Special Session 64: Reaction-diffusion equations and applications

Spreading speeds of a nonlocal diffusive epidemic model with a new weight-type free boundary condition
Rong Wang
Lanzhou University
Peoples Rep of China
Co-Author(s):    Xin Long
Abstract:
This talk is concerned with the spreading behavior of a nonlocal epidemic model with new weight-type free boundary conditions. Such conditions were originally introduced for the Fisher--KPP equation in Du et al. (submitted, 2024), and they are used here to describe the expansion of the epidemic region under weighted population effects. This work continues a previous study by Long and Wang (submitted, 2026), in which the model was shown to be well posed and to exhibit a spreading--vanishing dichotomy in its long-time dynamics, together with a threshold condition for finite spreading speed. The main focus of this talk is the accelerated spreading case, where the spreading speed is infinite. For some typical classes of kernel and weight functions, I will present the precise rates of accelerated expansion of the epidemic region. This talk is based on joint work with Dr. Xin Long.