报告题目：An eco-epidemiological prey-predator model with infectious diseases in prey

报 告 人：王明新

报告时间：2023年9月22日（星期五）10:00

报告地点：7JC214

报告摘要：Eco-epidemiology has become a new interdisciplinary subject and is the frontier and hotspot of mathematical biology research so far. In this talk, we first formulate the basic eco-epidemiological model combining the SI epidemic model and the prey-predator model. Then study the ODE model, and diffusive model with the homogeneous Neumann and Dirichlet boundary conditions, respectively. For the ODE model and the diffusive model with the homogeneous Neumann boundary conditions, we give a complete conclusion about the stabilities of nonnegative equilibrium states (nonnegative constant equilibrium solutions). The results show that these two problems has no periodic solutions, and the diffusive model with the homogeneous Neumann boundary conditions has no yet Turing patterns. For the diffusive model with the homogeneous Dirichlet boundary conditions, we first establish the necessary and sufficient conditions for the existence of positive equilibrium solutions, and prove that the positive equilibrium solution is unique when it exists. Then we study the global asymptotic stabilities of trivial and semi-trivial nonnegative equilibrium solutions.

报告人简介：王明新，河南理工大学特聘教授，1994年起享受国务院政府特殊津贴，1997年起任博士生导师。曾任江苏省数学会副理事长，东南大学理学院副院长、数学系主任、应用数学硕士和博士点学科负责人、特聘教授和二级教授, 博士生导师，江苏省重点学科“应用数学”首席科学家，哈尔滨工业大学特聘教授和二级教授。研究方向为反应扩散方程的定性性质，在Proc. London Math. Soc., Trans. Amer. Math. Soc., Indiana Univ. Math. J., Math. Models Methods Appl. Sci., J. Functional Analysis, SIAM系列, Nonlinearity, CVPDE, J. Differential Equations, J. London Math. Soc., Physica D, J. Dyn. Diff. Equat. 等国内外核心期刊上发表论文260 多篇，其中被SCI检索的有240篇，他引4千余篇次。CRC Press、科学出版社出版和高等教育出版社专著7本，参与编写了科学出版社出版的“数学大辞典”，清华大学出版社出版教材4本。主持完成国家自然科学基金项目10项，在研一项；主持完成省部级项目8项。获得教育部科技进步三等奖2次，江苏省科技进步二等奖和教育部自然科学二等奖各1次，江苏省首届青年科学家奖提名奖，河南省青年科技奖，河南省优秀专家，江苏省优秀研究生指导教师，华英文化教育基金奖。