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Assessing the transmission risk of multidrug-resistant Mycobacterium tuberculosis epidemics in regions of Taiwan

Open ArchivePublished:July 23, 2012DOI:https://doi.org/10.1016/j.ijid.2012.06.001

      Summary

      Objective

      The objective of this study was to link transmission dynamics with a probabilistic risk model to provide a mechanistically explicit assessment for estimating the multidrug-resistant tuberculosis (MDR TB) infection risk in regions of Taiwan.

      Methods

      A relative fitness (RF)-based MDR TB model was used to describe transmission, validated with disease data for the period 2006–2010. A dose–response model quantifying by basic reproduction number (R0) and total proportion of infected population was constructed to estimate the site-specific MDR TB infection risk.

      Results

      We found that the incidence rate of MDR TB was highest in Hwalien County (4.91 per 100 000 population) in eastern Taiwan, with drug-sensitive and multidrug-resistant R0 estimates of 0.89 (95% CI 0.23–2.17) and 0.38 (95% CI 0.05–1.30), respectively. The predictions were in apparent agreement with observed data in the 95% credible intervals. Our simulation showed that the incidence of MDR TB will be falling by 2013–2016. Our results indicated that the selected regions of Taiwan had only ∼1% probability of exceeding 50% of the population with infection attributed to MDR TB.

      Conclusions

      Our study found that the ongoing control programs implemented in Taiwan may succeed in curing most patients with MDR TB and will reduce the TB incidence countrywide.

      Keywords

      1. Introduction

      A recent World Health Organization (WHO) report documented that approximately one-third of the human population is infected with Mycobacterium tuberculosis, with 8.8 million new cases and 1.1 million deaths in 2010, and that the bacterium is becoming increasingly resistant to antibiotic therapy.

      World Health Organization. Global tuberculosis control 2011. Geneva: WHO; 2010. Available at: http://www.who.int/tb/publications/global_report/2011/gtbr11_full.pdf (accessed July 3, 2012).

      Therefore, tuberculosis (TB) remains a leading cause of death and results in high morbidity and mortality worldwide.

      World Health Organization. Global tuberculosis control 2011. Geneva: WHO; 2010. Available at: http://www.who.int/tb/publications/global_report/2011/gtbr11_full.pdf (accessed July 3, 2012).

      On the basis of these statistics, TB is among the top 10 causes of death worldwide. Despite predictions of a decline in global incidence, the number of new cases continues to grow.
      The emergence of strains resistant to multiple drugs has led to situations where treatment is no better than before the discovery of antibiotics.
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      The diagnosis of TB remains a major barrier to the control of the disease, because the standard method – the acid-fast smear using sputum – does not become positive until a few months after transmission has occurred.
      • Abu-Raddad L.J.
      • Sabatelli L.
      • Achterberg J.T.
      • Sugimoto J.D.
      • Longini Jr., I.M.
      • Dye C.
      • et al.
      Epidemiological benefits of more-effective tuberculosis vaccines, drugs, and diagnostics.
      Culture-based techniques are more sensitive, but still take weeks before providing results.
      • Russell D.G.
      • Barry 3rd, C.E.
      • Flynn J.L.
      Tuberculosis: what we don’t know can, and does, hurt us.
      Multidrug-resistant tuberculosis (MDR TB) has been documented in 114 countries and regions worldwide and has emerged as a global public health problem.

      World Health Organization. Multidrug and extensively drug-resistant TB (M/XDR-TB): 2010 global report on surveillance and response. Geneva: WHO; 2010. Available at: http://whqlibdoc.who.int/publications/2010/9789241599191_eng.pdf (accessed April 20, 2011).

      MDR TB is caused by strains resistant to at least isoniazid and rifampin, the two principal first-line drugs used in combination chemotherapy.
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      The treatment of MDR TB patients requires the use of second-line drugs for at least 24 months.
      • Iseman M.D.
      Treatment of multidrug-resistant tuberculosis.
      Thus, MDR TB is increasingly becoming a serious threat to TB control, and the recognition of extensively drug-resistant TB (XDR TB) has further highlighted this threat.
      • Shah N.S.
      • Wright A.
      • Bai G.H.
      • Barrera L.
      • Boulahbal F.
      • Martín-Casabona N.
      • et al.
      Worldwide emergence of extensively drug-resistant tuberculosis.
      Over 50% of global TB cases are found in Southeast Asia and the Western Pacific. In Taiwan, an estimated 149–164 new MDR TB cases emerged in the period 2007–2010.

      Centers for Disease Control. National notifiable disease surveillance system. Taiwan: Centers for Disease Control, Department of Health. Available at: /(accessed August 19, 2011).

      Although MDR TB represents only 1.2% of total new TB cases in Taiwan, controlling MDR TB is challenging because it is difficult to diagnose and treat.
      The simplest mathematical model for modeling MDR TB epidemics is that of Blower et al.
      • Blower S.M.
      • Small P.M.
      • Hopewell P.C.
      Control strategies for tuberculosis epidemics: new models for old problems.
      Over the past two decades, many expanded and sophisticated models have been used to predict the future burden of MDR TB.
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      • Dowdy D.W.
      • Chaisson R.E.
      • Maartens G.
      • Corbett E.L.
      • Dorman S.E.
      Impact of enhanced tuberculosis diagnosis in South Africa: a mathematical model of expanded culture and drug susceptibility testing.
      In view of these models, it is recognized that the assumptions about the relative fitness (RF) of drug-resistant (DR) strains play a crucial role in describing drug resistance dynamics.
      • Cohen T.
      • Sommers B.
      • Murray M.
      The effect of drug resistance on the fitness of Mycobacterium tuberculosis.
      • Borrell S.
      • Gagneux S.
      Infectiousness, reproductive fitness and evolution of drug-resistant Mycobacterium tuberculosis.
      Moreover, accurate estimates of the underlying parameters such as detection rates and treatment success rates are of critical importance for predicting the spread of MDR TB.
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      The transmission and population dynamics of MDR TB in the regions of Taiwan are poorly understood. To examine the MDR TB population dynamics and potential risk of infection in the Taiwan epidemic, a well-established mathematical model of MDR TB transmission built on previous MDR TB models
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      • Dowdy D.W.
      • Chaisson R.E.
      • Maartens G.
      • Corbett E.L.
      • Dorman S.E.
      Impact of enhanced tuberculosis diagnosis in South Africa: a mathematical model of expanded culture and drug susceptibility testing.
      was adopted to study the potential impact of MDR TB transmission. Although many excellent models for the transmission of MDR TB have been produced, an integrative, mechanistically explicit assessment on a regional scale for estimating the MDR TB infection risk is urgently needed.
      Given the importance of this question with regard to a large percentage of MDR TB cases that have resulted from recent transmission, we sought to extend previously published models of MDR TB transmission dynamics to incorporate a disease risk model. Therefore, a probabilistic risk assessment model linked with the MDR TB transmission model was developed to estimate MDR TB infection risks and to assess the potential impact of control measures on the emergence of a new DR strain in the regions of Taiwan.

