学术报告会：Asymptotic behavior of an epidemic model with infinitely many variants

报告题目：Asymptotic behavior of an epidemic model with infinitely many variants

报 告 人：Quentin Griette (法国诺曼底-勒阿弗尔大学  教授)

报告时间：2026年4月20日周一14：00

报告地点：S3-313

Abstract：We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that case and corresponds to a threshold between the persistence ($\mathcal{R}_0>1$) and the extinction ($\mathcal{R}_0\leq 1$) of the pathogen. When $\mathcal{R}_0>1$ and the maximal fitness is attained by at least one variant, we show that the systems reaches an equilibrium state that can be explicitly determined from the initial data. When $\mathcal{R}_0>1$ but none of the variants attain the maximal fitness, the situation is more intricate. We show that, in general, the pathogen is uniformly persistent and all families of variants that have a uniformly dominated fitness eventually get extinct. We derive a condition under which the total mass of pathogens converges to a limit which can be computed explicitly. We also find counterexamples that show that, when our condition is not met, the total mass of pathogen may converge to an unexpected value, or the system can even reach an eternally transient behaviour where the mass oscillates between several values. We illustrate our results with numerical simulation.

个人简介：

Quentin Griette教授，法国诺曼底-勒阿弗尔大学终身教授，其于2017年师从Matthieu Alfaro教授获蒙彼利埃大学博士学位，2017-2018年在日本学术振兴会跟随著名数学家Hiroshi Matano教授从事博士后合作研究，其主要研究领域包括微分方程与动力系统及其在生物中的应用，目前主持法国国家研究机构（ANR）资助的NONLOCAL等项目，已在多个著名数学顶级SCI期刊SIAM J. Appl. Math., J. Funct. Anal, Trans. Amer. Math. Soc., Math. Models Methods Appl. Sci., J. Math. Biol., J. Differential Equations, Nonlinearity等发表多篇论文及学术专著《Differential equations and population dynamics I. Introductory approaches》(微分方程与种群动力学：基本方法)，给出了生物数学领域中一些有影响力的结果。