1. Introduction
Tuberculosis (TB) is an infectious disease, one of the world’s leading causes of death [
1]. The World Health Organization (WHO) implemented the “Stop TB” strategy from 2006 to 2015 [
2] and initiated the “End TB” strategy beginning in 2015 [
3] with the goal of eliminating TB and related deaths worldwide by 2035. In particular, directly observed therapy (DOT) and public-private mix (PPM) are the most important key components for the two strategies to increase treatment coverage and success rates. In addition to DOT and PPM, WHO emphasized that proper baseline preparation to move the “End TB” strategy forward in the right direction and evaluation of the current epidemic situation are essential before rolling out key strategies [
3]. In line with the WHO, Korea is also pursuing a mid- to long-term national tuberculosis project to achieve eradication of TB by 2035. The reported number of new TB cases in South Korea decreased by approximately 50% from 168 per 100,000 population in 1990 to 80 per 100,000 population in 2015. Nevertheless, the TB infection rate and TB death rate are higher than those of countries in the Organization for Economic Co-operation and Development [
1].
The annual TB incidence in Korea has been on the decline since 2012 as a result of various policies, including PPM projects, consistent and comprehensive TB control strategies, and initiation of TB contact investigation (
Figure 1). PPM, which began on a pilot scale in 2007 and was expanded to entire South Korea in 2011, is believed to be an essential component for controlling TB. The national PPM TB control project was launched in 2009. In 2012, there were approximately 120 hospitals and 200 TB special nurses. A similar level has been maintained ever since [
4]. Treatment in the private sector has become more important in Korea. In 2001, the proportion of new patients reported from public health centers was 46.2%. In 2016, this number decreased to 7.8%, whereas the proportion of patients managed by private medical institutions increased to 92.2%. A government plan was established to intensify PPM to make the TB incidence zero as soon as possible. The government is reviewing an extension of the current monitoring period from 2 weeks to 8 months to increase the completion of treatment and the success rate. There is a need to assess the overall effectiveness of the PPM project before launching a new PPM plan in the future. Because full-fledged TB control by PPM has had an impact since 2012, it is necessary to compare the outcomes of 2001–2011 with those from 2012 to assess the effects of PPM on TB management.
It is challenging to measure epidemiological characteristics of TB transmission such as infection rates, recovery rates, and relapse rates owing to its long variable latency and complex interplays between hosts and environments. Moreover, many difficulties are involved in assessing the effectiveness of public health policies for TB, which have been implemented by the Korean government at a national level. Mathematical modeling can serve as a complementary tool to understand the complex dynamics of TB and evaluate the effectiveness of various TB prevention projects [
5,
6,
7]. Studies have been conducted on TB transmission with age structures [
8,
9,
10,
11,
12,
13]. A TB mathematical model with three age groups that incorporated human immunodeficiency virus infections in South Africa was developed [
8]. The study investigated age-specific patterns in human immunodeficiency virus-negative TB notification rates in Cape Town in 2009. Another TB mathematical model with three age groups investigated the roles of the recovery rate and infection rates on TB cases in the elderly group in China [
9]. Discrete network-based modeling of TB transmission was proposed in the United States using synthetic datasets [
13]. This study predicted that household infection was more dominant than in other locations.
In previous studies, a mathematical model with reinfection was proposed and optimal treatment strategies were identified in Korea [
14,
15]. None of these previous works incorporated age-specific features in mathematical models of TB transmission dynamics in Korea. However, susceptibility to Mycobacterium is quite different in the elderly group [
16,
17], and the incidence among the elderly is rapidly increasing in South Korea. The proportion of elderly patients aged 65 years or older among newly reported TB cases was 19% (6547 of 34,123) in 2001 but increased to 42% (11,798 of 28,161) in 2017 (
Table 1). The mortality rate of patients with TB is significantly high (82% of TB deaths) in the elderly in South Korea [
18,
19]. Considering these factors and the rapidly aging population of South Korea, an age-specific mathematical model is required to assess the epidemic of TB more precisely in Korea.