      2. Materials and methods

      2.1 Study data

      Monthly data on the disease burden of TB in Taiwan were obtained from the Centers for Disease Control of Taiwan (Taiwan CDC) for the period 2005–2008 (http://www.cdc.gov.tw/). The incidence rate, morality rate, relapse proportion, reinfection proportion, and reactivation proportion were estimated based on Taiwan CDC TB data for each county (http://www.cdc.gov.tw/). In this study counties were geographically designated to four areas: northern, central, southern, and eastern regions. We found that the incidence rates were highest in Pingtung County in the southern region of Taiwan (108 per 100 000 population) and Hwalien (124 per 100 000 population) and Taitung (104 per 100 000 population) counties in the eastern region of Taiwan. Taipei City in the northern region of Taiwan had the lowest average incidence rate (50 per 100 000 population). Therefore, we used the TB epidemic data of Taipei City and Pingtung, Hwalien, and Taitung counties to investigate the MDR TB transmission dynamics and infection risk. Furthermore, the annual disease burden of MDR TB was adopted from the Taiwan Tuberculosis Control Report

      Centers for Disease Control. Taiwan tuberculosis control report 2007, 2008, 2009, 2010. Taiwan: Centers for Disease Control, Department of Health. Available at: http://www.cdc.gov.tw (accessed August 13, 2010).

      and the Taiwan CDC national notifiable disease surveillance system

      Centers for Disease Control. National notifiable disease surveillance system. Taiwan: Centers for Disease Control, Department of Health. Available at: /(accessed August 19, 2011).

      for each year during the period 2006–2010 to estimate the MDR TB incidence rates.
      To model drug resistance dynamics, data on the RF of DR strains had to be determined. One of the methods to measure the RF of resistant strains is based on the results of genotype clustering studies, with a cluster defined as two or more cases having the same genetic fingerprint.
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      Based on the genotype clustering method, RF can be estimated by calculating the odds ratio as RF = (CR/NR)/(CS/NS) where CR, CS, NR, and NS are the numbers of resistant (R) and sensitive (S) cases that appear singly (N) or in clusters (C).
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      García-García et al.,
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      recently provided valuable data that can be used to estimate the RF of MDR TB that is resistant to isoniazid and rifampin. Briefly, García-García et al.
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      grouped TB patients with identical DNA fingerprints into clusters, with a cluster presumed to be epidemiologically linked. Twenty clusters were identified and investigated. They also excluded the possibility that resistance had been acquired since transmission by testing patients for drug susceptibility before treatment. Thus, a single cluster could only include sensitive or resistant strains.
      They found that the overall rate of resistance was 28.4%, with 10.8% having MDR TB. Based on genotype clustering analysis with multivariate risk factors associated with clustering, the odds ratio of MDR TB was estimated to be 0.16 (95% confidence interval (CI) 0.04–0.6). Based on this result, an optimal fitting technique was used to obtain a best-fitted distribution to capture the uncertainty. Their results indicated that drug resistance was a strong independent risk factor for treatment failure. They thus concluded that patients with DR TB had a dramatically increased probability of treatment failure and death.

      2.2 Resistant TB transmission model

      Previously developed DR TB transmission models
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      • Blower S.M.
      • Small P.M.
      • Hopewell P.C.
      Control strategies for tuberculosis epidemics: new models for old problems.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      were adopted and modified to describe the population dynamics of MDR TB in Taiwan. The present model captures the five group dynamics of susceptible (S), latently infected with drug-sensitive (DS) TB (LS), latently infected with MDR TB (LR), DS infectious TB (TS), and MDR infectious TB (TR) and can be referred to as the two-strain TB model. The essential features of the present model are depicted in Figure 1.
      Figure thumbnail gr1
      Figure 1Drug-sensitive and drug-resistant two-strain TB model describing MDR TB population transmission dynamics in the present study.
      Briefly, (1) susceptible individuals may be infected with either DS or MDR strains, (2) two types of TB are included – primary progressive TB (i.e., fast TB) and latently infected TB caused by endogenous reactivation or exogenous reinfection (i.e., slow TB), (3) a case may be spontaneously cured at a cure rate and move into the latent noninfection state, and (4) MDR TB may emerge when individuals are primary infected/reinfected with an MDR strain (i.e., primary resistance) or as a result of treatment failure (i.e., acquired resistance). Table 1 lists the system of ordinary differential equations with detailed explanations of the symbols for the two-strain TB model in Figure 1.
      Table 1Equations for the proposed two-strain TB model
      Equation
      Symbols: π=Nδ is the recruitment rate (per person-year) where δ is the birth rate (per year) and N is the total population size; p is the probability of new infections that develop progressive primary active TB within 1 year; ν is the progression rate from latency to active TB (per year); μ is the background mortality rate (per year); μS is the DS TB caused mortality rate (per year); μR is the MDR TB caused mortality rate (per year); σ is the factor reducing the risk of infection as a result of acquired immunity to a previous infection with sensitive and resistant TB; cs is the cure rate of active DS TB (per year); cR is the cure rate of active MDR TB (per year); cF is the proportion of DS TB treatment failure acquiring resistance; ECR is the effective contact rate (per year); βS is the transmission rate for DS TB (per person per year); βR is the transmission rate for MDR TB (per person per year).
      Meaning
      Two-strain TB model
      See Figure 1.
      S˙(t)=π(βSTS+βRTR+μ)S(T1)Susceptible individuals
      L˙S(t)=(1p)βSTSS+cSTS(ν+pσβSTS+σβRTR+μ)LS(T2)Latently infected individuals with DS TB
      L˙R(t)=(1p)βRTRS+(1p)σβRTRLS+cRTR(ν+pσβSTS+pσβRTR+μ)LR(T3)Latently infected individuals with MDR TB
      T˙S(t)=pβSTSS+(ν+pσβSTS)LS(cS+μ+μS+(1cS)cF)TS(T4)DS infectious TB
      T˙R(t)=pβRTRS+pσβRTRLS+(ν+pσβSTS+pσβRTR)LR+(1cS)cFTS(cR+μ+μR)TR(T5)MDR infectious TB
      Basic reproduction number
      R0S=βSNp(μ+ν)(μ+ν)(μ+μS+cS+(1cS)cF)cSν(T6)Basic reproduction number of DS TB
      R0R=βRNp(μ+ν)(μ+ν)(μ+μR+cR)cRν(T7)Basic reproduction number of MDR TB
      TB, tuberculosis; DS, drug-sensitive; MDR, multidrug-resistant.
      a Symbols: π =  is the recruitment rate (per person-year) where δ is the birth rate (per year) and N is the total population size; p is the probability of new infections that develop progressive primary active TB within 1 year; ν is the progression rate from latency to active TB (per year); μ is the background mortality rate (per year); μS is the DS TB caused mortality rate (per year); μR is the MDR TB caused mortality rate (per year); σ is the factor reducing the risk of infection as a result of acquired immunity to a previous infection with sensitive and resistant TB; cs is the cure rate of active DS TB (per year); cR is the cure rate of active MDR TB (per year); cF is the proportion of DS TB treatment failure acquiring resistance; ECR is the effective contact rate (per year); βS is the transmission rate for DS TB (per person per year); βR is the transmission rate for MDR TB (per person per year).
      b See Figure 1.
      The expressions for the basic reproduction number (R0),
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      • van den Driessche P.
      • Watmough J.
      Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.
      quantifying the transmission potential of M. tuberculosis due to the subepidemic driven by DS TB (R0S) and MDR TB (R0R), are summarized in Table 1. R0 is defined as the average number of successful secondary infection cases generated by a typical primary infected case in an entirely susceptible population.
      • Anderson R.M.
      • May R.M.
      Infectious diseases of humans: dynamics and control.
      When R0 > 1 it implies that the epidemic is spreading within a population and the incidence is increasing, whereas R0 < 1 means that the disease is dying out. An average R0 of 1 means the disease is in endemic equilibrium within the population. R0 essentially determines the rate of spread of an epidemic and how intensive a policy will need to be to control the epidemic.
      • Ferguson N.M.
      • Keeling M.J.
      • Edmunds W.J.
      • Gani R.
      • Grenfell B.T.
      • Anderson R.M.
      • et al.
      Planning for smallpox outbreaks.

