报告题目：Qualitative analysis on a reaction-diffusion host-pathogen model with incubation period and nonlinear incidence rate

报告人：戴斌祥 教授

单位：中南大学

时间：2022年12月10日19:00

腾讯会议：985-305-951

摘要：A degenerate reaction-diffusion host-pathogen model with an incubation period and a nonlinear incidence rate in a spatially heterogeneous environment is proposed in this talk. We analyze the dynamics of this model on a bounded domain. Firstly, we establish the well-posedness, including the global existence of solutions and the existence of a global attractor by defining a noncompact measure. Then, the basic reproduction number is given and a threshold dynamics is established. Finally, when there is a positive steady state, we investigate the asymptotic profiles of the positive steady state when host individuals disperse at small or large rate. Our results show that the incubation period can significantly enhance the persistence of the disease if the dispersal rate of susceptible hosts or exposed hosts is small or large.

简介：戴斌祥，中南大学数学与统计学院二级教授、博士生导师；湖南省数学学会常务理事、高等教育与大学数学竞赛工作委员会副主任委员；中国数学会生物数学专业委员会常务委员。主要从事时滞微分方程与离散动力系统、种群生态学与传染病学、反应扩散方程的定性理论与应用等领域的研究，先后在《Nonlinearity》、 《J. Dyn. Diff. Equ.》、 《J. Math. Anal. Appl.》、《Appl. Math. Model》、《Discrete Contin. Dyn. Sys.》、 《Nonlinear Anal.》等国内外权威期刊上发表学术论文160多篇，主持6项国家自然科学基金面上项目和多项省部级科研课题，获得湖南省科技进步奖一等奖和湖南省自然科学奖一等奖各1项，主编出版教材6部，是全国宝钢教育基金优秀教师奖获得者。