Application of the Time Derivative (TD) Method for Early Alert of Influenza Epidemics.

BACKGROUND: In order to minimize the spread of seasonal influenza epidemic to communities worldwide, the Korea Disease Control and Prevention Agency has issued an influenza epidemic alert using the influenza epidemic threshold formula based on the results of the influenza-like illness (ILI) rate. However, unusual changes have occurred in the pattern of respiratory infectious diseases, including seasonal influenza, after the coronavirus disease 2019 (COVID-19) pandemic. As a result, the importance of detecting the onset of an epidemic earlier than the existing epidemic alert system is increasing. Accordingly, in this study, the Time Derivative (TD) method was suggested as a supplementary approach to the existing influenza alert system for the early detection of seasonal influenza epidemics. METHODS: The usefulness of the TD method as an early epidemic alert system was evaluated by applying the ILI rate for each week during past seasons when seasonal influenza epidemics occurred, ranging from the 2013-2014 season to the 2022-2023 season to compare it with the issued time of the actual influenza epidemic alert. RESULTS: As a result of applying the TD method, except for the two seasons (2020-2021 season and 2021-2022 season) that had no influenza epidemic, an influenza early epidemic alert was suggested during the remaining seasons, excluding the 2017-2018 and 2022-2023 seasons. CONCLUSION: The TD method is a time series analysis that enables early epidemic alert in real-time without relying on past epidemic information. It can be considered as an alternative approach when it is challenging to set an epidemic threshold based on past period information. This situation may arise when there has been a change in the typical seasonal epidemic pattern of various respiratory viruses, including influenza, following the COVID-19 pandemic.

Evaluation of COVID-19 intervention policies in South Korea using the stochastic individual-based model.

The COVID-19 pandemic has swept the globe, and countries have responded with various intervention policies to prevent its spread. In this study, we aim to analyze the effectiveness of intervention policies implemented in South Korea. We use a stochastic individual-based model (IBM) with a synthetic population to simulate the spread of COVID-19. Using statistical data, we make the synthetic population and assign sociodemographic attributes to each individual. Individuals go about their daily lives based on their assigned characteristics, and encountering infectors in their daily lives stochastically determines whether they are infected. We reproduce the transmission of COVID-19 using the IBM simulation from November 2020 to February 2021 when three phases of increasingly stringent intervention policies were implemented, and then assess their effectiveness. Additionally, we predict how the spread of infection would have been different if these policies had been implemented in January 2022. This study offers valuable insights into the effectiveness of intervention policies in South Korea, which can assist policymakers and public health officials in their decision-making process.

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.

Forecasting Hospital Visits Due to Influenza Based on Emergency Department Visits for Fever: A Feasibility Study on Emergency Department-Based Syndromic Surveillance.

This study evaluated the use of chief complaint data from emergency departments (EDs) to detect the increment of influenza cases identified from the nationwide medical service usage and developed a forecast model to predict the number of patients with influenza using the daily number of ED visits due to fever. The National Health Insurance Service (NHIS) and the National Emergency Department Information System (NEDIS) databases from 2015 to 2019 were used. The definition of fever included having an initial body temperature ≥ 38.0 °C at an ED department or having a report of fever as a patient's chief complaint. The moving average number of visits to the ED due to fever for the previous seven days was used. Patients in the NHIS with the International Classification of Diseases-10 codes of J09, J10, or J11 were classified as influenza cases, with a window duration of 100 days, assuming the claims were from the same season. We developed a forecast model according to an autoregressive integrated moving average (ARIMA) method using the data from 2015 to 2017 and validated it using the data from 2018 to 2019. Of the 29,142,229 ED visits from 2015 to 2019, 39.9% reported either a fever as a chief complaint or a ≥38.0 °C initial body temperature at the ED. ARIMA (1,1,1) (0,0,1)7 was the most appropriate model for predicting ED visits due to fever. The mean absolute percentage error (MAPE) value showed the prediction accuracy of the model. The correlation coefficient between the number of ED visits and the number of patients with influenza in the NHIS up to 14 days before the forecast, with the exceptions of the eighth, ninth, and twelfth days, was higher than 0.70 (p-value = 0.001). ED-based syndromic surveillances of fever were feasible for the early detection of hospital visits due to influenza.

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.

Early detection of influenza outbreak using time derivative of incidence.

For mitigation strategies of an influenza outbreak, it can be helpful to understand the characteristics of regional and age-group-specific spread. In South Korea, however, there has been no official statistic related to it. In this study, we extract the time series of influenza incidence from National Health Insurance Service claims database, which consists of all medical and prescription drug-claim records for all South Korean population. The extracted time series contains the number of new patients by region (250 city-county-districts) and age-group (0-4, 5-19, 20-64, 65+) within a week. The number of cases of influenza (2009-2017) is 12,282,356. For computing an onset of influenza outbreak by region and age-group, we propose a novel method for early outbreak detection, in which the onset of outbreak is detected as a sudden change in the time derivative of incidence. The advantage of it over the cumulative sum and the exponentially weighted moving average control charts, which have been widely used for the early outbreak detection of infectious diseases, is that information on the previous non-epidemic periods are not necessary. Then, we show that the metro area and 5-19 age-group are earlier than the rural area and other age-groups for the start of the influenza outbreak. Also, the metro area and 5-19 age-group peak earlier than the rural area and other age-groups. These results would be helpful to design a surveillance system for timely early warning of an influenza outbreak in South Korea.

Time-variant reproductive number of COVID-19 in Seoul, Korea.

