Demographic Control Measure Implications of Tuberculosis Infection for Migrant Workers across Taiwan Regions

A sharp increase in migrant workers has raised concerns for TB epidemics, yet optimal TB control strategies remain unclear in Taiwan regions. This study assessed intervention efforts on reducing tuberculosis (TB) infection among migrant workers. We performed large-scale data analyses and used them to develop a control-based migrant worker-associated susceptible–latently infected–infectious–recovered (SLTR) model. We used the SLTR model to assess potential intervention strategies such as social distancing, early screening, and directly observed treatment, short-course (DOTS) for TB transmission among migrant workers and locals in three major hotspot cities from 2018 to 2023. We showed that social distancing was the best single strategy, while the best dual measure was social distancing coupled with early screening. However, the effectiveness of the triple strategy was marginally (1–3%) better than that of the dual measure. Our study provides a mechanistic framework to facilitate understanding of TB transmission dynamics between locals and migrant workers and to recommend better prevention strategies in anticipation of achieving WHO’s milestones by the next decade. Our work has implications for migrant worker-associated TB infection prevention on a global scale and provides a knowledge base for exploring how outcomes can be best implemented by alternative control measure approaches.


Introduction
Tuberculosis (TB) remains the leading cause of death from a single infectious agent and one of the top 10 causes of death worldwide; nearly 10 million people developed TB and 1.5 million died in 2020 [1]. There are 30 countries with high TB burdens, accounting for 86% of all estimated cases worldwide, of which eight of these countries account for two-thirds of the world's TB cases: India (26%), China (8.5%), Indonesia (8.4%), the Philippines (6.0%), Pakistan (5.8%), Nigeria (4.6%), Bangladesh (3.6%), and South Africa (3.3%) [1].
Nationwide epidemiological investigations have shown different risk factors among local and migrant groups [2]. It is evident that factors such as TB characteristics, population density, types of industries present in counties and cities, and variabilities between local and migrant workers can cause substantial differences in disease transmissions [2,8,9]. The substantial differences in TB incidence between Taiwanese and migrant workers might be partly due to high TB incidence after the arrival of migrant workers contributed by the reactivation of latent TB infections, as well as new TB infections in Taiwan [2,5]. Moreover, migrant workers experience more stress during their daily work and have less access to medical services, making them more vulnerable to infectious diseases [9].
The Taiwan Center of Disease Control (Taiwan CDC) has taken four strategies based on the signs and symptoms of TB to contain TB transmission in migrant workers: (i) active case finding by post-arrival medical examination and regular health examination, (ii) seeing a doctor when experiencing TB symptoms and culture-confirmed treatment, (iii) medical care through reimbursement policies, and (iv) implementing TB/multidrugresistant TB (MDR-TB) case management through directly observed treatment, short-course (DOTS)/DOTS-plus programs [11]. Hospitals using case management with DOTS can improve the adherence of TB patients and the control of TB-epidemic situations [12]. The rates of acquired MDR-TB were significantly lower after the implementation of DOTS and DOTS-plus programs [13].

Background
A mechanistic, population transmission dynamics-based model can offer a useful tool for analyzing the spread of infectious diseases and evaluating the relative effectiveness of different measures [14]. The first mathematical model describing the epidemiological trend of TB was developed by Waaler et al. [15]. It consisted of five discrete difference equations, and model parameters were estimated from observed datasets. The first continuous TB model composed of ordinary differential equations was constructed by Revelle et al. [16]. Then, a simple three-compartment TB model was constructed by Blower et al. [17]. They developed it further into a five-compartment model to incorporate TB endogenous reactivation and relapse.
Optimal control theory is a branch of mathematics recently developed to obtain optimal methods to control a dynamic system [18][19][20]. The optimal control theory applied to TB models could provide valuable insight into the decision-and policymaking of public health agents. For example, Kim et al. [19] used a classic susceptible-latent-infectedrecovery (SEIR) model to predict the effect of reducing the number of high-risk latent and infectious TB individuals and minimizing the cost of implementing control measures. These measures include reducing the contact between susceptible and infectious individuals, preventing the failure of treatment in infectious individuals, and increasing the treatment rate for target group such as people who have had close contact with TB patients and those who live with HIV patients.
Among various mathematical models of TB transmission, the factor of migration is rarely considered due to the assumption of closed populations [21]. We aimed to incorporate migrant workers as a subpopulation into a compartmental model to explore the intrinsic mechanism of TB transmission dynamics between migrant and local population.
This study focused on examining the migrant-based TB transmission along with multiple control measures in highly endemic Taiwan regions. Hence, there were three aims of this study: (i) to establish an enhanced TB dynamic model based on Jia et al. [22] with an additional transmission route from infectious local to migrant populations, (ii) to assess the efforts of potential control strategies (social distancing, early screening, and DOTS) on TB incidence dynamics projected from the reference year 2018 to 2020 and 2023 further, after performing a broad literature data analysis to implement model parameterization, and (iii) to present different combinations of interventions for the optimal infection control. The percentage reduction in the populations of latently infected and infectious TB with/without control measures was the determinant modeling outcome.

