Effective vaccination strategies to control COVID-19 in Korea: a modeling study.

OBJECTIVES: In Korea, as immunity levels of the coronavirus disease 2019 (COVID-19) in the population acquired through previous infections and vaccinations have decreased, booster vaccinations have emerged as a necessary measure to control new outbreaks. The objective of this study was to identify the most suitable vaccination strategy for controlling the surge in COVID-19 cases. METHODS: A mathematical model was developed to concurrently evaluate the immunity levels induced by vaccines and infections. This model was then employed to investigate the potential for future resurgence and the possibility of control through the use of vaccines and antivirals. RESULTS: As of May 11, 2023, if the current epidemic trend persists without further vaccination efforts, a peak in resurgence is anticipated to occur around mid-October of the same year. Under the most favorable circumstances, the peak number of severely hospitalized patients could be reduced by 43% (n=480) compared to the scenario without vaccine intervention (n=849). Depending on outbreak trends and vaccination strategies, the best timing for vaccination in terms of minimizing this peak varies from May 2023 to August 2023. CONCLUSIONS: Our findings suggest that if the epidemic persist, the best timing for administering vaccinations would need to be earlier than currently outlined in the Korean plan. It is imperative to continue monitoring outbreak trends, as this is key to determining the best vaccination timing in order to manage potential future surges.

Korea Seroprevalence Study of Monitoring of SARS-COV-2 Antibody Retention and Transmission (K-SEROSMART): findings from national representative sample.

OBJECTIVES: We estimated the population prevalence of antibodies to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), including unreported infections, through a Korea Seroprevalence Study of Monitoring of SARS-CoV-2 Antibody Retention and Transmission (K-SEROSMART) in 258 communities throughout Korea. METHODS: In August 2022, a survey was conducted among 10,000 household members aged 5 years and older, in households selected through two stage probability random sampling. During face-to-face household interviews, participants self-reported their health status, COVID-19 diagnosis and vaccination history, and general characteristics. Subsequently, participants visited a community health center or medical clinic for blood sampling. Blood samples were analyzed for the presence of antibodies to spike proteins (anti-S) and antibodies to nucleocapsid proteins (anti-N) SARS-CoV-2 proteins using an electrochemiluminescence immunoassay. To estimate the population prevalence, the PROC SURVEYMEANS statistical procedure was employed, with weighting to reflect demographic data from July 2022. RESULTS: In total, 9,945 individuals from 5,041 households were surveyed across 258 communities, representing all basic local governments in Korea. The overall population-adjusted prevalence rates of anti-S and anti-N were 97.6% and 57.1%, respectively. Since the Korea Disease Control and Prevention Agency has reported a cumulative incidence of confirmed cases of 37.8% through July 31, 2022, the proportion of unreported infections among all COVID-19 infection was suggested to be 33.9%. CONCLUSIONS: The K-SEROSMART represents the first nationwide, community-based seroepidemiologic survey of COVID-19, confirming that most individuals possess antibodies to SARS-CoV-2 and that a significant number of unreported cases existed. Furthermore, this study lays the foundation for a surveillance system to continuously monitor transmission at the community level and the response to COVID-19.

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.

Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study.

In May 2022, monkeypox started to spread in nonendemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the primary case to the detection of the index case (or until there are no more local infections). Different scenarios were set considering the delay in contact tracing and behavior of infectors. We found that the self-reporting behavior of a primary case is the most significant factor affecting outbreak size and duration. Scenarios with a self-reporting primary case have an 86% reduction in infections (average: 5-7, in a population of 10 000) and contacts (average: 27-72) compared with scenarios with a non-self-reporting primary case (average number of infections and contacts: 27-72 and 197-537, respectively). Doubling the number of close contacts per day is less impactful compared with the self-reporting behavior of the primary case as it could only increase the number of infections by 45%. Our study emphasizes the importance of the prompt detection of the primary case.

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.

Estimation of optimal antiviral stockpile for a novel influenza pandemic.

BACKGROUND: A stockpile of antiviral drugs is important for mitigating a novel influenza pandemic. Recently, intervention strategies against such a pandemic have improved significantly, affecting the required size and composition of the stockpile. Our goal is to estimate the optimal ratio of conventional to newer antiviral drugs. METHOD: We estimated epidemic parameters from daily-case data about H1N1pdm09 in the Republic of Korea, and used a deterministic ordinary differential equation model and stochastic simulation to predict the number of patients in a future pandemic. We considered an antiviral stockpile containing neuraminidase inhibitors (NAI) and a new drug, cap-dependent endonuclease inhibitor (CENI), seeking the optimum ratio of the two drugs under different epidemiological and economic assumptions. RESULTS: With an effective reproductive number of 1.36, the expected cumulative cases did not exceed 30 % of the population in all vaccination scenarios. If the non-pharmaceutical intervention strategy is intensified and the effective reproductive number is decreased to 1.29, a 20 % antiviral stockpile of the population is sufficient. Assuming that CENI is prescribed for 10 % of patients, the expected total number of cases is decreased from 30 % to approximately 25 % of the population. If the cost of CENI is triple that of NAI, no expenditures beyond the current budget are necessary; if it is quintuple, expenditures increase by 17 %. CONCLUSION: Stockpiling CENI reduces the number of patients by reducing the infectious period. However, the government needs to consider the cost-effective stockpile ratio of such new drugs. This will depend not only on the cost of the drugs, but on factors difficult to anticipate, such as the transmissibility of the virus, the time needed for vaccine development, and (especially) the emergence of resistance. If this information can be estimated, our model can be used to obtain the optimum.

