A multigroup approach to delayed prion production

TL;DR

This paper extends a prion infection model to a network of neurons using a multigroup approach, deriving the basic reproduction number and analyzing disease extinction or persistence through analytical and numerical methods.

Contribution

It introduces a multigroup framework for a delayed prion model, deriving the basic reproduction number and analyzing disease dynamics in neuron networks.

Findings

Disease goes extinct when R0<1

Disease persists when R0>1

Numerical simulations support analytical results

Abstract

We generalize the model proposed in [Adimy, Babin, Pujo-Menjouet, \emph{SIAM Journal on Applied Dynamical Systems} (2022)] for prion infection to a network of neurons. We do so by applying a so-called \emph{multigroup approach} to the system of Delay Differential Equations (DDEs) proposed in the aforementioned paper. We derive the classical threshold quantity $\mathcal{R}_0$, \textit{i.e.} the basic reproduction number, exploiting the fact that the DDEs of our model qualitatively behave like Ordinary Differential Equations (ODEs) when evaluated at the Disease Free Equilibrium. We prove analytically that the disease naturally goes extinct when $\mathcal{R}_0<1$, whereas it persists when $\mathcal{R}_0>1$. We conclude with some selected numerical simulations of the system, to illustrate our analytical results.