Risk estimation of lifted mask mandates and emerging variants using mathematical model.

Background: More than half of the population in Korea had a prior COVID-19 infection. In 2022, most nonpharmaceutical interventions, except mask-wearing indoors, had been lifted. And in 2023, the indoor mask mandates were eased. Methods: We developed an age-structured compartmental model that distinguishes vaccination history, prior infection, and medical staff from the rest of the population. Contact patterns among hosts were separated based on age and location. We simulated scenarios with the lifting of the mask mandate all at once or sequentially according to the locations. Furthermore, we investigated the impact of a new variant assuming that it has higher transmissibility and risk of breakthrough infection. Results: We found that the peak size of administered severe patients may not exceed 1100 when the mask mandate is lifted everywhere, and 800 if the mask mandate only remains in the hospital. If the mask mandate is lifted in a sequence (except hospital), then the peak size of administered severe patients may not exceed 650. Moreover, if the new variant has both higher transmissibility and immune reduction, the effective reproductive number of the new variant is approximately 3 times higher than that of the current variant, and additional interventions may be needed to keep the administered severe patients from exceeding 2,000, which is the critical level we set. Conclusion: Our findings showed that the lifting of the mask mandate, except in hospitals, would be more manageable if implemented sequentially. Considering a new variant, we found that depending on the population immunity and transmissibility of the variant, wearing masks and other interventions may be necessary for controlling the disease.

Modelling the effects of social distancing, antiviral therapy, and booster shots on mitigating Omicron spread.

As the COVID-19 situation changes because of emerging variants and updated vaccines, an elaborate mathematical model is essential in crafting proactive and effective control strategies. We propose a COVID-19 mathematical model considering variants, booster shots, waning, and antiviral drugs. We quantify the effects of social distancing in the Republic of Korea by estimating the reduction in transmission induced by government policies from February 26, 2021 to February 3, 2022. Simulations show that the next epidemic peak can be estimated by investigating the effects of waning immunity. This research emphasizes that booster vaccination should be administered right before the next epidemic wave, which follows the increasing waned population. Policymakers are recommended to monitor the waning population immunity using mathematical models or other predictive methods. Moreover, our simulations considering a new variant's transmissibility, severity, and vaccine evasion suggest intervention measures that can reduce the severity of COVID-19.

Multi-Faceted Analysis of COVID-19 Epidemic in Korea Considering Omicron Variant: Mathematical Modeling-Based Study.

BACKGROUND: The most recent variant of concern, omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness. METHODS: A mathematical model considering age-structure, vaccine, antiviral drugs, and influx of the omicron variant was developed. We estimated transmission rates among age groups using maximum likelihood estimation for the age-structured model. The impact of non-pharmaceutical interventions (NPIs; in community and border), quantified by a parameter µ in the force of infection, and vaccination were examined through a multi-faceted analysis. A theory-based endemic equilibrium study was performed to find the manageable number of cases according to omicron- and healthcare-related factors. RESULTS: By fitting the model to the available data, the estimated values of µ ranged from 0.31 to 0.73, representing the intensity of NPIs such as social distancing level. If µ < 0.55 and 300,000 booster shots were administered daily from February 3, 2022, the number of severe cases was forecasted to exceed the severe bed capacity. Moreover, the number of daily cases is reduced as the timing of screening measures is delayed. If screening measure was intensified as early as November 24, 2021 and the number of overseas entrant cases was contained to 1 case per 10 days, simulations showed that the daily incidence by February 3, 2022 could have been reduced by 87%. Furthermore, we found that the incidence number in mid-December 2021 exceeded the theory-driven manageable number of daily cases. CONCLUSION: NPIs, vaccination, and antiviral drugs influence the spread of omicron and number of severe cases in the Republic of Korea. Intensive and early screening measures during the emergence of a new variant is key in controlling the epidemic size. Using the endemic equilibrium of the model, a formula for the manageable daily cases depending on the severity rate and average length of hospital stay was derived so that the number of severe cases does not surpass the severe bed capacity.

