Exploring the role of superspreading events in SARS-CoV-2 outbreaks

Abstract

The novel coronavirus SARS-CoV-2 emerged in 2019 and subsequently spread throughout the world, causing over 600 million cases and 6 million deaths as of September 7th, 2022. Superspreading events (SSEs), defined here as public or social events that result in multiple infections over a short time span, have contributed to SARS-CoV-2 spread. In this work, we compare the dynamics of SSE-dominated SARS-CoV-2 outbreaks, defined here as outbreaks with relatively higher SSE rates, to the dynamics of non-SSE-dominated SARS-CoV-2 outbreaks. To accomplish this, we derive a continuous-time Markov chain (CTMC) SARS-CoV-2 model from an ordinary differential equation (ODE) SARS-CoV-2 model and incorporate SSEs using an events-based framework. We simulate our model under multiple scenarios using Gillespie's direct algorithm. The first scenario excludes hospitalization and quarantine; the second scenario includes hospitalization, quarantine, premature hospital discharge, and quarantine violation; and the third scenario includes hospitalization and quarantine but excludes premature hospital discharge and quarantine violation. We also vary quarantine violation rates. Results indicate that, with either no control or imperfect control, SSE-dominated outbreaks are more variable but less severe than non-SSE-dominated outbreaks, though the most severe SSE-dominated outbreaks are more severe than the most severe non-SSE-dominated outbreaks. We measure severity by the time it takes for 50 active infections to be achieved; more severe outbreaks do so more quickly. SSE-dominated outbreaks are also more sensitive to control measures, with premature hospital discharge and quarantine violation substantially reducing control measure effectiveness.

Keywords: Continuous-time Markov chain; Gillespie’s direct algorithm; Human behavior; SARS-CoV-2; Superspreading events.

Fig. 1

Compartmental flow diagram for the baseline COVID-19 model (1). Susceptible individuals are exposed upon initial infection, and exposed individuals are either asymptomatic or symptomatic once infectious. Asymptomatic individuals are removed upon recovery or death, while symptomatic individuals may be hospitalized or quarantined and are removed upon recovery or death. Hospitalized and quarantined individuals may be prematurely discharged from the hospital or violate quarantine and are removed upon recovery or death.

Fig. 2

(a) Distributions of stops times (NHQ) (b) Variances of stop times for NHQ (c) Probabilities of extinction for NHQ (d) Means of cumulative total of SSE- and non-SSE-related infections for NHQ; their curves are labeled as SSE and non-SSE.

Fig. 3

(a) Distributions of stops times (RHQ) (b) Variances of stop times for RHQ (c) Probabilities of extinction for RHQ (d) Means of cumulative total of SSE- and non-SSE-related infections for RHQ; their curves are labeled as SSE and non-SSE.

Fig. 4

(a) Distributions of stops times (b) Variances of stop times for IHQ (c) Probabilities of extinction for IHQ (d) Means of cumulative total of SSE- and non-SSE-related infections for IHQ; their curves are labeled as SSE and non-SSE.

Fig. 5

(a) Means of stops times for RHQ${}_{lqv}$, RHQ, and RHQ${}_{hqv}$ (b) Variances of stop times for RHQ${}_{lqv}$, RHQ, and RHQ${}_{hqv}$ (c) Probabilities of extinction for RHQ${}_{lqv}$, RHQ, and RHQ${}_{hqv}$ (d) Means of cumulative total of SSE-related infections for RHQ${}_{lqv}$, RHQ, and RHQ${}_{hqv}$. Curves for RHQ${}_{lqv}$, RHQ, and RHQ${}_{hqv}$ are labeled as low quarantine violation, medium quarantine violation, and high quarantine violation.

Fig. 6

(a) Variances of stop times across scenarios (b) Probabilities of extinction across scenarios (c) Means of total cumulative SSE-related infections across scenarios.