Suppressing the endemic equilibrium in SIS epidemics: A state dependent approach

TL;DR

This paper introduces a state-dependent approach to control SIS epidemic models on networks, demonstrating how social distancing informed by infection rates can keep infection levels below 50% and eliminate endemic equilibrium.

Contribution

It proposes a modified SIS model with a state-dependent interaction parameter and establishes conditions for disease eradication and endemic stability based on spectral radius analysis.

Findings

Infection fraction can be maintained below 50% with proper social distancing.

Spectral radius conditions determine convergence to healthy or endemic states.

The model provides a control strategy to suppress endemic equilibrium.

Abstract

This paper considers the susceptible-infected-susceptible (SIS) epidemic model with an underlying network structure among subpopulations and focuses on the effect of social distancing to regulate the epidemic level. We demonstrate that if each subpopulation is informed of its infection rate and reduces interactions accordingly, the fraction of the subpopulation infected can remain below half for all time instants. To this end, we first modify the basic SIS model by introducing a state dependent parameter representing the frequency of interactions between subpopulations. Thereafter, we show that for this modified SIS model, the spectral radius of a suitably-defined matrix being not greater than one causes all the agents, regardless of their initial sickness levels, to converge to the healthy state; assuming non-trivial disease spread, the spectral radius being greater than one leads to the existence of a unique endemic equilibrium, which is also asymptotically stable. Finally, by leveraging the aforementioned results, we show that the fraction of (sub)populations infected never exceeds half.