Infinite dimensional metapopulation SIS model with generalized incidence rate

TL;DR

This paper analyzes an advanced infinite-dimensional SIS epidemiological model with a generalized incidence rate, characterizing equilibria and convergence properties, and extending results to models with reservoirs or immigration.

Contribution

It generalizes the infinite-dimensional SIS model by incorporating a broader incidence rate and provides a comprehensive analysis of equilibria and convergence behaviors.

Findings

Existence of endemic equilibria when the basic reproduction number exceeds 1

Characterization of all equilibria using transmission operator decomposition

Proven convergence of infected proportion to a unique equilibrium

Abstract

We consider an infinite-dimension SIS model introduced by Delmas, Dronnier and Zitt, with a more general incidence rate, and study its equilibria. Unsurprisingly, there exists at least one endemic equilibrium if and only if the basic reproduction number is larger than 1. When the pathogen transmission exhibits one way propagation, it is possible to observe different possible endemic equilibria. We characterize in a general setting all the equilibria, using a decomposition of the space into atoms, given by the transmission operator. We also prove that the proportion of infected individuals converges to an equilibrium, which is uniquely determined by the support of the initial condition.We extend those results to infinite-dimensional SIS models with reservoir or with immigration.