報告題目🚦📠：Dynamical behavior in a reaction-diffusion virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence
報告人：滕誌東 教授（新疆大學）
報告時間：2023年5月21日（星期日）上午9:00-10:00
報告地點🧮：必一体育平台會議室（卓越樓810）
報告摘要🌷：We investigate a reaction–diffusion virus infection model with humoral immunity and nonlinear incidence in heterogeneous environment. The model includes simultaneously the virus-to-cell and cell-to-cell transmissions of the infection.
In complete diffusion case, the well-posedness of solutions, including the existence of global solutions and the ultimate boundedness, is established. The virus infection reproduction number $R_0$ is calculated. When $R_0<1$, it is proved that the infection-free steady state is globally asymptotically stable. Otherwise, when $R_0>1$ then the infection with antibody-free response is uniformly persistent. Some open problems are proposed.
In degenerated diffusion case, the model is assumed that the uninfected and infected cells do not diffuse and the virus and $B$ cells have diffusion. The reproduction number $R_0$ account for virus infection is calculated, and some useful properties of $R_0$ are obtained by means of the Kuratowski measure of non-compactness and the principle eigenvalue. When $R_0<1$, the infection-free steady state is proved to be globally asymptotically stable. To discuss the antibody response reproduction number $R_1$ and the global dynamics of virus infection, a special case of the model is considered. When $R_0>1$ and $R_1<1$ (or $R_1>1$), the sufficient conditions on the global asymptotic stability of the antibody-free infection steady state (or the uniform persistence and global asymptotic stability of infection with antibody response) are established.
Finally, the global asymptotic stability in spatially homogeneous case for the complete diffusion case is investigated.
滕誌東教授簡介:原蘇聯副博士學位，教授👨🏿🦲，博士生導師。獲新疆自治區有突出貢獻優秀專家和政府特殊津貼專家稱號。
主要開展微分方程理論及應用、生物數學模型、神經網絡模型等方向的科學研究，先後主持國家自然科學基金項目4項👨🏻⚕️，教育部留學回國基金、重點項目、博士點基金各1項🗻，新疆自治區重點實驗室項目、高校科研計劃重點項目、創新群體項目各1項，發表學術論文300多篇，其被SCI🤴🏼、EI收錄300多篇, 2003年獲得了新疆自治區科技進步二等獎（排名第一）🚴🏻🪂，2006年獲得了新疆自治區優秀專業技術工作者一等獎🖤，2010年獲自治區科技進步二等獎（排名第一），2012年獲自治區科技進步一等獎（排名第二）👎🏿，2016年獲得自治區科技進步獎二等獎（排名第二）💁🏼，2020年獲得自治區自然科學一等獎（排名第二）。目前已培養博士後5人，博士研究生21人，碩士研究生70多人。培養的博士、碩士分別獲新疆自治區優秀博士學位論文2篇、優秀碩士學位論文2篇🕵🏼♂️。