  We investigate phase transitions associated with three control methods for
epidemics on small world networks. Motivated by the behavior of SARS-CoV-2, we
construct a theoretical SIR model of a virus that exhibits presymptomatic,
asymptomatic, and symptomatic stages in two possible pathways. Using
agent-based simulations on small world networks, we observe phase transitions
for epidemic spread related to: 1) Global social distancing with a fixed
probability of adherence. 2) Individually initiated social isolation when a
threshold number of contacts are infected. 3) Viral shedding rate. The primary
driver of total number of infections is the viral shedding rate, with
probability of social distancing being the next critical factor. Individually
initiated social isolation was effective when initiated in response to a single
infected contact. For each of these control measures, the total number of
infections exhibits a sharp phase transition as the strength of the measure is
varied.