      2.3 Probabilistic DS/MDR TB risk model

      To develop a probabilistic DS/MDR TB risk model, a dose–response model describing the relationships of the transmission potential of DS/DR M. tuberculosis quantifying by R0 and the total proportion of infected population has to be constructed. Generally, the probability of infection for each susceptible person each day is based on the transmission probabilities for each potentially infected contact. According to Anderson and May,
      • Anderson R.M.
      • May R.M.
      Infectious diseases of humans: dynamics and control.
      in a homogeneous and unstructured population, the total proportion of infected population during the epidemic (I) depends only on R0, and can theoretically be expressed as,
      I=1exp(R0I)
      (1)


      Equation 1 cannot be solved analytically. Thus, we solved Equation 1 numerically using a nonlinear regression model to best-fit the profile describing the relationship between I and R0
      • Anderson R.M.
      • May R.M.
      Infectious diseases of humans: dynamics and control.
      for R0 ranging from 1 to 5. Finally, I can be expressed as a function of R0 only,
      I(R0)=1exp(1.631.66R0),1<R0<5,r2=0.99
      (2)


      Equation 2 can be seen as a conditional response distribution describing the dose–response relationship between I and R0 and can be expressed as: P(I|R0). Thus, followed by Bayesian inference, the DS/DR TB infection risk (the posterior probability) can be calculated as the product of the probability distribution of R0 (the prior probability) and the conditional response probability of the proportion of the population expected to be infected, given R0 (the likelihood P(I|R0)). This results in a joint probability distribution or a risk profile. This can be expressed mathematically as,
      R(I)=P(R0)×P(I|R0),
      (3)


      where R(I) is the cumulative distribution function (cdf) describing the probabilistic infection risk of a TB epidemic in a susceptible population at specific R0, and P(R0) is the probability density function (pdf) of R0. The exceedance risk profile can be obtained by 1 − R(I). Each point on the exceedance risk curve represents both the probability that the total proportion will be infected and also the frequency with which that level of infection would be exceeded. The x-axis of the exceedance risk curve can be interpreted as a magnitude of effect (total proportion of infection), and the y-axis can be interpreted as the probability that an effect of at least that magnitude will occur.

      2.4 Model parameterization and validation

      The likely values of key parameters in the two-strain TB model (Table 1, equations T1–T5) can be parameterized based on available site-specific TB data provided by the Taiwan CDC, Department of Statistics, Ministry of the Interior, Taiwan,

      Department of Statistics. Statistical yearbook of interior: population by age. Taiwan: Department of Statistics, Ministry of the Interior. Available at: http://www.moi.gov.tw/stat/index.aspx (accessed January 14, 2010).

      and otherwise based on data adopted from the literature.
      • Dye C.
      • Garnett G.P.
      • Sleeman K.
      • Williams B.G.
      Prospects for worldwide tuberculosis control under the WHO DOTS strategy.
      • Blower S.M.
      • McLean A.R.
      • Porco T.C.
      • Small P.M.
      • Hopewell P.C.
      • Sanchez M.A.
      • et al.
      The intrinsic transmission dynamics of tuberculosis epidemics.
      • Dye C.
      • Espinal M.A.
      Will tuberculosis become resistant to all antibiotics?.
      • Porco T.C.
      • Blower S.M.
      Quantifying the intrinsic transmission dynamics of tuberculosis.
      • Yeh Y.P.
      • Luh D.L.
      • Chang S.H.
      • Suo J.
      • Chang H.J.
      • Chen T.H.
      Tuberculin reactivity in adults after 50 years of universal bacille Calmette–Guérin vaccination in Taiwan.
      We used the model to project future site-specific TB incidence dynamics for 2006–2016 with the 95% credible interval.
      We validated the two-strain TB model by comparing predicted site-specific MDR TB incidence with observed MDR TB incidence provided by the Taiwan CDC for 2006–2010. To compare modeled and observed results, the best fit was evaluated using the root mean squared error (RMSE), computed from RMSE = n=1N(Io,nIs,n)2/N where N denotes the number of observations, Io,n is the observed incidence, and Is,n is the simulation result corresponding to data point n.

