报告题目：Dynamical behavior in a reaction-diffusion virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence
报告人：滕志东 教授（新疆大学）
报告时间：2023年5月21日（星期日）上午9:00-10:00
报告地点：理学院会议室（卓越楼810）
报告摘要：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.
滕志东教授简介:原苏联副博士学位，教授，博士生导师。获新疆自治区有突出贡献优秀专家和政府特殊津贴专家称号。
主要开展微分方程理论及应用、生物数学模型、神经网络模型等方向的科学研究，先后主持国家自然科学基金项目4项，教育部留学回国基金、重点项目、博士点基金各1项，新疆自治区重点实验室项目、高校科研计划重点项目、创新群体项目各1项，发表学术论文300多篇，其被SCI、EI收录300多篇, 2003年获得了新疆自治区科技进步二等奖（排名第一），2006年获得了新疆自治区优秀专业技术工作者一等奖，2010年获自治区科技进步二等奖（排名第一），2012年获自治区科技进步一等奖（排名第二），2016年获得自治区科技进步奖二等奖（排名第二），2020年获得自治区自然科学一等奖（排名第二）。目前已培养博士后5人，博士研究生21人，硕士研究生70多人。培养的博士、硕士分别获新疆自治区优秀博士学位论文2篇、优秀硕士学位论文2篇。