How Important Is Behavioral Change during the Early Stages of the COVID-19 Pandemic? A Mathematical Modeling Study.

How important is the speed and intensity of behavioral change due to government policies, such as enhanced social distancing or lockdown, when an emerging infectious disease occurs? In this study, we introduce a deterministic SEIR model considering the behavior-changed susceptible group to investigate the effect of the speed and intensity of behavioral change on the transmission dynamics of COVID-19. We used epidemiological data from South Korea and Italy for the simulation study, because South Korea and Italy were the first countries to report an outbreak of COVID-19 after China and the prevention and response policy of each government were similar during the first outbreak of COVID-19. Simulation results showed that it took approximately twenty fewer days in Korea than in Italy until 90% of susceptible individuals changed their behavior during the first outbreak. It was observed that the behavior-changed susceptible individuals reduced the COVID-19 transmission rate by up to 93% in Korea and 77% in Italy. Furthermore, if the intensity and speed of behavioral change in Italy were the same as in Korea, the expected number of cumulative confirmed cases would have been reduced by approximately 95%, from 210,700 to 10,700, until the end of the lockdown period. We assumed that behavioral change is influenced by the number of confirmed cases and does not take into account social and cultural differences, as well as the state of the healthcare system, between the two countries. Our mathematical modeling showed how important the high intensity and fast speed of behavioral change to reduce the number of confirmed cases in the early period of an epidemic are.

Risk of COVID-19 transmission in heterogeneous age groups and effective vaccination strategy in Korea: a mathematical modeling study.

OBJECTIVES: This study aims to analyze the possibility and conditions of maintaining an effective reproductive number below 1 using a mathematical model. METHODS: The total population was divided into five age groups (0-17, 18-29, 30-59, 60-74, and ≥75 years). Maximum likelihood estimation (MLE) was used to estimate the transmission rate of each age group. Mathematical model simulation was conducted until December 31, 2021, by establishing various strategies for vaccination and social distancing without considering variants. RESULTS: MLE results revealed that the group aged 0-17 years had a lower risk of transmission than other age groups, and the older age group had relatively high risks of infection. If 70% of the population will be vaccinated by the end of 2021, then simulations showed that even if social distancing was eased, the effective reproductive number would remain below 1 near August if it was not at the level of the third re-spreading period. However, if social distancing was eased and it reached the level of the re-spreading period, the effective reproductive number could be below 1 at the end of 2021. CONCLUSIONS: Considering both stable and worsened situations, simulation results emphasized that sufficient vaccine supply and control of the epidemic by maintaining social distancing to prevent an outbreak at the level of the re-spreading period are necessary to minimize mortality and maintain the effective reproductive number below 1.

COVID-19 Vaccine Priority Strategy Using a Heterogenous Transmission Model Based on Maximum Likelihood Estimation in the Republic of Korea.

(1) Background: The vaccine supply is likely to be limited in 2021 due to constraints in manufacturing. To maximize the benefit from the rollout phase, an optimal strategy of vaccine allocation is necessary based on each country's epidemic status. (2) Methods: We first developed a heterogeneous population model considering the transmission matrix using maximum likelihood estimation based on the epidemiological records of individual COVID-19 cases in the Republic of Korea. Using this model, the vaccine priorities for minimizing mortality or incidence were investigated. (3) Results: The simulation results showed that the optimal vaccine allocation strategy to minimize the mortality (or incidence) was to prioritize elderly and healthcare workers (or adults) as long as the reproductive number was below 1.2 (or over 0.9). (4) Conclusion: Our simulation results support the current Korean government vaccination priority strategy, which prioritizes healthcare workers and senior groups to minimize mortality, under the condition that the reproductive number remains below 1.2. This study revealed that, in order to maintain the current vaccine priority policy, it is important to ensure that the reproductive number does not exceed the threshold by concurrently implementing nonpharmaceutical interventions.

Keeping Low Reproductive Number Despite the Rebound Population Mobility in Korea, a Country Never under Lockdown during the COVID-19 Pandemic.