In this study, we developed a mathematical model for 1-group TB transmission dynamics and extended this model to and age-specific TB model with 2 age groups (<65 years vs. ≥65 years). Age-specific parameters were estimated based on actual TB incidence data in Korea from 2001 to 2018. These parameters included transmission rate, relapse rate, and treatment rate (or recovery rate). In particular, due to PPM had a full-fledged impact since 2012, the current study was divided into two periods (2001–2011 vs. 2012–2018). Therefore, these parameters were estimated before and after 2012 to assess how they were changed by various policies. Furthermore, we investigated the impacts of these parameters on TB incidence by performing sensitivity analyses.
4. Discussion
In this study, we developed a mathematical model of the current TB transmission dynamics from 2001 to 2018. The population was divided by the following four epidemiological statuses: susceptible (S), exposed (E), infectious (I), and recovered (R). Some key parameters were estimated based on the epidemiological data for the entire population in South Korea. These parameters included transmission rates, and relapse rate, , recovery rates, , and early detection and treatment rate for latent TB, . Since TB case of the elderly population increase, we have refined the each epidemiological status into 2-age groups (elderly ≥65 and non-elderly <65). Furthermore, due to the nationwide expansion of PPM, the period also was divided into 2001–2011 and 2012–2018 in order to investigate the effectiveness of PPM from 2012 to 2018.
We conducted age-specific and time-specific parameter estimation of the 1-age group and 2-age group models based on the actual TB data. TB incidence (or reported cases) was the outcome of complex interactions between various interventions and TB transmission dynamics. Because there were too many hidden factors, it was very challenging to separate them effectively in our model. Thus, we selected the most critical factors and investigated the impacts of such interventions implicitly on the transmission rates, and relapse rate, , and recovery rates, . There was one clear factor that we could model explicitly: an early detection/treatment effort () is included as a separate parameter in our model.
The total number of TB cases decreased since 2012 due to a significant reduction in the number of TB cases among the non-elderly. However, the number of new TB cases in the elderly group is increasing mainly due to the aging trend in South Korea. The number of new TB cases in the elderly increased 1.84 times from 6547 in 2011 to 12,029 in 2018 (
Table 2), but the elderly population increased 2.33 times from 4,161,574 (8.7% of the total population) to 9,688,023 (18.9% of the total population) during the same period (
Table 1). Infectivity of infectious TB patients varied by age [
16,
17,
27], and as the aging population is rapidly progressing in Korea, this study aimed to evaluate key parameters on TB transmission dynamics according to age group. Under our 2-age group model, the transmission rate was lower than that of the non-elderly group (<65), which may be less exposed to the vicious cycle of moving and transferring because the elderly population has less contact with the public than younger people [
27]. However, given that the relapse and treatment success rates were poorer than those in the non-elderly population, TB treatment for the elderly needs to focus more on strategies to improve the relapse and treatment success rates. Since these results are hidden in the 1-age group model, the 2-age group model may help establish TB treatment priorities by age group.
This study estimated key parameters on transmission and treatment outcome to assess how they affected TB incidence before and after 2012. The results of this study showed that all the key parameters improved during the second period (2012–2018, Period 2) compared with that during the first period (2001–2011, Period 1). This implies that the nationwide anti-TB policies such as PPM, National Strategic Plan for TB Control, and Contact-tracing Investigation since the late 2000s have been effective in reducing TB transmission and improving treatment outcomes. Under the 1- and 2-group models, we achieved consistent results. The transmission rates and relapse rates were decreased in both age groups and the recovery rates were increased in both age groups during Period 2. These results highlight that the nationwide PPM projects and other policies were successful in reducing the transmission and relapse rates and in increasing the recovery rates (or the treatment rates). However, the results about transmission rates should be interpreted carefully considering the slow progression of TB in our models. Since it can take months to decades to become infectious TB from latent TB [
28,
29], the current outcomes of transmission are the results of gradual activation of latent TB in the past. Therefore, the results of Period 2 are also a combination of the results of many interventions that have been implemented during and before Period 1, and interventions implemented in Period 2 are expected to affect future transmission rates. There were some differences in the estimated parameters between the results of the 1-group TB model and the 2-group TB model. Therefore, we need to conduct further extensive investigation on how to interpret the results of the 1- and 2-group models.
