報告題目: Non-monotone waves of a stage-structured SLIRM epidemic model with
latent period
報告人: 吳楚芬教授(佛山科學技術(shù)學院)
報告時間: 2021年4月22日(星期四), 11:30-12:30
報告地點: 騰訊會議, 會議號: 453 638 813
內(nèi)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.
報告人簡介: 吳楚芬，教授，碩士生導師，佛山科學技術(shù)學院數(shù)學與大數(shù)據(jù)學院副院長，上海交通大學博士后，華南師范大學優(yōu)秀校友，美國《數(shù)學評論》評論員，國家自然科學基金、廣東省自然科學基金同行評議專家，中國仿真學會不確定性系統(tǒng)分析與仿真專業(yè)委員會委員，廣東數(shù)學會理事，《Applicable Analysis》、《Nonlinear Analysis(RWA)》、《J. Math. Anal. Appl.》、《Chaos》、《Applied Mathematics Letters》等國際雜志的審稿專家，研究方向包括生物數(shù)學、非線性分析、應用動力系統(tǒng)等領(lǐng)域，目前已經(jīng)在國際頂尖期刊《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.》等雜志上發(fā)表了近30篇學術(shù)論文；曾經(jīng)主持國家自然科學基金項目3項，廣東省自然科學基金項目2項。
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