Simulating Phase Transitions and Control Measures for Network Epidemics Caused by Infections with Presymptomatic, Asymptomatic, and Symptomatic Stages

We investigate phase transitions associated with three control methods forepidemics on small world networks. Motivated by the behavior of SARS-CoV-2, weconstruct a theoretical SIR model of a virus that exhibits presymptomatic,asymptomatic, and symptomatic stages in two possible pathways. Usingagent-based simulations on small world networks, we observe phase transitionsfor epidemic spread related to: 1) Global social distancing with a fixedprobability of adherence. 2) Individually initiated social isolation when athreshold number of contacts are infected. 3) Viral shedding rate. The primarydriver of total number of infections is the viral shedding rate, withprobability of social distancing being the next critical factor. Individuallyinitiated social isolation was effective when initiated in response to a singleinfected contact. For each of these control measures, the total number ofinfections exhibits a sharp phase transition as the strength of the measure isvaried.