      2.5 Sensitivity and uncertainty analyses

      A sensitivity analysis was performed to examine the influence of critical variables on the basic reproduction number. TableCurve 2D package (AISN Software Inc., Mapleton, OR, USA) and Statistica (version 9; Statsoft, Inc., Tulsa, OK, USA) were used to perform model fitting techniques and statistical analyses. A Monte Carlo (MC) technique was implemented to quantify the uncertainty and its impact on the estimation of expected risk. An MC simulation was also performed with 10 000 iterations to generate the 2.5 and 97.5 percentiles as the 95% CI for all fitted models. Crystal Ball software (Version 2000.2, Decisioneering, Inc., Denver, CO, USA) was employed to implement the MC simulation. Model simulations were performed using Berkeley Madonna 8.0.1 (Berkeley Madonna was developed by Robert Macey and George Oster of the University of California at Berkeley).
      Figure 2 illustrates the overall computational algorithm of this study.
      Figure thumbnail gr2
      Figure 2Schematic representation of the principal algorithms and approach methodology used in this study.

      3. Results

      3.1 Population dynamics of DS/MDR TB

      Table 2 summarizes the estimates of the MDR TB incidence rate for Hwalien, Taitung, and Pingtung counties and Taipei City in the period 2006–2010. We found that the incidence rate of MDR TB was highest in Hwalien County (4.91 per 100 000 population). Taipei City had the lowest average MDR TB incidence rate of 0.43 per 100 000 population.
      Table 2MDR TB incidence rates (per 100 000 population) during 2006–2010
      Incidence rate (per 100 000 population): annual region confirmed MDR TB cases/total regional population number. Adopted from the Taiwan tuberculosis control report18 and Taiwan CDC national notifiable disease surveillance system.9
      Sites20062007200820092010Average
      Mean±standard deviation.
      Hwalien County8.664.632.144.994.124.91 ± 2.37
      Taitung County5.852.941.871.292.162.82 ± 1.79
      Pingtung County1.331.260.990.570.680.97 ± 0.34
      Taipei City0.620.360.460.380.350.43 ± 0.11
      MDR TB, multidrug-resistant tuberculosis.
      a Incidence rate (per 100 000 population): annual region confirmed MDR TB cases/total regional population number. Adopted from the Taiwan tuberculosis control report

      Centers for Disease Control. Taiwan tuberculosis control report 2007, 2008, 2009, 2010. Taiwan: Centers for Disease Control, Department of Health. Available at: http://www.cdc.gov.tw (accessed August 13, 2010).

      and Taiwan CDC national notifiable disease surveillance system.

      Centers for Disease Control. National notifiable disease surveillance system. Taiwan: Centers for Disease Control, Department of Health. Available at: /(accessed August 19, 2011).

      b Mean ± standard deviation.
      The results of the model parameterization are listed in Table 3. Published data
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      were optimal-fitted to obtain the likelihood distribution of RF by MC simulation. This resulted in a normal (N) distribution of RF with a mean of 0.32 and standard deviation (SD) of 0.14 (Table 3). We incorporated the estimated probability distributions of the model parameter with site-specific initial population sizes (Table 3) into the two-strain TB model (Table 1, equations T1–T5) to project future site-specific population dynamics of MDR TB incidence for 2006–2016 (Figure 3, Figure 4).
      Table 3Probability distributions (N = normal, LN = log-normal) of parameter values and initial population sizes used in the two-strain TB model, and basic reproduction number (R0) estimations
      See Table 1 for symbol meanings.
      Probability distribution
      Hwalien CountyTaitung CountyPingtung CountyTaipei City
      Model parameter
      p
      Estimated as 0.04 (0.015–0.14) for <15 years old and 0.14 (0.08–0.25) for>15 years old.24
      N (0.08, 0.03)
      ν (per year)
      ECR (effective contact rate) and ν are estimated based on Blower et al.25
      N (0.00392, 0.0007)
      μ (per year)
      Estimated based on data from the Department of Statistics, Ministry of the Interior, Taiwan (http://www.moi.gov.tw/stat/index.aspx).23
      LN (0.031, 2.05)LN (0.031, 2.05)LN (0.030, 2.11)LN (0.027, 2.00)
      μS (per year)
      Estimated based on Taiwan CDC data (http://www.cdc.gov.tw/).
      N (0.037, 0.015)N (0.040, 0.019)N (0.052, 0.021)N (0.033, 0.013)
      μR (per year)
      Estimated based on Dye and Espinal.26
      N (0.30, 0.05)
      cS (per year)
      Estimated based on Taiwan CDC data (http://www.cdc.gov.tw/).
      N (0.64, 0.07)N (0.61, 0.08)N (0.68, 0.09)N (0.72, 0.01)
      cR (per year)
      Estimated based on Dye and Espinal.26
      LN (0.10, 2.68)LN (0.08, 2.83)LN (0.18, 1.89)LN (0.28, 1.41)
      cF
      Estimated based on Taiwan CDC data (http://www.cdc.gov.tw/).
      N (0.034, 0.018)N (0.024, 0.022)N (0.017, 0.007)N (0.016, 0.005)
      ECR (per year)
      ECR (effective contact rate) and ν are estimated based on Blower et al.25
      LN (7.40, 1.33)
      N (person)
      Estimated based on data from the Department of Statistics, Ministry of the Interior, Taiwan (http://www.moi.gov.tw/stat/index.aspx).23
      N (345 297, 2748)N (236 156, 3174)N (893 289, 5625)N (2 625 962, 8435)
      π (per person year)29602228728421217
      RF
      RF is the relative fitness estimated based on García-García et al.19
      N (0.32, 0.14)
      σ
      Adopted from Rodrigues et al.14
      0.25
      βS (per person per year)
      βS=ECR/N, where N is the total population size.27
      LN (2.14 × 10−5, 1.33)LN (3.13 × 10−5, 1.33)LN (8.28 × 10−6, 1.33)LN (2.82 × 10−6, 1.33)
      βR (per person per year)
      βR=RF×βS.11,13,14
      LN (6.11 × 10−6, 1.91)LN (8.93 × 10−6, 1.91)LN (2.36 × 10−6, 1.91)LN (8.03 × 10−7, 1.91)
      Initial population size
      The initial population sizes in 2006 of N, TS, and TR are adopted from the Taiwan Tuberculosis Control Report.18 S=N − LS − LR − TS − TR. LS=0.004×0.92×0.99×N, and LR=0.004×0.92×0.01×N, where 0.004 is adopted from Yeh et al.,28 0.92=(1 − 0.08),24 and the proportions of infections that develop LS (0.99) and LR (0.01) are assumed.
      N346 301237 450893 5292 624 309
      S344 338236 153888 5542 612 793
      LS126286532419561
      LR1393397
      TS65940916901843
      TR30141216
      TB, tuberculosis.
      a See Table 1 for symbol meanings.
      b Estimated as 0.04 (0.015–0.14) for <15 years old and 0.14 (0.08–0.25) for > 15 years old.
      • Dye C.
      • Garnett G.P.
      • Sleeman K.
      • Williams B.G.
      Prospects for worldwide tuberculosis control under the WHO DOTS strategy.
      c ECR (effective contact rate) and ν are estimated based on Blower et al.
      • Blower S.M.
      • McLean A.R.
      • Porco T.C.
      • Small P.M.
      • Hopewell P.C.
      • Sanchez M.A.
      • et al.
      The intrinsic transmission dynamics of tuberculosis epidemics.
      d Estimated based on data from the Department of Statistics, Ministry of the Interior, Taiwan (http://www.moi.gov.tw/stat/index.aspx).