Nonpharmaceutical intervention has been one of the most important strategies to prevent the spread of the SARS-CoV-2 in the communities during the COVID-19 pandemic. Korea has a unique experience that we had the first large outbreak during the early pandemic and could flatten the epidemic curve without lockdown. In this study, the effective reproductive numbers were calculated for the entire nation and Seoul (the capital city) Metropolitan Area from February 16-15 July, where 60% of the population reside. We compared the changes in population mobility data and reproductive number trends according to the changes in the government's nonpharmaceutical intervention strategy. The total daily mobility decreased when Korea had the first wave of a large outbreak in February-March 2020, which was mainly caused by the decrease of daily noncommuting mobility. However, daily commuting mobility from 16 February to 30 June 2020 was maintained at a similar level since there was no national lockdown for workers who commute between home and work. During the first half-year of 2020, Korea could control the outbreak to a manageable level without a significant decrease in daily public mobility. However, it may be only possible when the public follows personal hygiene principles and social distancing without crisis fatigue or reduced compliance.

Keeping Low Reproductive Number Despite the Rebound Population Mobility in Korea, a Country Never under Lockdown during the COVID-19 Pandemic

Nonpharmaceutical intervention has been one of the most important strategies to prevent the spread of the SARS-CoV-2 in the communities during the COVID-19 pandemic. Korea has a unique experience that we had the first large outbreak during the early pandemic and could flatten the epidemic curve without lockdown. In this study, the effective reproductive numbers were calculated for the entire nation and Seoul (the capital city) Metropolitan Area from February 16–15 July, where 60% of the population reside. We compared the changes in population mobility data and reproductive number trends according to the changes in the government’s nonpharmaceutical intervention strategy. The total daily mobility decreased when Korea had the first wave of a large outbreak in February–March 2020, which was mainly caused by the decrease of daily noncommuting mobility. However, daily commuting mobility from 16 February to 30 June 2020 was maintained at a similar level since there was no national lockdown for workers who commute between home and work. During the first half-year of 2020, Korea could control the outbreak to a manageable level without a significant decrease in daily public mobility. However, it may be only possible when the public follows personal hygiene principles and social distancing without crisis fatigue or reduced compliance.

The impact of social distancing and public behavior changes on COVID-19 transmission dynamics in the Republic of Korea.

BACKGROUND: In the Republic of Korea (ROK), social distancing and public behavior changes mitigated COVID-19 spread. However, a second wave of the epidemic is expected in the fall if neither vaccine nor antiviral drugs become available. This study investigated the impact of non-pharmaceutical measures on short- and long-term outbreak dynamics. METHODS: A mathematical model based on Susceptible-Exposed-Infectious-Recovered model is developed considering isolated and behavior-changed groups. Using the least-squares fitting method, transmission and behavior change rates were estimated using cases reported from February 16 to April 20, 2020. FINDINGS: The estimated transmission rate of COVID-19 was 4·6180 and behavior change rate was 2·6044. The model predicted the number of new cases to continuously decrease, with less than one case expected after May 6, 2020. Concurrently, a 25% reduction in behavioral changes during the outbreak would increase the case count by 60,000, resulting in 4,000 cases at maximum, exceeding the medical system's capacity. As behavioral restrictions are eased, local transmission will likely increase, with forecasted second wave peak in October 2020. INTERPRETATION: Social distancing and public behavior changes have curbed the spread of COVID-19 in the ROK. Mathematical modeling demonstrates the importance of these measures in reducing and delaying outbreaks. Nevertheless, non-pharmaceutical interventions cannot eliminate the disease. In the future, vaccines and antiviral treatments combined with social distancing and public behavior changes will be paramount to ending COVID-19 epidemic.

Risk estimation of the SARS-CoV-2 acute respiratory disease outbreak outside China.

