Critical behavior of the SIS epidemic model with time-dependent infection rate

TL;DR

This paper investigates a modified SIS epidemic model with an exponentially decaying infection rate that saturates, revealing a critical decay rate for persistent infection and suggesting an upper critical dimension of 6, similar to the SIR model.

Contribution

It introduces a novel SIS model with a time-dependent infection rate and analyzes its critical behavior through mean-field theory and simulations.

Findings

Existence of a critical decay rate (l) for sustained infection.

Upper critical dimension is 6, like the SIR model.

Model maps to ordinary percolation at criticality.

Abstract

In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $\lambda$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate $\epsilon_{c}(l)$ above which a finite fraction of the population becomes permanently infected. From the mean-field solution and computer simulations on hypercubic lattices we find evidences that the upper critical dimension is 6 like in the SIR model, which can be mapped in ordinary percolation.