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.

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.

Country-specific intervention strategies for top three TB burden countries using mathematical model.

Tuberculosis (TB) is one of the top 10 causes of death globally and the leading cause of death by a single infectious pathogen. The World Health Organization (WHO) has declared the End TB Strategy, which targets a 90% reduction in the incidence rate by the year 2035 compared to the level in the year 2015. In this work, a TB model is considered to understand the transmission dynamics in the top three TB burden countries-India, China, and Indonesia. Country-specific epidemiological parameters were identified using data reported by the WHO. If India and Indonesia succeed in enhancing their treatment protocols and increase treatment and treatment success rate to that of China, the incidence rate could be reduced by 65.99% and 68.49%, respectively, by the end of 2035. Evidently, complementary interventions are essential to achieve the WHO target. Our analytical approach utilizes optimal control theory to obtain time-dependent nonpharmaceutical and latent case finding controls. The objective functional of the optimal control problem includes a payoff term reflecting the goal set by WHO. Appropriate combinations of control strategies are investigated. Based on the results, gradual enhancement and continuous implementation of intervention measures are recommended in each country.

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.

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.

Ebola virus disease outbreak in Korea: use of a mathematical model and stochastic simulation to estimate risk.

OBJECTIVES: According to the World Health Organization, there have been frequent reports of Ebola virus disease (EVD) since the 2014 EVD pandemic in West Africa. We aim to estimate the outbreak scale when an EVD infected person arrives in Korea. METHODS: Western Africa EVD epidemic mathematical model SEIJR or SEIJQR was modified to create a Korean EVD outbreak model. The expected number of EVD patients and outbreak duration were calculated by stochastic simulation under the scenarios of Best case, Diagnosis delay, and Case missing. RESULTS: The 2,000 trials of stochastic simulation for each scenario demonstrated the following results: The possible median number of patients is 2 and the estimated maximum number is 11 when the government intervention is proceeded immediately right after the first EVD case is confirmed. With a 6-day delay in diagnosis of the first case, the median number of patients becomes 7, and the maximum, 20. If the first case is missed and the government intervention is not activated until 2 cases of secondary infection occur, the median number of patients is estimated at 15, and the maximum, at 35. CONCLUSIONS: Timely and rigorous diagnosis is important to reduce the spreading scale of infection when a new communicable disease is inflowed into Korea. Moreover, it is imperative to strengthen the local surveillance system and diagnostic protocols to avoid missing cases of secondary infection.

Prioritization of vaccine strategy using an age-dependent mathematical model for 2009 A/H1N1 influenza in the Republic of Korea.

We developed a mathematical model of the 2009 A/H1N1 influenza epidemic in the Republic of Korea by considering five age groups and suggested the best way to prioritize an age-dependent vaccination strategy for mitigating the epidemic. An age-structured SEIAR influenza model was constructed based on the laboratory confirmed data obtained from the Korea Centers for Disease Control and Prevention (KCDC). The estimated transmission matrix captured one of the main characteristics of the 2009 A/H1N1 influenza, the transmission rate of which is high among young people, unlike that of seasonal influenza. We investigated the impact of age-dependent vaccination priority on the transmission dynamics of the 2009 A/H1N1 influenza and evaluated the Korean government vaccination policy when the vaccination started being administered 90 days (or 120 days) after the onset of the outbreak. We found that the government's age priority vaccination policy (Group 2, Group 1, Group 5, Group 4, and Group 3 in order) was a good strategy for reducing 62.06% of the cumulative cases when the vaccination was applied 90 days after the onset of the outbreak, while the proposed model's best suggestion (Group 2, Group 1, Group 3, Group 4, and Group 5 in order) showed 64.52% reduction. Furthermore, we studied the region-specific vaccination policy. For instance, the best age-priority of vaccination in Gwangwon province showed a different order (Group 3, Group 1, Group 2, Group 4, and Group 5 in order) and it reduced the incidence by 58.1%, which is 5.54% higher than that of the 2009 Korean government policy.

Effective control measures considering spatial heterogeneity to mitigate the 2016-2017 avian influenza epidemic in the Republic of Korea.

During the winter of 2016-2017, an epidemic of highly pathogenic avian influenza (HPAI) led to high mortality in poultry and put a serious burden on the poultry industry of the Republic of Korea. Effective control measures considering spatial heterogeneity to mitigate the HPAI epidemic is still a challenging issue. Here we develop a spatial-temporal compartmental model that incorporates the culling rate as a function of the reported farms and farm density in each town. The epidemiological and geographical data of two species, chickens and ducks, from the farms in the sixteen towns in Eumseong-gun and Jincheon-gun are used to find the best-fitted parameters of the metapopulation model. The best culling radius to maximize the final size of the susceptible farms and minimize the total number of culled farms is calculated from the model. The local reproductive number using the next generation method is calculated as an indicator of virus transmission in a given area. Simulation results indicate that this parameter is strongly influenced not only by epidemiological factors such as transmissibility and/or susceptibility of poultry species but also by geographical and demographical factors such as the distribution of poultry farms (or density) and connectivity (or distance) between farms. Based on this result, we suggest the best culling radius with respect to the local reproductive number in a targeted area.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy.

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451-AMPK-mTOR-cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.