BACKGROUND: On December 31, 2019, the World Health Organization was alerted to the occurrence of cases of pneumonia in Wuhan, Hubei Province, China, that were caused by an unknown virus, which was later identified as a coronavirus and named the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We aimed to estimate the reproductive number of SARS-CoV-2 in the Hubei Province and evaluate the risk of an acute respiratory coronavirus disease (COVID-19) outbreak outside China by using a mathematical model and stochastic simulations. RESULTS: We constructed a mathematical model of SARS-CoV-2 transmission dynamics, estimated the rate of transmission, and calculated the reproductive number in Hubei Province by using case-report data from January 11 to February 6, 2020. The possible number of secondary cases outside China was estimated by stochastic simulations in various scenarios of reductions in the duration to quarantine and rate of transmission. The rate of transmission was estimated as 0.8238 (95% confidence interval [CI] 0.8095-0.8382), and the basic reproductive number as 4.1192 (95% CI 4.0473-4.1912). Assuming the same rate of transmission as in Hubei Province, the possibility of no local transmission is 54.9% with a 24-h quarantine strategy, and the possibility of more than 20 local transmission cases is 7% outside of China. CONCLUSION: The reproductive number for SARS-CoV-2 transmission dynamics is significantly higher compared to that of the previous SARS epidemic in China. This implies that human-to-human transmission is a significant factor for contagion in Hubei Province. Results of the stochastic simulation emphasize the role of quarantine implementation, which is critical to prevent and control the SARS-CoV-2 outbreak outside China.

Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea.

OBJECTIVES: Since the report of the first confirmed case in Daegu on February 18, 2020, local transmission of coronavirus disease 2019 (COVID-19) in Korea has continued. In this study, we aimed to identify the pattern of local transmission of COVID-19 using mathematical modeling and predict the epidemic size and the timing of the end of the spread. METHODS: We modeled the COVID-19 outbreak in Korea by applying a mathematical model of transmission that factors in behavioral changes. We used the Korea Centers for Disease Control and Prevention data of daily confirmed cases in the country to estimate the nationwide and Daegu/Gyeongbuk area-specific transmission rates as well as behavioral change parameters using a least-squares method. RESULTS: The number of transmissions per infected patient was estimated to be about 10 times higher in the Daegu/Gyeongbuk area than the average of nationwide. Using these estimated parameters, our models predicts that about 13,800 cases will occur nationwide and 11,400 cases in the Daegu/Gyeongbuk area until mid-June. CONCLUSIONS: We mathematically demonstrate that the relatively high per-capita rate of transmission and the low rate of changes in behavior have caused a large-scale transmission of COVID-19 in the Daegu/Gyeongbuk area in Korea. Since the outbreak is expected to continue until May, non-pharmaceutical interventions that can be sustained over the long term are required.

School Opening Delay Effect on Transmission Dynamics of Coronavirus Disease 2019 in Korea: Based on Mathematical Modeling and Simulation Study.

BACKGROUND: Nonpharmaceutical intervention strategy is significantly important to mitigate the coronavirus disease 2019 (COVID-19) spread. One of the interventions implemented by the government is a school closure. The Ministry of Education decided to postpone the school opening from March 2 to April 6 to minimize epidemic size. We aimed to quantify the school closure effect on the COVID-19 epidemic. METHODS: The potential effects of school opening were measured using a mathematical model considering two age groups: children (aged 19 years and younger) and adults (aged over 19). Based on susceptible-exposed-infectious-recovered model, isolation and behavior-changed susceptible individuals are additionally considered. The transmission parameters were estimated from the laboratory confirmed data reported by the Korea Centers for Disease Control and Prevention from February 16 to March 22. The model was extended with estimated parameters and estimated the expected number of confirmed cases as the transmission rate increased after school opening. RESULTS: Assuming the transmission rate between children group would be increasing 10 fold after the schools open, approximately additional 60 cases are expected to occur from March 2 to March 9, and approximately additional 100 children cases are expected from March 9 to March 23. After March 23, the number of expected cases for children is 28.4 for 7 days and 33.6 for 14 days. CONCLUSION: The simulation results show that the government could reduce at least 200 cases, with two announcements by the Ministry of education. After March 23, although the possibility of massive transmission in the children's age group is lower, group transmission is possible to occur.