告人簡(jiǎn)介：寧夏大學(xué)數(shù)學(xué)統(tǒng)計(jì)學(xué)院二級(jí)教授，博士研究生導(dǎo)師，寧夏自治區(qū)313人才。中國(guó)生物數(shù)學(xué)學(xué)會(huì)常務(wù)理事，中國(guó)人口學(xué)會(huì)理事和寧夏統(tǒng)計(jì)學(xué)會(huì)理事。長(zhǎng)期以來(lái)一直從事隨機(jī)種群模型、流行病模型及生態(tài)模型動(dòng)力學(xué)、最優(yōu)控制及數(shù)值計(jì)算理論研究工作。主持國(guó)家自然基金4項(xiàng)、國(guó)家社科基金1項(xiàng)、寧夏自然基金目4項(xiàng)及寧夏重點(diǎn)研發(fā)項(xiàng)目1項(xiàng)。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。