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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.

BackgroundIt was found that 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. Discussions about easing the indoor mask mandate are ongoing.MethodsWe 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.FindingsWe found that the peak size of administered severe patients might not exceed 1,100 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 did not exceed 650. Moreover, if the new variant have both of higher transmissibility and immune reduction therefore the effective reproductive number of the new variant is approximately 3 times higher than the current variant, additional interventions may be needed to keep the administered severe patients from exceeding 2,000, which is the critical level we set.InterpretationOur findings showed that the lifting of the mask mandate, except in hospitals, would be applicable more manageable if it is 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.FundingThis paper is supported by the Korea National Research Foundation (NRF) grant funded by the Korean government (MEST) (NRF-2021M3E5E308120711). This paper is also supported by the Korea National Research Foundation (NRF) grant funded by the Korean government (MEST) (NRF-2021R1A2C100448711). This research was also supported by a fund (2022-03-008) by Research of Korea Disease Control and Prevention Agency.Research in contextEvidence before this studyThere are numerous studies in modelling transmission dynamics of COVID-19 variants but only a few published works tackle the lifting of mask mandate considering the omicron variant, although these studies did not consider unreported cases, variants, and waning immunity. Furthermore, there is no age-structured modeling study which investigated the effect of lifting mask mandate considering high immune state of the population, contributed by both of natural infection and vaccination.Added value of this studyOur mathematical model considered key factors such as vaccine status, age structure, medical staff, prior infection, and unreported cases to study the COVID-19 epidemic in Korea. Updated data and variant-specific parameters were used in the model. Contact patterns in the household, school, work, hospital and other places are considered separately to make the model applicable to the mask mandate issue. Seasonality and scenarios on possible future variants are also included in this study.Implications of all the available evidenceWith mask wearing as one of the remaining non-pharmaceutical interventions in Korea and other countries, this study proposes strategies for lifting the mask mandates while ensuring that cases remain manageable. A variant-dependent factor is incorporated into the model so that policymakers could prepare proactive intervention policies against future variants.

BackgroundIn May 2022, monkeypox started to spread in non-endemic countries. After the number of confirmed cases reached more than 16,000 in July, the World Health Organization declared the highest alert over the outbreak.MethodsTo investigate the effects of contact tracing and self-reporting of primary cases in the local community, a stochastic model is developed. A delay simulation algorithm based on Gillespie’s stochastic chemical kinetics is used to quantify the number of infections, contacts made by the infectors, and duration from the arrival of the primary case until the detection of the index case (and until there are no more local infections), under various scenarios.ResultsWe found that if the primary case does not self-report, taking into account a population of 10,000, the average number of infections could range from 30 to 67, while the number of contacts made by infectors could range from 221 to 498. On the other hand, if the primary case self-reports, the average number of infections and contacts could range from 5 to 7 and 40 to 52, respectively. The average duration from the primary case arrival until the first index case detection (or until there are no more local infections) ranged from 8 to 10 days (18 to 21 days) if the primary case does not self-report, and approximately 3 days (8 days) if the primary case self-reports. Moreover, if the number of close contacts per day is doubled in our simulation settings, then the number of infections could increase by 53%.ConclusionThe number and duration of the infections are strongly affected by the self-reporting behavior of the primary case and the delay in the detection of the index case. Our study emphasizes the importance of border control, which aims to immediately detect the primary case before secondary infections occur.

BackgroundThe 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.MethodsA mathematical model considering age-structure, vaccine, antiviral treatment, 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 nonpharmaceutical interventions (in community and border), quantified by a parameter μin 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.ResultsBy fitting the model to the available data, the estimated values of μ ranged from 0.31 to 0.73, representing the intensity of nonpharmaceutical interventions 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.ConclusionNonpharmaceutical interventions, vaccination, and antiviral therapy 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.

We propose a COVID-19 mathematical model that considers Omicron and previous variants, booster shots, waning, breakthrough infections, and antiviral therapy. We quantify the effects of social distancing (SD) in the Republic of Korea by estimating the reduction in transmission µ induced by government policies from February 26, 2021 to January 16, 2022. The time-dependent µ has a value between 0 and 1, with 1 being the strictest SD. Simulations show that by February 28, 2022, 92% of infections are caused by Omicron. Strict SD (µ = 0.81) is necessary to reduce the number of cases. However, if the focus is shifted towards reducing the severe instead of daily cases, relaxed SD (µ = 0.66) is possible if the administered booster shots have at least 90% effectiveness. Furthermore, if the available antiviral pill is at least 89% effective against severe infections with Omicron, then a more relaxed SD (µ = 0.54) can be implemented.

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.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.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 μ0.55 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.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.

BackgroundEarly vaccination efforts and non-pharmaceutical interventions were insufficient to prevent a surge of coronavirus disease 2019 (COVID-19) cases triggered by the Delta variant. This study aims to understand how vaccination and variants contribute to the spread of COVID-19 so that appropriate measures are implemented.MethodsA compartment model that includes age, vaccination, and infection with the Delta or non-Delta variants was developed. We estimated the transmission rates using maximum likelihood estimation and phase-dependent reduction effect of non-pharmaceutical interventions (NPIs) according to government policies from 26 February to 8 October 2021. We extended our model simulation until 31 December considering the initiation of eased NPIs. Furthermore, we also performed simulations to examine the effect of NPIs, arrival timing of Delta variant, and speed of vaccine administration.ResultsThe estimated transmission rate matrices show distinct pattern, with the transmission rates of younger age groups (0 39 years) much larger than non-Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.64 to 0.69 and 0.70 to 0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below the capacity of Korea’s healthcare system. Simulation results also showed that a surge prompted by the spread of the Delta variant can be prevented if the number of people vaccinated daily was larger.ConclusionsSimulations showed that the timing of easing and intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave.2Key MessagesMaximum likelihood estimation can be utilized to determine the transmission rates of the Delta and non-Delta variants.The phase-dependent NPIs implemented by the Korean government were effectively quantified in the modelling study.Even with fast vaccination, resurgence of cases is still possible if NPIs are eased too early or screening measures are relaxed.The model can be used as a guide for policy makers on deciding appropriate SD level that considers not only disease control, but also the socio-economic impact of maintaining strict measures.