Study Design
Concerning data availability and model implications on control measures, we adopted the model from Jia et al. [22] as our base model describing TB spread through horizontal transmission in the presence of exposed immigrants in host areas. The approach was the same with respect to considering the epidemiological and demographic factors that adequately explained regional TB incidence in the partitioned subpopulation: migrants and locals. In particular, we proposed a simple modification by considering the additional influence of the local population on the migrants, which was the limitation of Jia's study [22]. Hence, we developed a migration-based susceptible-latently infected-infectious-recovered (SLTR) model to explore the TB mutual transmission between the infectious local population and migrant workers, as well as to evaluate how effectively various control measures are able to reduce infectives in the whole population ( Figure 1).

Setting, Sample, and Data Collection
Here, we constructed a population−TB case dataset using the available visibility data in Taiwan regions based on a large-scale meta-analysis. Demographic data of nationality-based migrant workers in various productive industries in the period 2013-2019 were adopted from Taiwan Workforce Development Agency, Ministry of Labor (Supplementary Table S1) [27]. We showed that the three largest populations of migrant workers were located in Taoyuan City (91,898) and New Taipei City (56,041) of northern Taiwan and Taichung City (78,423) of central Taiwan (Supplementary Table S1). We, therefore, chose these three key administrative regions as our study areas. The TB incidence rates in the period 2012-2019 in Taiwan regions and source countries of migrant workers were adopted from data reported by the Taiwan CDC [28] and WHO [1], respectively. The yearly numbers of newly reported TB cases in the period 2006-2019 were also obtained from the Taiwan CDC [28].

Migrant-BASED SLTR Model
In the migrant-based SLTR model, the total population (N) comprised the migrant subpopulation (N M ) and local subpopulation (N L ), where N = N M + N L . According to the natural history of TB, each subpopulation was further subdivided into four classes: susceptible (S), latently infected (L), those with infectious TB (T), and those that have recovered (R), resulting in eight groups of S M , L M , T M , R M , S L , L L , T L , and R L ( Figure 1A, Table 1).

Migrant-based SLTR model
Control-based SLTR model

Migrant population (N M )
Local population (N L ) Briefly, susceptible individuals can be infected by frequent contact with infectious TB cases (T M and T L ) and may progress from susceptible to latent TB. The parameter Λ SM is the recruitment rate into S M (persons·year −1 ), and Λ SL is the crude birth rate into S L (year −1 ). Newborn individuals are assumed susceptible (Λ SL ). Parameters for arrivals of migrant workers include potentially susceptible (Λ SM ), latently infected (Λ LM ), or infectious TB (Λ TM ), in that β M and β L are the transmission rates for migrant and local subpopulations (person −1 ·year −1 ), respectively, β LM and β ML are the transmission rates from locals to migrants and from migrants to locals (person −1 ·year −1 ), respectively, and µ is the background mortality rate (year −1 ).
Individuals with latent TB infection (LTBI) may develop active TB disease through a slow route, i.e., reactivation of TB in the remote future at rates k M and k L , or a fast route, i.e., reinfection at rates p(β M T M + β LM T L ) and p(β L T L + β ML T M ), in that k M and k L are the reactivation rates in L M and L L (year −1 ), respectively, p represents the previous infection affording partial immunity against reinfection, and µ TM and µ TL are the TB-induced mortality rates in T M and T L (year −1 ), respectively. The progression rates from infectious TB to recovery determined by γ M and γ L are the recovery rates of T M and T L (year −1 ), respectively. Additionally, p and q are the partial immunities that decrease the probability of progression to TB after reinfection for latent and recovered individuals, respectively.

