A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19.

The COVID-19 pandemic has ravaged global health and national economies worldwide. Testing and isolation are effective control strategies to mitigate the transmission of COVID-19, especially in the early stage of the disease outbreak. In this paper, we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19. We derive the control reproduction number R C , which gives the threshold for disease elimination or prevalence. Using data from New York State in the early stage of the disease outbreak, we estimate R C = 7.989 . Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R C and disease prevalence. Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission. The testing starting date is also crucial: the earlier testing is implemented, the more impact it has on reducing the infection. The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.

Exploration of Superspreading Events in 2015 MERS-CoV Outbreak in Korea by Branching Process Models.

South Korea has learned a valuable lesson from the Middle East respiratory syndrome (MERS) coronavirus outbreak in 2015. The 2015 MERS-CoV outbreak in Korea was the largest outbreak outside the Middle Eastern countries and was characterized as a nosocomial infection and a superspreading event. To assess the characteristics of a super spreading event, we specifically analyze the behaviors and epidemiological features of superspreaders. Furthermore, we employ a branching process model to understand a significantly high level of heterogeneity in generating secondary cases. The existing model of the branching process (Lloyd-Smith model) is used to incorporate individual heterogeneity into the model, and the key epidemiological components (the reproduction number and the dispersive parameter) are estimated through the empirical transmission tree of the MERS-CoV data. We also investigate the impact of control intervention strategies on the MERS-CoV dynamics of the Lloyd-Smith model. Our results highlight the roles of superspreaders in a high level of heterogeneity. This indicates that the conditions within hospitals as well as multiple hospital visits were the crucial factors for superspreading events of the 2015 MERS-CoV outbreak.

The Characteristics of Middle Eastern Respiratory Syndrome Coronavirus Transmission Dynamics in South Korea.

OBJECTIVES: The outbreak of Middle Eastern respiratory syndrome coronavirus (MERS-CoV) was one of the major events in South Korea in 2015. In particular, this study pays attention to formulating a mathematical model for MERS transmission dynamics and estimating transmission rates. METHODS: Incidence data of MERS-CoV from the government authority was analyzed for the first aim and a mathematical model was built and analyzed for the second aim of the study. A mathematical model for MERS-CoV transmission dynamics is used to estimate the transmission rates in two periods due to the implementation of intensive interventions. RESULTS: Using the estimates of the transmission rates, the basic reproduction number was estimated in two periods. Due to the superspreader, the basic reproduction number was very large in the first period; however, the basic reproduction number of the second period has reduced significantly after intensive interventions. CONCLUSION: It turned out to be the intensive isolation and quarantine interventions that were the most critical factors that prevented the spread of the MERS outbreak. The results are expected to be useful to devise more efficient intervention strategies in the future.

Modeling optimal treatment strategies in a heterogeneous mixing model.

BACKGROUND: Many mathematical models assume random or homogeneous mixing for various infectious diseases. Homogeneous mixing can be generalized to mathematical models with multi-patches or age structure by incorporating contact matrices to capture the dynamics of the heterogeneously mixing populations. Contact or mixing patterns are difficult to measure in many infectious diseases including influenza. Mixing patterns are considered to be one of the critical factors for infectious disease modeling. METHODS: A two-group influenza model is considered to evaluate the impact of heterogeneous mixing on the influenza transmission dynamics. Heterogeneous mixing between two groups with two different activity levels includes proportionate mixing, preferred mixing and like-with-like mixing. Furthermore, the optimal control problem is formulated in this two-group influenza model to identify the group-specific optimal treatment strategies at a minimal cost. We investigate group-specific optimal treatment strategies under various mixing scenarios. RESULTS: The characteristics of the two-group influenza dynamics have been investigated in terms of the basic reproduction number and the final epidemic size under various mixing scenarios. As the mixing patterns become proportionate mixing, the basic reproduction number becomes smaller; however, the final epidemic size becomes larger. This is due to the fact that the number of infected people increases only slightly in the higher activity level group, while the number of infected people increases more significantly in the lower activity level group. Our results indicate that more intensive treatment of both groups at the early stage is the most effective treatment regardless of the mixing scenario. However, proportionate mixing requires more treated cases for all combinations of different group activity levels and group population sizes. CONCLUSIONS: Mixing patterns can play a critical role in the effectiveness of optimal treatments. As the mixing becomes more like-with-like mixing, treating the higher activity group in the population is almost as effective as treating the entire populations since it reduces the number of disease cases effectively but only requires similar treatments. The gain becomes more pronounced as the basic reproduction number increases. This can be a critical issue which must be considered for future pandemic influenza interventions, especially when there are limited resources available.

What does a mathematical model tell about the impact of reinfection in korean tuberculosis infection?

OBJECTIVES: According to the Korea Centers for Disease Control and Prevention, new active tuberculosis (TB) cases have increased since 2001. Some key factors explain and characterize the transmission dynamics of Korean TB infection, such as a higher ratio of latent individuals and a new reporting system implemented in 2001, among others. METHODS: We propose a mathematical TB model that includes exogenous reinfection to gain a better understanding of the recent trend for TB incidence. We divide the simulation time window into two periods, 1970-2000 and 2001-2012, according to the implementation date of a new TB detection system. RESULTS: Two sets of parameters, including the transmission rate, the latent period, the recovery rate, and the proportion of exogenous reinfection, are estimated using the least-squares method and calibrated to data on the incidence of active TB. CONCLUSION: Among some key parameters in the model, the case finding effort turned out to be the most significant impacting component on the reduction in the active TB cases.

Assessment of the intensive countermeasures in the 2009 pandemic influenza in Korea.

OBJECTIVES: It is critical to implement effective multiple countermeasures to mitigate or retain the spread of pandemic influenza. We propose a mathematical pandemic influenza model to assess the effectiveness of multiple countermeasures implemented in 2009. METHODS: Age-specific parameters, including the transmission rate, the proportion of asymptomatic individuals, the vaccination rate, the social distancing rate, and the antiviral treatment rate are estimated using the least-square method calibrated to the incidence data. RESULTS: The multiple interventions (intensive vaccination, social distancing, antivrial treatment) were successfully implemented resulting in the dramatic reduction in the total number of incidence. CONCLUSION: The model output is sensitive to age-specific parameters and this leads to the fact that a more elaborate age group model should be developed and extensive further studies must be followed.