Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies

Antoine Perasso (1) , Ulrich Razafison (2)

1 LCE - Laboratoire Chrono-environnement (UMR 6249)
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this article is studied an infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination. We perform the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds, such as the basic reproduction number, that ensure extinction or persistence of the disease in the contagion process. Moreover, a numerical scheme adapted to the model is developped and analyzed. This scheme is then used to illustrate the model with simulations, applying this last to the transmission of prion pathologies.

Mots clés: Structured population dynamics; epidemic models; transport equations; nonlinear PDE; stability analysis; finite volume method

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Perasso, Ulrich Razafison. Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies. 2013. ⟨hal-00907819v1⟩