OBJECTIVES: To estimate time-variant reproductive number (Rt) of coronavirus disease 19 based on either number of daily confirmed cases or their onset date to monitor effectiveness of quarantine policies. METHODS: Using number of daily confirmed cases from January 23, 2020 to March 22, 2020 and their symptom onset date from the official website of the Seoul Metropolitan Government and the district office, we calculated Rt using program R's package "EpiEstim". For asymptomatic cases, their symptom onset date was considered as -2, -1, 0, +1, and +2 days of confirmed date. RESULTS: Based on the information of 313 confirmed cases, the epidemic curve was shaped like 'propagated epidemic curve'. The daily Rt based on Rt_c peaked to 2.6 on February 20, 2020, then showed decreased trend and became <1.0 from March 3, 2020. Comparing both Rt from Rt_c and from the number of daily onset cases, we found that the pattern of changes was similar, although the variation of Rt was greater when using Rt_c. When we changed assumed onset date for asymptotic cases (-2 days to +2 days of the confirmed date), the results were comparable. CONCLUSIONS: Rt can be estimated based on Rt_c which is available from daily report of the Korea Centers for Disease Control and Prevention. Estimation of Rt would be useful to continuously monitor the effectiveness of the quarantine policy at the city and province levels.

Intervention effects in the transmission of COVID-19 depending on the detection rate and extent of isolation.

OBJECTIVE: In 2020, the coronavirus disease 2019 (COVID-19) respiratory infection is spreading in Korea. In order to prevent the spread of an infectious disease, infected people must be quickly identified and isolated, and contact with the infected must be blocked early. This study attempted to verify the intervention effects on the spread of an infectious disease by using these measures in a mathematical model. METHODS: We used the susceptible-infectious-recovery (SIR) model for a virtual population group connected by a special structured network. In the model, the infected state (I) was divided into I in which the infection is undetected and Ix in which the infection is detected. The probability of transitioning from an I state to Ix can be viewed as the rate at which an infected person is found. We assumed that only those connected to each other in the network can cause infection. In addition, this study attempted to evaluate the effects of isolation by temporarily removing the connection among these people. RESULTS: In Scenario 1, only the infected are isolated; in Scenario 2, those who are connected to an infected person and are also found to be infected are isolated as well. In Scenario 3, everyone connected to an infected person are isolated. In Scenario 3, it was possible to effectively suppress the infectious disease even with a relatively slow rate of diagnosis and relatively high infection rate. CONCLUSION: During the epidemic, quick identification of the infected is helpful. In addition, it was possible to quantitatively show through a simulation evaluation that the management of infected individuals as well as those who are connected greatly helped to suppress the spread of infectious diseases.

Individual-based simulation model for COVID-19 transmission in Daegu, Korea.

OBJECTIVES: The aims of this study were to obtain insights into the current coronavirus disease 2019 (COVID-19) epidemic in the city of Daegu, which accounted for 6,482 of the 9,241 confirmed cases in Korea as of March 26, 2020, to predict the future spread, and to analyze the impact of school opening. METHODS: Using an individual-based model, we simulated the spread of COVID-19 in Daegu. An individual can be infected through close contact with infected people in a household, at work/school, and at religious and social gatherings. We created a synthetic population from census sample data. Then, 9,000 people were randomly selected from the entire population of Daegu and set as members of the Shincheonji Church. We did not take into account population movements to and from other regions in Korea. RESULTS: Using the individual-based model, the cumulative confirmed cases in Daegu through March 26, 2020, were reproduced, and it was confirmed that the hotspot, i.e., the Shincheonji Church had a different probability of infection than non-hotspot, i.e., the Daegu community. For 3 scenarios (I: school closing, II: school opening after April 6, III: school opening after April 6 and the mean period from symptom onset to hospitalization increasing to 4.3 days), we predicted future changes in the pattern of COVID-19 spread in Daegu. CONCLUSIONS: Compared to scenario I, it was found that in scenario III, the cumulative number of patients would increase by 107 and the date of occurrence of the last patient would be delayed by 92 days.

Effects of temperature, humidity, and diurnal temperature range on influenza incidence in a temperate region.

BACKGROUND: The effect of temperature and humidity on the incidence of influenza may differ by climate region. In addition, the effect of diurnal temperature range on influenza incidence is unclear, according to previous study findings. OBJECTIVES: The aim of this study was to analyze the effects of temperature, humidity, and diurnal temperature range on the incidence of influenza in Seoul, Republic of Korea, which is located in a temperate region. METHODS: We used Korean National Health insurance data to assess the weekly influenza incidence between 2010 and 2016, and used meteorological data from Seoul. To investigate the effect of temperature, relative humidity, and diurnal temperature range levels on influenza incidence, we used a distributed lag non-linear model. RESULTS: The risk of influenza incidence was significantly increased with low daily temperatures of 0-5°C and low (30%-40%) or high (70%) relative humidity. We found a positive significant association between diurnal temperature range and influenza incidence in this study. CONCLUSIONS: Influenza incidence increased with low temperature and low/high humidity in a temperate region. Influenza incidence also increased with high diurnal temperature range, after considering temperature and humidity.

Oscillation death in coupled counter-rotating identical nonlinear oscillators.

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-parity-time-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Exceptional points in coupled dissipative dynamical systems.

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

Transport control in a deterministic ratchet system.

We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of the deterministic inertia ratchet system. Also, we show that the extended delay feedback method can be utilized for separation of particles in the deterministic inertia ratchet system as a particle's initial condition varies.

Current reversal with type-I intermittency in deterministic inertia ratchets.

The intermittency is investigated when the current reversal occurs in a deterministic inertia ratchet system. To determine which type the intermittency belongs to, we obtain the return map of velocities of particle by using stroboscopic recordings, and by numerically calculating the distribution of the average laminar length . The distribution follows the scaling law of proportional to epsilon(-1/2), the characteristic relation of type-I intermittency.