  We present and analyze an actively controlled
Susceptible-Infected-Susceptible (actSIS) model of interconnected populations
to study how risk aversion strategies, such as social distancing, 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 contact network that defines which populations come into contact with
which other populations and 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 other populations and thus how
information spreads. We prove that the model, with these two networks and
populations using risk aversion strategies, exhibits a transcritical
bifurcation in which an endemic equilibrium 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 equilibrium loses stability in a secondary bifurcation. Simulations show
that a new stable solution emerges with nonuniform infection levels.
