题    目：Dynamics of Spatial Propagation in May-Nowak Viral Model with Local-Nonlocal Hybrid Diffusion

主讲人：王杰

单    位：兰州理工大学

时    间：2025年10月21日19:00

腾讯ID：116-111-279

摘    要：This study investigates the existence and non-existence of traveling wave solutions in a reaction-diffusion May-Nowak system with hybrid diffusion to explore the spatial dynamics of viral spread between host cells. A critical wave speed threshold c* is defined to determine the existence of traveling wave solutions when the basic reproduction number R0 > 1. By employing the method of upper and lower solutions combined with Schauder's fixed point theorem, it is demonstrated that traveling wave solutions connecting the uninfected and infected steady states exist for every wave speed c ≥ c*. Conversely, utilizing the negative one-sided Laplace transform method, the non-existence of traveling waves is rigorously established for 0 < c < c*. Furthermore, it is proven that no traveling wave solutions exist when R0 ≤ 1. To address the practical characteristics of mixed diffusion, novel coupled numerical algorithms are developed to analyze viral waves and their asymptotic spreading speeds. The results unequivocally indicate that the inclusion of nonlocal diffusion significantly accelerates viral infection.

    Building upon this foundation, the influence of inflammatory responses on viral propagation is examined. The proposed model innovatively incorporates time delays and spatial heterogeneity, thereby providing a more accurate characterization of viral transmission dynamics. Through rigorous mathematical analysis, the criteria for the existence and non-existence of forced traveling wave solutions are refined. Numerical simulations reveal that spatiotemporal heterogeneity induced by inflammation substantially affects both the speed of viral spread and infection dynamics.

简    介： 王杰，兰州理工大学副教授，硕士生导师，主要从事微分方程，特别是变区域上反应扩散方程的研究工作，研究的主题一方面是探索生物数学特别是数学生态学当中自由边界问题的建模、分析和应用，另一方面则尝试揭示种群空间扩张行为的定性特征和生物含义。目前已在Journal of Differential Equations，Journal of Dynamics and Differential Equations，Zeitschrift Angewandte Mathematik und Physik 和Nonlinear Analysis Real World Applications等杂志上发表论文10余篇； 现主持国家自然科学基金、省自然科学基金项目各1项，主持完成国家自然科学基金1项，作为主要参与人完成国家自然科学基金2项。