Control-Based SLTR Model
Here, we considered three TB constant control strategies: social distancing control (u 1 ), early screening (u 2 ), and DOTS (u 3 ). We incorporated the selected control measures into the SLTR model to form the control-based SLTR model ( Figure 1B, Table 2). We used the present developed control-based SLTR model to assess the efforts of potential control strategies on TB incidence dynamics projected from the reference year 2018 to 2020 and 2023 further.
Briefly, the coefficient 1 − u 1 represents the effort of reducing susceptible individuals that become infected by infectious individuals (β L , β M , β ML , and β LM ), such as isolation of infectious people or health education for disease prevention and control. The coefficient 1 − u 2 represents the effort of reducing the risk of progression to the infectious state (k L and k M ), through measures such as identification and screening of latent individuals who are at high risk of developing TB. Notably, two controls u 1 and u 2 are bound within 10-90%. In light of DOTS, 1 + u 3 represents the effort of increasing γ M and γ L , such as improving medication adherence in patients, which is essential at least during the intensive phase of treatment (the first 2 months) to ensure that the drugs are taken in the right combinations and for the appropriate duration. The DOTS strategy can be used to treat the infectious TB cases. Thus, the completely cured TB patients will shift into the recovery/treated classes. Based on the Taiwan CDC report [29], the recovery rate for treatment cases has reached 70%; hence, we propose a simulation of much higher medical care with the interval ranging from 80-95%. To investigate the impact or effectiveness of the control strategies, different control intervention schemes were considered in single (u 1 , u 2 , and u 3 ), dual (u 1 + u 2 , u 1 + u 3 , and u 2 + u 3 ), and triple (u 1 + u 2 + u 3 ) combinations ( Figure 1C). Therefore, the percentage reduction in the populations of latently infected L (L L + L M ) and infectious TB T (T L + T M ) as the modeling outcomes could be estimated. Table 2. System equations used in the control-based SLTR model based on three control measures u 1 , u 2 , and u 3 denoting the efforts of social distancing control, early screening control, and directly observed treatment, short-course (DOTS) control, respectively (see text for symbol meanings).

Model Parameterization
Initial population sizes and parameters used in the migrant-based SLTR model involving Taoyuan City, Taichung City, and New Taipei City were estimated on the basis of the available site-country-specific visibility TB data in the reference year of 2018 provided by the Taiwan CDC and the published literature.

Data Interpretations
Nationality-based migrant workers from Indonesia, the Philippines, and Vietnam substantially increased from 45,919, 67,442, and 104,590 in 2013 to 74,764, 126,661, and 196,162, respectively, in 2019 ( Figure 2A). This accounts for increases of 63% (Indonesia), 88% (the Philippines), and 88% (Vietnam) of foreign-born workers during the 6 years, implying that the largest two groups of migrant workers were consistently from Vietnam and the Philippines. As a matter of fact, Vietnam and the Philippines accounted for 43% and 28% (16% for Indonesia; 13% for Thailand) of the total numbers of migrant workers in Taiwan in 2019. Generally, the nationality-based migrant workers as percentages of the total numbers in each city and county varied substantially varied on the basis of a geographic distribution with a median of 7200 (2.5th-97.5th percentile: 60-91,900) ( Figure 2B,C; Supplementary Table S1). We found that the incidence rate in the Philippines was 554 per 100,000 population in 2019, which was much higher than that in Indonesia (312 per 100,000 population), We found that the incidence rate in the Philippines was 554 per 100,000 population in 2019, which was much higher than that in Indonesia (312 per 100,000 population), Vietnam (176 per 100,000 population), Thailand (150 per 100,000 population), and Taiwan (37 per 100,000 population) ( Figure 3A). Our results indicated a substantial increase in TB cases among migrant workers from 2006 to 2014, while the confirmed cases (600-700) have remained steady since 2014 ( Figure 3B). Furthermore, of the total 6416 (2006-2019 summation) migrant TB cases, Indonesia was the largest contributor (47%), followed by the Philippines (25%), Vietnam (18%), Thailand (9%), and others (1%: 38 cases from Malaysia, Japan, Korea, and unknown nationalities) ( Figure 3C).

