  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.
