Active Risk Aversion in SIS Epidemics on Networks

We present and analyze an actively controlled SIS (actSIS) model of interconnected populations to study how risk aversion strategies affect network epidemics. A population using a risk aversion strategy reduces its contact rate with other populations when it perceives an increase in infection risk. The network actSIS model relies on two distinct networks. One is a physical network that defines which populations come into contact with which others, thus how infection spreads. The other is a communication network, such as an online social network, that defines which populations observe the infection level of which others, thus how information spreads. We prove that the system exhibits a transcritical bifurcation where an endemic equilibrium (EE) emerges. For regular graphs, we prove that the endemic infection level is uniform across populations and reduced by the risk aversion strategy, relative to the network SIS endemic level. We show that when communication is sufficiently sparse, this initially stable EE loses stability in a secondary bifurcation. Simulations show that a new stable solution emerges with nonuniform infection levels.