Dynamics for a Diffusive Epidemic Model With a Free Boundary: Spreading Speed

ABSTRACT We study the spreading speed of a diffusive epidemic model proposed by Li et al. [Dynamics for a diffusive epidemic model with a free boundary: spreading‐vanishing dichotomy, Zeitschrift für Angewandte Mathematik und Physik 75 (2024): Article No. 202], where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading‐vanishing dichotomy and some sharp criteria were obtained in Li et al. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component . Our arguments depend crucially on some detailed understandings for a corresponding semi‐wave problem and a steady‐state problem.