Epidemic model on a network: analysis and applications to COVID-19

F Bustamante-Castañeda , Jean-Guy G Caputo (1) , G Cruz-Pacheco , A Knippel (1) , F Mouatamide (2)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 UCA - Université Cadi Ayyad [Marrakech]

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic.

Domaines: Formation de Structures et Solitons [nlin.PS]; Biodiversité et Ecologie

F Bustamante-Castañeda, Jean-Guy G Caputo, G Cruz-Pacheco, A Knippel, F Mouatamide. Epidemic model on a network: analysis and applications to COVID-19. 2020. ⟨hal-02558195⟩