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- Title
A multigroup approach to delayed prion production.
- Authors
Adimy, Mostafa; Chekroun, Abdennasser; Pujo-Menjouet, Laurent; Sensi, Mattia
- Abstract
We generalize the model proposed in [Adimy, Babin, Pujo-Menjouet, SIAM Journal on Applied Dynamical Systems (2022)] for prion infection to a network of neurons. We do so by applying a so-called multigroup approach to the system of Delay Differential Equations (DDEs) proposed in the aforementioned paper. We derive the classical threshold quantity $ \mathcal{R}_0 $, 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.
- Subjects
DELAY differential equations; BASIC reproduction number; PRIONS; ORDINARY differential equations; PRION diseases
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2024, Vol 29, Issue 7, p1
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2023209