Spreading properties for SIR models on homogeneous trees

Christophe Besse (1) , Grégory Faye (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the interactions within the population of infected individuals. When the degree is one, the homogeneous tree is nothing but the standard lattice on the integers and our model reduces to a SIR model with discrete diffusion for which the spreading properties are very similar to the continuous case. On the other hand, when the degree is larger than two, we observe some new features in the spreading properties. Most notably, there exists a critical value of the strength of interactions above which spreading of the epidemic in the tree is no longer possible.

Mots clés: SIR model; homogeneous tree; spreading speed; epidemic invasion; discrete reaction-diffusion equations

Domaines: Equations aux dérivées partielles [math.AP]; Evolution [q-bio.PE]

Christophe Besse, Grégory Faye. Spreading properties for SIR models on homogeneous trees. Bulletin of Mathematical Biology, 2021. ⟨hal-03251359⟩