Sensitivity Performance
An overall presentation of all sensitivity tests against the four transmission rates (β M , β L , β LM , and β ML ) and reactivation rate (k) for Taoyuan City, Taichung City, and New Taipei City is available in Supplementary Figures S1-S3. Our results showed that the dynamic modeling with transmission rates for the migrant population (β M =~6 × 10 −5 ) and transmission rates for the local subpopulation (β L = 5 × 10 −5 ) were crucial compared to other estimates. The migrant subpopulation (T M ) and local subpopulation (T L ) will approximately reach a maximum population by 2022-2023 in Taoyuan City. When the reactivation rate (k) was increased, both migrant subpopulation (T M ) and local subpopulation (T L ) slowly grew among three study cities, but there were no significant effects on N M , S M , N L , or S L (Supplementary Figures S1-S3).

Single Control Effects
The estimates of initial population sizes in the reference year of 2018 in the three selected TB hotspot cities applied in the control-based SLTR model are listed in Table 3. Results of model parameterizations in the SLTR model are shown in Table 4. Our simulation results showed that, in terms of reducing the total numbers of L + T, distancing (u 1 ) was the most efficient intervention when a single control strategy was used, followed by early screening (u 2 ) and DOTS (u 3 ) ( Figure 4, Table 5, and Supplementary Table S2). Recovered cases in the migrant subpopulation 0 0 0 a Adopted from [11]. b Estimated by multiplying T L (0) with cured rate in a specific city: 73.1% (Taoyuan City), 76.1% (Taichung City), and 71.4% (New Taipei City) [11]. c L L (0) = 0.004 × (1 − 0.08) × N L (0) = 8173, 10,318, and 14,704, respectively, where 0.004 is the annual infection risk [32], and 0.08 is the probability of new infections that develop progressive primary active TB [33] with total local subpopulations. N L (0) = 2,220,792 (Taoyuan City)
Taken together, in all single control strategies ( Figure 4A-C), we showed that a higher control effort led to a more pronounced reduction in the L + T group, and a longer time control resulted in a better effort. Therefore, if only one control strategy is to be selected, distancing (u 1 ) would be the most effective one.

Dual and Triple Combination Control Strategies Effects
In this study, dual and triple combination control strategies (u 1 + u 2 , u 1 + u 3 , u 2 + u 3 and u 1 + u 2 + u 3 ) were also simulated ( Figure 4D, Supplementary Table S2). Here, we used the efforts of u 1 = 70%, u 2 = 70%, and u 3 = 85% to simplify our results. In a 2 year projection in Taoyuan City ( Figure 4D), L + T could be reduced by~39% through u 1 + u 2 control. In the 5 year simulation, u 1 + u 2 effort could reduce L + T by~74% in Taoyuan City,~83% in Taichung City, and~96% in New Taipei City ( Figure 4D). Moreover, the dual control u 1 + u 2 had the same effort as u 1 + u 3 . In New Taipei City ( Figure 4D), distancing (u 1 ) coupled with early screening (u 2 ) or DOTS (u 3 ) was the most effective combination in curtailing L + T. Furthermore, the u 1 + u 2 + u 3 combination could reduce L + T by~97% in a 5 year projection ( Figure 4D).

