Global stability for the prion equation with general incidence

TL;DR

This paper analyzes the stability of steady states in a generalized prion equation using spectral gap techniques and a reduction method, contributing to understanding prion disease dynamics.

Contribution

It introduces a novel stability analysis for the prion equation with general incidence, combining spectral gap results and a reduction to ODEs.

Findings

Established conditions for stability of steady states.

Extended previous models to more general incidence terms.

Provided a framework for analyzing prion equations with advanced mathematical tools.

Abstract

We consider the so-called prion equation with the general incidence term introduced in [Greer et al., 2007], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [Gabriel, 2012]. The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.