The results of this study showed that the decreased TB incidence in Period 2 could be related to the decreased transmission rate. In addition, the decrease can be linked to an increase in treatment completion rate and treatment success rate. Based on the annual report on the notified TB in Korea, the treatment success rate increased to 83.1% (range, 81.6–84.5%) in Period 2 from 78.7% (range, 74.3–82.3%) in Period 1 [
18,
30]. Subsequently, the increased treatment success could lead to the decrease in the probability of infection and relapse. Thus, far, few studies have been published on the TB relapse rate in South Korea. One nested case-control study observed 12,183 TB patients and found that 0.9% of patients relapsed during the follow-up [
31]. Another retrospective review study on patients with MDR-TB patients reported that the 39-month relapse rate was 4.4%, which converted to a relapse rate of approximately 1.4% over 1 year [
32]. The relapse rate assessed in this study was much lower than the previously reported results because the population in this study included patients with latent TB. Therefore, it should be noted more on the decreasing trend of relapse rates in this study. Treatment adherence and completion also affect relapse and continuous attention should be paid to increase compliance and the completion rate of TB treatment [
33]. Along with the PPM project and other interventions, health authorities have been trying to change the paradigm of future TB management policies from treatment to prevention before an outbreak; The Korea Disease Control and Prevention Agency has recommended diagnosis and treatment of latent TB as an independent chapter in the 2011 TB treatment guidelines, the TB prevention Act was amended in 2016 to oblige community workers in congregated settings to undergo latent TB tests and treatments, and screening and treatment was first recommended for healthcare workers in the 2017 TB treatment guidelines [
19,
34]. In the present study, we evaluated that early detection and treatment for latent TB in the high-risk group (>65 years) would be most effective to reduce the incidence of active TB in Korea. Therefore, it is necessary to set up and strengthen more careful management policies regarding latent TB elimination and treatment in the future.
This study has some limitations. First, our model can be improved by refining the exposed class (the fast and slow progression rates from exposed to infectious TB), as reported in [
28]. In addition, more precise data (such as relapse rates and fast and slow progression rates from E to I) would be helpful to draw more meaningful insights from the basic reproduction number. In general, most active TB cases arise from latent TB, with only a minor fraction (approximately 10%) undergoing fast progression from primary exposure to active TB [
29], and the risk of active TB from latent TB increases with co-infection of HIV [
35,
36] but prevalence of HIV co-infection in South Korea is very low. Considering these factors and the lack of Korean data currently available to distinguish fast and slow progression of TB, this study focused on the age-specific TB dynamic model. We would like to develop a model incorporating fast and slow progression in our future research. Second, the role of the relapse rate, the basic reproduction, or the contact rate should be further investigated. In TB dynamics, it is very challenging to measure these parameters accurately because of various complex factors such as long latent periods, variable population sizes, transmission rates, which are changing in time along with living conditions, social behaviors, and environmental changes. Therefore, it is difficult to elucidate the role of the relapse rate, the basic reproduction number, or the contact rate in our current study. Further investigation should be carefully carried out in future research. Third, this study did not separately assume parameters for MDR-TB, including extensively drug-resistant TB (XDR-TB), which accounted for approximately 3.4% of new TB cases. The parameters in this study were estimated in patients with TB, including those with MDR-TB, and the estimated parameters and outcomes in this study reflected the effects of MDR-TB and XDR-TB in a weighted manner. Lastly, this study assumed that approximately one-third of the total population was LTBI and that direct treatment for LTBI has been increasing very slowly since 2012. To complement the uncertainty of this limitation, various sensitivity analyses were conducted. It should be considered that the results of this study may vary depending on the LTBI ratio and the direct treatment rate from LTBI to recovery.
In conclusion, this study presents an age-specific TB dynamic model, and key parameters on TB transmission were estimated using the model to evaluate the treatment outcomes of TB in South Korea. The evaluation results showed the same tendency as previous reports, indicating that this study can be used as a supplement to the evaluation and treatment strategy for future TB management in South Korea.