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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2023

A multigroup approach to delayed prion production

Résumé

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.
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hal-04162164 , version 1 (08-01-2024)

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Mostafa Adimy, Abdennasser Chekroun, Laurent Pujo-Menjouet, Mattia Sensi. A multigroup approach to delayed prion production. Discrete and Continuous Dynamical Systems - Series B, 2023, ⟨10.3934/dcdsb.2023209⟩. ⟨hal-04162164⟩
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