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.