      Department of Statistics. Statistical yearbook of interior: population by age. Taiwan: Department of Statistics, Ministry of the Interior. Available at: http://www.moi.gov.tw/stat/index.aspx (accessed January 14, 2010).

      e Estimated based on Taiwan CDC data (http://www.cdc.gov.tw/).
      f Estimated based on Dye and Espinal.
      • Dye C.
      • Espinal M.A.
      Will tuberculosis become resistant to all antibiotics?.
      g RF is the relative fitness estimated based on García-García et al.
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      h Adopted from Rodrigues et al.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      i βS = ECR/N, where N is the total population size.
      • Porco T.C.
      • Blower S.M.
      Quantifying the intrinsic transmission dynamics of tuberculosis.
      j βR = RF × βS.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      k The initial population sizes in 2006 of N, TS, and TR are adopted from the Taiwan Tuberculosis Control Report.

      Centers for Disease Control. Taiwan tuberculosis control report 2007, 2008, 2009, 2010. Taiwan: Centers for Disease Control, Department of Health. Available at: http://www.cdc.gov.tw (accessed August 13, 2010).

      S = NLSLRTSTR. LS = 0.004 × 0.92 × 0.99 × N, and LR = 0.004 × 0.92 × 0.01 × N, where 0.004 is adopted from Yeh et al.,
      • Yeh Y.P.
      • Luh D.L.
      • Chang S.H.
      • Suo J.
      • Chang H.J.
      • Chen T.H.
      Tuberculin reactivity in adults after 50 years of universal bacille Calmette–Guérin vaccination in Taiwan.
      0.92 = (1 − 0.08),
      • Dye C.
      • Garnett G.P.
      • Sleeman K.
      • Williams B.G.
      Prospects for worldwide tuberculosis control under the WHO DOTS strategy.
      and the proportions of infections that develop LS (0.99) and LR (0.01) are assumed.
      Figure thumbnail gr3
      Figure 3Modeling incidence rates (per 100 000 population) of MDR TB varying with different βR estimates of 25th, 50th, and 75th percentiles during 2006–2016 by two-strain TB model and the comparison of incidence rates between predictions with βS- and βR-adjusted model simulation outcomes and observed data during 2006–2010 in (A) Taipei City, (B) Hwalien County, (C) Pingtung County, and (D) Taitung County.
      Figure thumbnail gr4
      Figure 4Incidence rates (per 100 000 population) of MDR TB estimates based on the justified βS estimate varying with different RF values for 2006–2016 and the comparison of the incidence data with RF-adjusted model simulation outcomes with 95% credible intervals during 2006–2010 in (A) Hwalien County, (B) Taitung County, (C) Pingtung County, and (D) Taipei City.
      Figure 3A–D demonstrates the comparison of the MDR TB incidence rates between predictions adjusted by βS and βR estimates of the 25th, 50th, and 75th percentiles. The results indicated that the predictions with the 50th percentile were consistent with the observed data in Taipei City (Figure 3A), whereas for Pingtung and Taitung Counties, the predictions with the 25th percentile were in a good agreement with the observations (Figure 3C and D) for the period 2007–2010. However, the observed MDR TB incidence in Hwalien County showed a decreasing trend of predictions that was fairly consistent with the 50th percentile data points (Figure 3B). Thus, we modeled based on the justified βS estimate of the 25th percentile for Pingtung and Taitung counties and the 50th percentile for Hwalien County and Taipei City, varying with different RF values to further validate the model against the justified RF estimate (Figure 4).
      Figure 4A–D shows the comparison of the MDR TB incidence data with our RF-adjusted model simulation outcomes with 95% credible intervals, indicating that the predictions were in apparent agreement with the observed data during the period 2007–2010. The model was also extended to project the MDR TB incidence rate for the period 2011–2016. Despite the simplicity of the model, we found a fair quantitative agreement between model predictions and observed data (the average RMSE ranging from 0.11 to 1.58, comparable to the data average standard deviation of 0.11–2.37). Our model had the lowest RMSE values for the predictions with the 75th (RMSE = 1.10), 50th (RMSE = 0.50), 50th (RMSE = 0.16), and 50th percentiles (RMSE = 0.05) in Hwalien, Taitung, and Pingtung counties and Taipei City, respectively, indicating that all RMSE values are less than the standard deviation of the observed data (Figure 4 and Table 2). Overall, the model captures the transmission and population dynamics of MDR TB in high TB incidence areas in Taiwan for the period 2007–2010.