Discussion
This study used the city-specific demographic characteristics in the control-based SLTR model with identity transmission rates (the most sensitive parameter) in the three cities due to the lack of available data. Despite this limitation, the present study demonstrated that, among the single control strategies, distancing control (u 1 ) was the most effective in curtailing cases of latent and active TB (L + T), consistent with previous findings [18,19]. Our simulations showed that implementing distancing control would reduce L + T bỹ 35-57% in 2 years and~70-95% in 5 years. Not surprisingly, a combination of control strategies would yield more additional reductions. Distancing coupled with latent case finding (u 1 + u 2 ) was the most effective combination, further reducing the L + T by~5%. Since this coupled control implementation would continuously decrease L + T, it is expected to attain the WHO's 2025 milestone (50% reduction in incidence rate by the year 2025) and 2035 target (90% reduction in the incidence rate by the year 2035).
Pre-entry screening programs for TB in migrant workers are believed to be a high-yield policy targeting active TB [5]. According to Taiwan's policy [36,37], newly arrived migrant workers from highly endemic countries are required to have a verified normal chest X-ray (CXR) performed overseas 3 months prior to entry and at various times post entry, i.e., post-entry screenings at 0-3 days (first round), 6 months (second round), 18 months (third round), and 30 months (fourth round) after arrival to obtain residency for a maximum of 3 years [38]. When employed migrants are confirmed by health examination to have active TB, TB pleurisy, or Hansen's disease, except for cases of multiple drug resistance, the employer should submit documents to the municipality or county (city) competent health authorities to apply for DOTS services within 15 days from the next day after receiving the diagnosis certificate [37]. However, the current screening tool and chest radiography are sensitive to detect active pulmonary TB but insufficient to catch LTBI [2]. Hence, improved diagnosis and effective treatment for LTBI among newly arrived individuals at risk are a major focus for the control and elimination of TB in the United States and other low-incidence countries [39][40][41][42].
Countries with a high burden of MDR-TB such as the Philippines, Indonesia, Vietnam, and Thailand are neighboring countries with close and frequent contacts with the Taiwanese population, and they represent the main importing countries of Taiwan's migrant workers. In recent years, China and Vietnam have imported the most MDR-TB cases from abroad (or have a history of going abroad), accounting for about 13% of reported MDR-TB cases [43]. Statistics show that the number of foreigners diagnosed with TB has increased from~450 in 2008 and remained at~850 in the past 5 years [43]. There are no relevant data to assist in estimating the transmission rate, reinfection rate, and other parameters among different regions, ages, and genders. To conduct model validations on the basis of the current available data, we compared the actual TB cases with our modeling outcomes and observed a trend of underestimations in model simulations in 2019 and 2020. However, the trend of decreasing case numbers from 2019 to 2020 in model simulation was in accordance with the changes in real case numbers in the same period [11]. We, thus, inferred that the lower estimates of the infected population in the three target cities could be ascribed to the lower reactivation rate in the latent population. We constructed a conservative model differentiating latent and infected TB cases into two different populations of the targeted three cities with most migrants in Taiwan. However, reactivation rates have been found to have high discrepancies in many studies [31,44,45]. We adopted the most conservative reactivation rate estimate (0.004) for the model simulations. However, the annual trend of TB case numbers could be predicted. The established model and derivations of the epidemiological parameters are also adaptable to different countries or regions with the issue of TB-infected migrant workers. Hence, with applications of the current constructed mathematical models, we considered a completely mixed and homogeneous system to simplify the complicated infection process. Furthermore, this study only assumed that the effectiveness of the control strategy reached a certain value. We did not consider the cost-effectiveness analysis associated with the type of control strategy since there is a lack of relevant data for calculating cost-related weights in Taiwan.

Conclusions
We used a parsimonious control-based SLTR transmission model to account for the mutual TB transmission between local populations and migrant workers for assessing the impact of potential control strategies on TB infection in three major hotspot cities in Taiwan regions, and we provided suggestions for sound control strategies that should be implemented. Overall, our findings suggest that the social distancing is the best single control strategy, while the best dual control is social distancing together with early screening. However, the effectiveness of the triple control strategy was marginally (1-3%) better than the dual measure. Therefore, if there are sufficient resources, a dual strategy should be implemented, which will reduce the total numbers of latently infected and infectious individuals more effectively than a single control, while also ensuring lower costs than the triple strategy. Our work has implications for migrant worker-associated TB infection prevention on a global scale and provides a knowledge base for exploring how outcomes can be best implemented by alternative control measure approaches.