Abstract
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.
Highlights
The SARS-CoV-2 virus that has spread throughout the globe has created societal disruption and had a massive impact on global health [1]
While many models related to SARS-CoV-2 are designed to be forecasting tools, our study is intended as a contribution to the theoretical literature regarding qualitative aspects of control measures for viruses with these pathways of disease progression
We develop a theoretical model in which we investigate how three types of control measures are associated with sharp phase transitions for the total number of infected individuals
Summary
The SARS-CoV-2 virus that has spread throughout the globe has created societal disruption and had a massive impact on global health [1]. Public policy and human behavior are currently the only tools that are available to mitigate the spread [2]. A fundamental characteristic of SARS-CoV-2 is that after an individual is exposed, that individual passes through an extended presymptomatic stage followed by either an asymptomatic or symptomatic stage [3]. Our goal in this work is to construct a theoretical network disease model with these qualities and investigate phase transitions associated with three types of control measures. While many models related to SARS-CoV-2 are designed to be forecasting tools, our study is intended as a contribution to the theoretical literature regarding qualitative aspects of control measures for viruses with these pathways of disease progression.
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