      3.2 DS/MDR TB infection risk estimates

      To estimate the probability of DS/MDR TB infection risk, the transmission potential quantified by basic reproduction number (R0S and R0R) had to be determined. The site-specific R0S and R0R due to a subepidemic driven by primary progression, reactivation/reinfection, and cure were calculated based on equations listed in Table 1 (equations T6 and T7) (Figure 5). The MC simulation result showed that the optimized log-normal distribution was the most suitable fitted model for R0S and R0R. We found that, for instance, in the highest TB epidemic area of Hwalien County, the R0S and R0R estimates were 0.89 (95% CI 0.23–2.17) and 0.38 (95% CI 0.05–1.30), respectively, whereas R0S and R0R values were estimated to be 0.94 (95% CI 0.24–2.28) and 0.38 (95% CI 0.05–1.33), respectively, in Taitung County. The R0S and R0R estimates in Pingtung County were 0.85 (95% CI 0.21–2.08) and 0.34 (95% CI 0.04–1.13), respectively, whereas Taipei City had the lowest values with R0S and R0R estimates of 0.84 (95% CI 0.21–2.00) and 0.30 (95% CI 0.04–0.97), respectively.
      Figure thumbnail gr5
      Figure 5Box and whisker plot illustrating the basic reproduction number of DS TB (R0S) and MDR TB (R0R) in Hwalien, Taitung, and Pingtung counties and Taipei City.
      Figure 6A demonstrates the conditional dose–response profile of P(I|R0) based on Equation 2. Given the site-specific R0S and R0R distributions (Figure 5) and conditional dose–response relationship P(I|R0) (Figure 6A), the site-specific exceedance risk probability of DS/MDR TB infection can then be estimated by Equation 3 (Figure 6B and C). We found that the total DS TB incidences in Hwalien, Taitung, and Pingtung counties and Taipei City had respective probabilities of nearly 13%, 16%, 11%, and 9.7% for the total proportion of infected population exceeding 50%, whereas there were 18–27% probabilities of having exceeded 20% of the total proportion of infected population (Figure 6B). Our results also indicated that the selected four regions had only ∼1% probability of exceeding 50% of the population with infection attributed to MDR TB (Figure 6C).
      Figure thumbnail gr6
      Figure 6(A) Dose–response profile representing the estimate of the total proportion of TB-infected population, P(I), based on R0 estimated from Equation 2. Exceedance risks of the total proportions of TB infections estimated for (B) DS TB and (C) MDR TB in Hwalien, Taitung, and Pingtung counties and Taipei City.

      3.3 Sensitivity analysis

      Our sensitivity analysis indicated that an increase in R0R was attributed mainly to: (1) relative fitness (RF), (2) the probability of new infections that develop progressive primary active TB within 1 year (p), and (3) the transmission rate for DS TB (βS) (Table 4). However, an increase in the cure rate of active MDR TB (cR) can decrease R0R moderately.
      Table 4Probabilistic sensitivity analysis for the basic reproduction number of MDR TB (R0R)
      Input parameter
      See Tables 1 and 2 for symbol meanings.
      Contribution (%)
      Hwalien CountyTaitung CountyPingtung CountyTaipei City
      RF41.20%40.51%41.81%44.35%
      p30.67%31.98%30.63%32.70%
      βS14.59%14.07%51.68%15.45%
      ν0.00%0.02%0.02%0.02%
      N0.00%0.01%0.00%0.00%
      μ−1.18%−0.80%−1.34%−1.34%
      μR−3.19%−2.32%−2.05%−1.58%
      cR−9.16%−10.29%−8.47%−4.57%
      MDR TB, multidrug-resistant tuberculosis.
      a See Table 1, Table 2 for symbol meanings.
      In our four selected study areas, the most important input variables for R0R appeared to be RF and p, which contributed to 40.51–44.35% and 30.63–32.70% of output variances, respectively (Table 4). Thus our results indicate that RF is the key parameter in shaping R0R. Therefore, the rate of spread of an MDR TB epidemic could be controlled by reducing RF.

