Estimating the instantaneous reproduction number (Rt) by using particle filter.

Background: Monitoring the transmission of coronavirus disease 2019 (COVID-19) requires accurate estimation of the effective reproduction number (Rt). However, existing methods for calculating Rt may yield biased estimates if important real-world factors, such as delays in confirmation, pre-symptomatic transmissions, or imperfect data observation, are not considered. Method: To include real-world factors, we expanded the susceptible-exposed-infectious-recovered (SEIR) model by incorporating pre-symptomatic (P) and asymptomatic (A) states, creating the SEPIAR model. By utilizing both stochastic and deterministic versions of the model, and incorporating predetermined time series of Rt, we generated simulated datasets that simulate real-world challenges in estimating Rt. We then compared the performance of our proposed particle filtering method for estimating Rt with the existing EpiEstim approach based on renewal equations. Results: The particle filtering method accurately estimated Rt even in the presence of data with delays, pre-symptomatic transmission, and imperfect observation. When evaluating via the root mean square error (RMSE) metric, the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided, and substantially better when Rt exhibited short-term fluctuations and the data was right truncated. Conclusions: The SEPIAR model, in conjunction with the particle filtering method, offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies. This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.

Subcritical Transmission in the Early Stage of COVID-19 in Korea.

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

Rapid transmission of coronavirus disease 2019 within a religious sect in South Korea: A mathematical modeling study.

Rapid transmission of coronavirus disease 2019 (COVID-19) was observed in the Shincheonji Church of Jesus, a religious sect in South Korea. The index case was confirmed on February 18, 2020 in Daegu City, and within two weeks, 3081 connected cases were identified. Doubling times during these initial stages (i.e., February 18 - March 2) of the outbreak were less than 2 days. A stochastic model fitted to the time series of confirmed cases suggests that the basic reproduction number (R0) of COVID-19 was 8.5 [95% credible interval (CrI): 6.3, 10.9] among the church members, whereas (R0 = 1.9 [95% CrI: 0.4, 4.4]) in the rest of the population of Daegu City. The model also suggests that there were already 4 [95% CrI: 2, 11] undetected cases of COVID-19 on February 7 when the index case reportedly presented symptoms. The Shincheonji Church cluster is likely to be emblematic of other outbreak-prone populations where R0 of COVID-19 is higher. Understanding and subsequently limiting the risk of transmission in such high-risk places is key to effective control.