Sunhwa Choi

Mathematical modeling is a powerful tool for understanding and predicting complex dynamical systems, ranging from gene regulatory networks to population-level dynamics. However, model predictions are highly sensitive to initial conditions, which are often unknown. In infectious disease models, for instance, the initial number of exposed individuals (E) at the time the model simulation starts is frequently unknown. This initial condition has often been estimated using an unrealistic, history-independent assumption for simplicity: the chance that an exposed individual becomes infectious is the same regardless of the timing of their exposure (i.e., exposure history). Here, we show that this history-independent method can yield serious bias in the estimation of the initial condition. To address this, we developed a history-dependent initial condition estimation method derived from a master equation expressing the time-varying likelihood of becoming infectious during a latent period. Our method consistently outperformed the history-independent method across various scenarios, including those with measurement errors and abrupt shifts in epidemics, for example, due to vaccination. In particular, our method reduced estimation error by 55% compared to the previous method in real-world COVID-19 data from Seoul, Republic of Korea, which includes likely infection dates, allowing us to obtain the true initial condition. This advancement of initial condition estimation enhances the precision of epidemic modeling, ultimately supporting more effective public health policies. We also provide a user-friendly package, Hist-D, to facilitate the use of this history-dependent initial condition estimation method.

Human papillomavirus (HPV) vaccination, primarily targeting females aged 9–14 years, is pivotal in preventing HPV infections. This case study evaluates the effects of HPV vaccination in South Korea within the primary target group using incidence data and proposes optimal intervention strategies for maximizing the effectiveness of HPV mitigation programs. We developed a mathematical model to simulate HPV transmission dynamics in South Korea, incorporating sex-stratified groups. We assessed vaccination rates before and after HPV inclusion in the National Immunization Program (NIP). Using the optimal control theory, we identified effective strategies involving HPV treatment and vaccination for females and males and analyzed their implementation costs and effectiveness. The inclusion of female HPV vaccination in the NIP increased the transmission rate from females to males, increasing HPV prevalence among males. As a standalone intervention, treatment is more cost effective and can minimize HPV infections by 2030. In dual control strategies, simultaneously treating both sexes is more effective in reducing infections and improving the average cost effectiveness ratio (ACER) compared to vaccination alone. Targeting males exclusively could potentially achieve greater reductions than targeting females. In triple strategies, combining treatment interventions for both sexes with either male or female vaccination achieves a lower ACER and higher reductions in HPV infections. Overall, implementing a combined (quadruple) strategy is projected to reduce infections by approximately 266,000 in 2030. Simultaneous implementation of controls significantly reduces the burden on vaccination control and treatment duration. Treatment control provides an immediate reduction in HPV infections but requires consistent implementation. Increasing vaccination rates by expanding the target population enlarges the protected group. Although vaccination control may not yield rapid reductions compared to treatment, it demonstrates more sustained effects. Combining intervention strategies reduces the cost for each measure and significantly increases the total infections averted. These results can aid public health decision-making in South Korea and guide HPV prevention strategies in other countries.

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Jang M, et al. J Korean Med Sci. 2024 Aug;39(40):e267. https://doi.org/10.3346/jkms.2024.39.e267

Hong H, et al. Immune Netw. 2022 May;22(3):e23. https://doi.org/10.4110/in.2022.22.e23

During the 6 months since the first coronavirus disease 2019 (COVID-19) patient was diagnosed in Korea on January 20, 2020, various prevention and control measures have been implemented according to the COVID-19 epidemic pattern. Therefore, this study aimed to estimate the reproductive numbers (R) for each epidemic stage to analyze the effects of the preventive measures and to predict the COVID-19 transmission trends. We estimated the transmission rates for each epidemic stage by fitting a COVID-19 transmission model, based on a deterministic mathematical model, to the data on confirmed cases. The effects of preventive measures such as social distancing by time period were analyzed, and the size and trends of future COVID-19 outbreaks were estimated. The value of R was 3.53 from February18, 2020 to February 28, 2020, and the mean R reduced to 0.45 from March 14, 2020 to April 29, 2020, but it significantly increased to 2.69 from April 30, 2020 to May13, 2020 and it was maintained at 1.03 from May 14, 2020 to July 23, 2020. According to the estimated R, it had fallen to below 1 and was maintained at that level owing to the isolation of infected persons by the public health authorities and social distancing measures followed by the general public. Then, the estimated R increased rapidly as the contact among individuals increased during the long holiday period from April 30, 2020 to May 5, 2020. Thereafter, the value of R dropped, with the continued use of preventive measures but remained higher than 1.00, indicating that the COVID-19 outbreak can be prolonged and develop into a severe outbreak at any time.

OBJECTIVES: Since the first novel coronavirus disease 2019 (COVID-19) patient in Korea was diagnosed on January 20, 2020, 30 patients were diagnosed until February 17, 2020. However, 5,298 additional patients were confirmed until March 4, 2020. Therefore, our objective was to estimate the reproduction number (R) and evaluate the effectiveness of preventive measures.METHODS: A COVID-19 transmission model (SEIHR) was established to suit the Korean outbreak. The number of daily confirmed cases in Daegu and North Gyeongsang Province (NGP), the main area of outbreak, was used. The first patient’ symptom onset date in the Daegu/NGP outbreak was assumed as January 22, 2020. The R according to the start date of the effect of preventive measures was estimated.RESULTS: The estimated R in Hubei Province, China, was 4.0281, whereas the estimated initial R in Korea was 0.555, but later in Daegu/NGP, the value was between 3.472 and 3.543. When the transmission period decreases from 4-day to 2-day, the outbreak ends early, but the peak of the epidemic increases, and the total number of patients does not change greatly. It was found that, if transmission rate decreases, the outbreak ends early, and the size of the peak and the total number of patients also decreases.CONCLUSIONS: To end the COVID-19 epidemic, efforts to reduce the spread of the virus, such as social distancing and wearing masks, are absolutely crucial with the participation of the public, along with the policy of reducing the transmission period by finding and isolating patients as quickly as possible through the efforts of the quarantine authorities.