      4. Discussion

      4.1 Population dynamics of DR TB

      Although it is recognized that exogenous reinfection plays an important role in DR TB epidemics,
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Blower S.M.
      • Chou T.
      Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance.
      several mathematical models to predict the future spread of DR TB have not taken it into consideration.
      • Luciani F.
      • Sisson S.A.
      • Jiang H.
      • Francis A.R.
      • Tanaka M.M.
      The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis.
      • Blower S.M.
      • Small P.M.
      • Hopewell P.C.
      Control strategies for tuberculosis epidemics: new models for old problems.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      There are a few DR TB models that have considered reinfection,
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Blower S.M.
      • Chou T.
      Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance.
      but the implementations have varied significantly. Blower and Chou
      • Blower S.M.
      • Chou T.
      Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance.
      and Dye and Williams
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      incorporated reinfection at a reduced rate by partial immunity applying to latently infected individuals only.
      Cohen and Murray
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      considered that latent and recovered individuals have partial immunity against reinfection and have identical susceptibilities to reinfection. Furthermore, several epidemiological studies have demonstrated that DR and MDR strains have heterogeneity in fitness.
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      • Cohen T.
      • Sommers B.
      • Murray M.
      The effect of drug resistance on the fitness of Mycobacterium tuberculosis.
      • Borrell S.
      • Gagneux S.
      Infectiousness, reproductive fitness and evolution of drug-resistant Mycobacterium tuberculosis.
      Most models have indicated that RF is the most important parameter influencing the disease burden of DR and MDR TB. However, these did not directly estimate the impact of heterogeneity of RF for DR strains on transmission dynamics, especially for MDR strains.
      • Blower S.M.
      • Small P.M.
      • Hopewell P.C.
      Control strategies for tuberculosis epidemics: new models for old problems.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Rodrigues P.
      • Gomes M.G.
      • Rebelo C.
      Drug resistance in tuberculosis—a reinfection model.
      A few studies have allowed for variation in RF of MDR strains to model the emergence of an MDR TB epidemic.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Blower S.M.
      • Chou T.
      Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance.
      We constructed a two-strain TB model based on the past well-developed DR TB transmission models that have incorporated reinfection, emergence of multidrug resistance during therapy, heterogeneity of RF of MDR strains, and competition between DS and MDR strains to describe the transmission and population dynamics of MDR TB in Taiwan.
      Practically, our present model captures the transmission and population dynamics of MDR TB in high TB incidence areas of Taiwan for the period 2007–2010. Our study found that the incidence rate of MDR TB was highest in eastern Taiwan (4.91 per 100 000 population) compared to the lowest average incidence of 0.43 per 100 000 population in northern Taiwan. Several studies have indicated that MDR TB is a major problem in the aboriginal population in eastern Taiwan.
      • Hsueh P.R.
      • Liu Y.C.
      • So J.
      • Liu C.Y.
      • Yang P.C.
      • Luh K.T.
      Mycobacterium tuberculosis in Taiwan.
      • Tsai H.T.
      • Liu T.M.
      Challenges and solutions in improving tuberculosis care among aboriginal people in Taiwan.
      • Hsu A.H.
      • Lin C.B.
      • Lee Y.S.
      • Chiang C.Y.
      • Chen L.K.
      • Tsai Y.S.
      • et al.
      Molecular epidemiology of multidrug-resistant Mycobacterium tuberculosis in Eastern Taiwan.
      However, the observed MDR TB incidence at our four study sites showed a decreasing trend due to improvements in TB control measures in Taiwan, in particular the implementation of the MDR TB program (Multi-Drug Resistant TB Medicare System) in 2007. Given the high frequency of MDR TB in eastern Taiwan, our simulation showed that the incidence of MDR TB will be falling by 2013–2016. Our results also indicated that there was only a ∼1% probability of exceeding 50% of the population with infection attributed to MDR TB. Therefore, the annual decline in the incidence of MDR TB in Taiwan can be expected with good TB control programs.
      Our results also showed that the basic reproduction number of MDR strains (R0R) was lower than that of non-MDR strains (R0S), indicating that the RF of MDR strains is less than 1. If we maintained this situation, the number of MDR strains could be decreased to the lower numbers generated by mutation. Our findings also implicitly provide information that the ongoing control programs implemented in Taiwan may succeed in curing most patients with MDR TB and reduce the TB incidence countrywide.
      However, TB is a very complex disease and, in addition to host–pathogen parameters, one has to consider several socio-economic factors for modeling population dynamics of TB or DR TB.
      • Abu-Raddad L.J.
      • Sabatelli L.
      • Achterberg J.T.
      • Sugimoto J.D.
      • Longini Jr., I.M.
      • Dye C.
      • et al.
      Epidemiological benefits of more-effective tuberculosis vaccines, drugs, and diagnostics.
      • Dowdy D.W.
      • Chaisson R.E.
      • Maartens G.
      • Corbett E.L.
      • Dorman S.E.
      Impact of enhanced tuberculosis diagnosis in South Africa: a mathematical model of expanded culture and drug susceptibility testing.
      • Dowdy D.W.
      • Steingart K.R.
      • Pai M.
      Serological testing versus other strategies for diagnosis of active tuberculosis in India: a cost-effectiveness analysis.
      • Koul A.
      • Arnoult E.
      • Lounis N.
      • Guillemont J.
      • Andries K.
      The challenge of new drug discovery for tuberculosis.
      Socio-economic factors such as the paucity of medical service resources, information barriers, financial difficulties, and the inconvenience of transportation could result in less effective TB control among aborigines in eastern Taiwan.
      • Tsai H.T.
      • Liu T.M.
      Challenges and solutions in improving tuberculosis care among aboriginal people in Taiwan.
      It is also important to consider the immune system that is affected by co-infections, past therapeutic history, and age.
      • Keeker E.
      • Perkins M.D.
      • Small P.
      • Hanson C.
      • Reed S.
      • Cunningham J.
      • et al.
      Reducing the global burden of tuberculosis: the contribution of improved diagnostics.
      Recently, evidence has also indicated a strong association between smoking and TB. den Boon et al.
      • den Boon S.
      • van Lill S.W.
      • Borgdorff M.W.
      • Verver S.
      • Bateman E.D.
      • Lombard C.J.
      • et al.
      Association between smoking and tuberculosis infection: a population survey in a high tuberculosis incidence area.
      reported that more than 80% of current smokers or ex-smokers were positive for the TB skin test as compared to less than 3% of nonsmokers. Aborigines in the eastern Taiwan region are subpopulations with high smoking frequencies. We thus anticipate that future studies may include some of these parameters in the analysis to forecast the reduction in the incidence of TB or MDR TB.

      4.2 Infection risk estimates of DS/MDR TB

      Our results on R0 estimates showed that R0S was larger than R0R at the four study sites. The persistence of both DS and DR TB (i.e., coexistence) occurs if R0S > 1 and R0S > R0R. Under these conditions, the coexistence can even occur when R0R < 1.
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      We also found that the incidence of DS TB in Hwalien, Taitung, and Pingtung counties and Taipei City had respective probabilities of nearly 13%, 16%, 11%, and 9.7% of the total proportion of infected population exceeding 50%, whereas there was only ∼1% probability of having exceeded 50% of the population with infection attributed to MDR TB.
      Although it appears unlikely that MDR TB will result in an emergence, the case reproduction numbers of DS TB are alarming from a conservative point of view. As long as patients carry sensitive strains, there will always be some relative MDR TB cases, due to MDR TB arising from treatment failure, mutation at some constant frequency, and the occasional transmission of MDR strains. However, in the worst case scenario, when the basic reproduction number of DR strains exceeds that of DS strains, resistant cases can out-compete sensitive cases and all patients will eventually carry resistant strains.

      4.3 Limitations and implications

      A key weakness of this approach is that in many cases the true uncertainty around key parameter values may not be captured adequately. It is difficult, if not impossible, to assess the validity of either the individual adjustment parameters or the final estimate, because, to our knowledge, well-established standard values for comparison do not exist. Our sensitivity analysis shows that RF is the key parameter influencing the basic reproduction number of MDR TB (R0R). Several studies on the population dynamics of DR TB have shown RF to be a key determinant in assessing the future burden of DR TB
      • Blower S.M.
      • Gerberding J.L.
      Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework.
      and MDR TB.
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Dye C.
      • Espinal M.A.
      Will tuberculosis become resistant to all antibiotics?.
      In the present study, the most unknown important parameter is RF of MDR strains as compared with DS strains.
      We found a wide range of molecular epidemiological RF of MDR strain estimates.
      • Dye C.
      • Williams B.G.
      • Espinal M.A.
      • Raviglione M.C.
      Erasing the world's slow strain: strategies to beat multidrug-resistant tuberculosis.
      • Cohen T.
      • Sommers B.
      • Murray M.
      The effect of drug resistance on the fitness of Mycobacterium tuberculosis.
      The RF estimates for MDR TB ranged from an almost 10-fold higher fitness compared to DS strains in Russia, to a nearly 10-fold lower fitness in Mexico. The possible reasons for this high variability in RF of MDR strains are differences in study design and setting, differences in sample size, and different methodologies.
      • Cohen T.
      • Sommers B.
      • Murray M.
      The effect of drug resistance on the fitness of Mycobacterium tuberculosis.
      Although, there is a wide range of RF, several researchers
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      • Dye C.
      • Espinal M.A.
      Will tuberculosis become resistant to all antibiotics?.
      have used low RF for mathematical modeling of MDR TB. Dye and Williams
      • Dye C.
      • Williams B.C.
      Criteria for the control of drug-resistant tuberculosis.
      used a parameter value for RF of MDR strains ranging from 0.7 to 1.0. Dye and Espinal
      • Dye C.
      • Espinal M.A.
      Will tuberculosis become resistant to all antibiotics?.
      modified their RF estimates for MDR strains to uniform distribution between 0.04 and 0.6 based on a TB cluster study.
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      Cohen and Murray
      • Cohen T.
      • Murray M.
      Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness.
      assumed that the ‘unfit’ MDR strains had a low fitness (0.3) relative to the DS strain, whereas the ‘fit’ MDR strain had RF ranging from 0.8 to 1.2.
      García-García et al.
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      recently provided valuable data from a molecular epidemiology study in Mexico that can be used to estimate RF of MDR TB. The MDR TB incidence rate in Mexico in 2008 was estimated to be 0.6 (95% CI 0.3–0.9) per 100 000 population.

