Analysis of Superspreading Potential from Transmission Clusters of COVID-19 in South Korea

The COVID-19 pandemic has been spreading worldwide with more than 246 million confirmed cases and 5 million deaths across more than 200 countries as of October 2021. There have been multiple disease clusters, and transmission in South Korea continues. We aim to analyze COVID-19 clusters in Seoul from 4 March to 4 December 2020. A branching process model is employed to investigate the strength and heterogeneity of cluster-induced transmissions. We estimate the cluster-specific effective reproduction number Reff and the dispersion parameter κ using a maximum likelihood method. We also compute Rm as the mean secondary daily cases during the infection period with a cluster size m. As a result, a total of 61 clusters with 3088 cases are elucidated. The clusters are categorized into six groups, including religious groups, convalescent homes, and hospitals. The values of Reff and κ of all clusters are estimated to be 2.26 (95% CI: 2.02–2.53) and 0.20 (95% CI: 0.14–0.28), respectively. This indicates strong evidence for the occurrence of superspreading events in Seoul. The religious groups cluster has the largest value of Reff among all clusters, followed by workplaces, schools, and convalescent home clusters. Our results allow us to infer the presence or absence of superspreading events and to understand the cluster-specific characteristics of COVID-19 outbreaks. Therefore, more effective suppression strategies can be implemented to halt the ongoing or future cluster transmissions caused by small and sporadic clusters as well as large superspreading events.

A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions

A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is governed by a multi-type continuous-time branching process. The limiting behaviour of the network is studied by mathematical methods. We prove that the number of triangles and edges have the same magnitude on the event of non-extinction, and it is eαt, where α is the Malthusian parameter. The probability of the extinction and the degree process of a fixed vertex are also studied. The results are illustrated by simulations.

Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination

We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.

Homogeneous Branching Processes with Non-Homogeneous Immigration

The stationary immigration has a limited effect over the asymptotic behavior of the underlying branching process. It affects mostly the limiting distribution and the life-period of the process. In contrast, if the immigration rate changes over time, then the asymptotic behavior of the process is significantly different and a variety of new phenomena are observed. In this review we discuss branching processes with time non-homogeneous immigration. Our goal is to help researchers interested in the topic to familiarize themselves with the current state of research.

Likelihood of infecting or getting infected with COVID-19 as a function of vaccination status, as investigated with a stochastic model for New Zealand (Aotearoa)

Aim: The New Zealand government is transitioning from the Alert Level framework, which relies on government action and population level controls, to the COVID-19 Protection Framework, which relies on vaccination rates and allows for greater freedoms (for the vaccinated). As restrictions are eased, there is significant interest in understanding the relative risk of spreading COVID-19 posed by unvaccinated and vaccinated individuals. Methods: A stochastic branching process model is used to simulate the spread of COVID-19 for outbreaks seeded by unvaccinated or vaccinated individuals. The likelihood of infecting or getting infected with COVID-19 is calculated based on vaccination status. Results: A vaccinated traveler infected with COVID-19 is 9x less likely to seed an outbreak than an unvaccinated traveler infected with COVID-19. For a vaccination rate of 50%, unvaccinated individuals are responsible for 87% of all infections whereas 3% of infections are from vaccinated to vaccinated. When normalized by population, a vaccinated individual is 6.8x more likely to be infected by an unvaccinated individual than by a vaccinated individual. For a total population vaccination rate of 78.7%, which is equivalent to the 90% vaccination target for the eligible population (over 12 years old), this means that vaccinated individuals are 1.9x more likely to be infected by an unvaccinated individual than by a vaccinated, even though there are 3.7x more vaccinated individuals in the population. Conclusions: This work demonstrates that most new infections are caused by unvaccinated individuals. These simulations illustrate the importance of vaccination in stopping individuals from becoming infected with COVID-19 and in preventing onward transmission.

Simulating the impact of vaccination rates on the initial stages of a COVID-19 outbreak in New Zealand (Aotearoa) with a stochastic model

Aim: The August 2021 COVID-19 outbreak in Auckland has caused the New Zealand government to transition from an elimination strategy to suppression, which relies heavily on high vaccination rates in the population. As restrictions are eased and as COVID-19 leaks through the Auckland boundary, there is a need to understand how different levels of vaccination will impact the initial stages of COVID-19 outbreaks that are seeded around the country. Method: A stochastic branching process model is used to simulate the initial spread of a COVID-19 outbreak for different vaccination rates. Results: High vaccination rates are effective at minimizing the number of infections and hospitalizations. Increasing vaccination rates from 20% (approximate value at the start of the August 2021 outbreak) to 80% (approximate proposed target) of the total population can reduce the median number of infections that occur within the first four weeks of an outbreak from 1011 to 14 (25th and 75th quantiles of 545-1602 and 2-32 for V=20% and V=80%, respectively). As the vaccination rate increases, the number of breakthrough infections (infections in fully vaccinated individuals) and hospitalizations of vaccinated individuals increases. Unvaccinated individuals, however, are 3.3x more likely to be infected with COVID-19 and 25x more likely to be hospitalized. Conclusion: This work demonstrates the importance of vaccination in protecting individuals from COVID-19, preventing high caseloads, and minimizing the number of hospitalizations and hence limiting the pressure on the healthcare system.