Travelling waves for delayed reaction–diffusion systems with semi-mixed quasi-monotonicity: a prion disease model
Abstract
Abstract In this paper, we study the existence of travelling wave solutions in a system of delayed reaction–diffusion equations (DRDEs) satisfying the semi-mixed quasi-monotonicity condition. As an application, we analyse a mathematical model of a prion disease, whose reaction terms fall within the framework of our approach. Under biologically motivated assumptions, we construct appropriate upper and lower solutions and apply an existence theorem tailored to such systems. We then use the contracting rectangle method to describe the asymptotic behaviour of the solutions as they converge to a non-trivial positive equilibrium. The paper concludes with numerical simulations.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Differential Equations Analysis
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
- Volume
- 482
- Issue
- 2332
- Pages
- 20250630
- Publication date
- 15 February 2026
- Language
- EN