      World Health Organization. Towards universal access to diagnosis and treatment of multidrug-resistant and extensively drug-resistant tuberculosis by 2015. WHO progress report 2011. Geneva: WHO; 2011. Available at: http://whqlibdoc.who.int/publications/2011/9789241501330_eng.pdf (accessed April 2, 2012).

      The average MDR TB incidence rate for Taiwan during 2007–2010 (0.7 per 100 000 population) provided by the Taiwan CDC was similar to that of Mexico. Thus, we estimated RF for MDR strains with a normal (N) distribution of a mean 0.32 and a standard deviation 0.14 based on García-García et al.
      • García-García M.L.
      • Ponce de León A.
      • Jiménez-Corona M.E.
      • Jiménez-Corona A.
      • Palacios-Martínez M.
      • Balandrano-Campos S.
      • et al.
      Clinical consequences and transmissibility of drug-resistant tuberculosis in Southern Mexico.
      Epidemiological studies in Taiwan have demonstrated that MDR TB is attributed to acquired resistance rather than primary resistance.
      • Hsueh P.R.
      • Liu Y.C.
      • So J.
      • Liu C.Y.
      • Yang P.C.
      • Luh K.T.
      Mycobacterium tuberculosis in Taiwan.
      • Yu C.C.
      • Chang C.Y.
      • Liu C.E.
      • Shin L.F.
      • Hsiao J.H.
      • Chen C.H.
      Drug resistance pattern of Mycobacterium tuberculosis complex at a medical center in central Taiwan, 2003–2007.
      Burgos et al.
      • Burgos M.
      • DeRiemer K.
      • Small P.M.
      • Hopewell P.C.
      • Daley C.L.
      Effect of drug resistance on the generation of secondary cases of tuberculosis.
      estimated the relative secondary-case ratio of MDR TB to DS TB, indicating that there were no secondary cases associated with MDR strains. All of the above results indicate that MDR strains may have lower transmissibility than DS strains. Thus, MDR strains may have a low RF value.
      The proposed two-strain TB model only implicitly accounts for the patterns of mixing among infectious cases and their contacts, and the risks of TB among those infected are constant through time. Styblo
      • Styblo K.
      Epidemiology of tuberculosis.
      assumed an average duration of infectiousness of 2 years, suggesting that on average each smear-positive case contacted 10 individuals per year. A more recent study carried out in the Netherlands found that the number of individuals contacted by each TB case had changed over time, declining from nearly 22 individuals contacted in 1900 to nearly 10 individuals contacted in 1950.
      • Vynnycky E.
      • Fine P.E.
      Interpreting the decline in tuberculosis: the role of secular trends in effective contact.
      In a recent meta-analysis, Trunz et al.
      • Trunz B.B.
      • Fine P.
      • Dye C.
      Effect of BCG vaccination on childhood tuberculous meningitis and miliary tuberculosis worldwide: a meta-analysis and assessment of cost-effectiveness.
      used the available data from 11 countries and estimated the contact rate from the ratio of annual risk of infection/prevalence. There was a wide range of contact rates ranging from 3.1 to 13.2. Based on Blower et al.,
      • Blower S.M.
      • McLean A.R.
      • Porco T.C.
      • Small P.M.
      • Hopewell P.C.
      • Sanchez M.A.
      • et al.
      The intrinsic transmission dynamics of tuberculosis epidemics.
      our estimated effective contact rate (ECR) of 7.40 (95% CI 4.20–13.23) is similar to that of Styblo,
      • Styblo K.
      Epidemiology of tuberculosis.
      Vynnycky and Fine,
      • Vynnycky E.
      • Fine P.E.
      Interpreting the decline in tuberculosis: the role of secular trends in effective contact.
      and Trunz et al.
      • Trunz B.B.
      • Fine P.
      • Dye C.
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      In addition to RF and ECR, model parameters such as the cure rate of DS (cS) and MDR TB (cR) and treatment failure acquiring resistance (cF) have also been proposed as important epidemiological factors.
      • Blower S.M.
      • Gerberding J.L.
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      The design of effective treatment programs will need to take into account both the magnitude of the RF and its future evolution via compensatory mutation.
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      • Tanaka M.M.
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      The practical implications of this study might be used for risk management. First, the quality of the local data allowed us a rare opportunity to generate data-driven models for MDR TB transmission dynamics. Dynamic models rooted in local data are important for providing clear recommendations for control strategies. Second, a theoretical understanding will improve our ability to interpret data variability. With limited information on site-specific parameters, numerical simulations can be undertaken for randomly selected parameter values in an attempt to discern typical behaviors. Models of the type described in this paper have largely been explored through simulation in terms of their predictive power. More data are needed to validate the model predictions.
      In conclusion, the MDR TB transmission model incorporated with the quantitative risk assessment together with time trends in DS and DR TB cases in Taiwan can be used to predict the MDR TB infection risk potential. We suggest that an annual decline in MDR TB incidence in Taiwan can be anticipated from ongoing control programs. The models, data on trends in DS/DR TB cases, and model simulations used in this study can be applied to assess the efficacy of potential control strategies on the emergence of a new DR strain.
      Conflict of interest: No conflict of interest to declare.

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