报告题目: Non-monotone waves of a stage-structured SLIRM epidemic model with

                      latent period

报告人: 吴楚芬教授(佛山科学技术学院)

报告时间:  2021年4月22日(星期四),  11:30-12:30

报告地点: 腾讯会议, 会议号: 453 638 813

内容摘要:  We propose and investigate a stage-structured SLIRM epidemic model with latent period in a spatially continuous habitat. We first show the existence of semi-traveling waves that connect the unstable disease-free equilibrium as the wave coordinate goes to $-\infty$, provided that the basic reproduction number $\mathcal {R}_0>1$ and $c>c_*$ for some positive number $c_*$. We then use a combination of asymptotic estimates, Laplace transform and Cauchy's integral theorem to show the persistence of semi-traveling waves. Based on the persistent property, we construct a Lyapunov functional to prove the convergence of the semi-traveling wave to an endemic (positive) equilibrium as the wave coordinate goes to $+\infty$. In addition, by the Laplace transform technique, the non-existence of bounded semi-traveling wave is also proved when $\mathcal {R}_0>1$ and $0<c<c_*$. This indicates that $c_*$ is indeed the minimum wave speed.Finallywe show the existence of critical waves for $\mathcal {R}_0>1$ and $c=c_*$ by limiting arguments.

报告人简介: 吴楚芬，教授，硕士生导师，佛山科学技术学院数学与大数据学院副院长，上海交通大学博士后，华南师范大学优秀校友，美国《数学评论》评论员，国家自然科学基金、广东省自然科学基金同行评议专家，中国仿真学会不确定性系统分析与仿真专业委员会委员，广东数学会理事，《Applicable Analysis》、《Nonlinear Analysis(RWA)》、《J. Math. Anal. Appl.》、《Chaos》、《Applied Mathematics Letters》等国际杂志的审稿专家，研究方向包括生物数学、非线性分析、应用动力系统等领域，目前已经在国际顶尖期刊《J. Diff. Eqns.》、《J. Dyna. Diff. Eqns.》、《Disc. Contin. Dyn. Sys.》、《Proceedings of the Royal Society of Edinburgh Section A: Mathematics》、《IMA J. Appl. Math.》等杂志上发表了近30篇学术论文；曾经主持国家自然科学基金项目3项，广东省自然科学基金项目2项。

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