The persistence of tuberculosis in the age of DOTS: reassessing the effect of case detection
David W Dowdy a & Richard E Chaisson a
a. Center for Tuberculosis Research, Johns Hopkins University, 1550 Orleans Street, Baltimore, MD, 21221, United States of America.
Correspondence to Richard E Chaisson (e-mail: email@example.com).
(Submitted: 04 May 2008 – Revised version received: 04 September 2008 – Accepted: 17 September 2008 – Published online: 10 February 2009.)
Bulletin of the World Health Organization 2009;87:296-304. doi: 10.2471/BLT.08.054510
In 1991, Styblo & Bumgarner quantified the expected effect of detecting and treating cases of tuberculosis (TB) and found that TB incidence could be reduced by 5–10% per year by detecting at least 70% of TB cases and successfully treating 85% of the cases detected.1 Based largely on these initial projections – which were subsequently corroborated by more complex models2 – WHO adopted a 70% case detection rate (CDR) for new sputum-smear positive cases and a treatment success rate of 85% as its primary targets for TB control.3 These targets have remained a constant benchmark for over 15 years and are currently the basis of the TB control strategy outlined in the international Stop TB strategy4 and the United Nations’ Millennium Development Goals.5 However, despite dramatic progress in TB case detection and treatment under the DOTS strategy,6 estimated global TB incidence has remained relatively stable over the past decade.7 Among the 22 countries with the highest TB burden worldwide, only two (Kenya and Zimbabwe) achieved a 5% reduction in TB incidence (as estimated by WHO) between 2005 and 2006.8 Furthermore, although four high-burden countries (China, Myanmar, the Philippines and Viet Nam) were declared to have met the global targets for case detection and treatment in 2005, the estimated TB incidence in each of these countries declined by ≤ 1.0% in the following year.8
Although numerous factors – including the co-epidemic of HIV infection,9,10 TB drug resistance,11,12 diabetes,13 smoking14 and urban crowding15 – may explain the unchanged TB incidence in the face of improving control efforts, these factors are not markedly more prominent in countries where TB incidence is stable compared with those where it has rapidly declined. An alternative explanation is that models of rapid expansion in TB control do not apply more generally to situations where TB case detection and treatment improve slowly or stabilize at target levels. Such considerations have important policy implications in an era when 93% of the world’s population is covered by DOTS8 and further gains in case detection and treatment are likely to be incremental. Thus, we developed a novel mathematical model to further investigate the relationship between TB CDRs and incidence.
We developed a compartmental difference-equation model of a TB epidemic as depicted in Fig. 1, with parameter estimates shown in Table 1 and model equations given in Appendix A (available at: http://www.tbhiv-create.org). Our treatment of basic TB disease states is similar to that applied in prior TB models2,34, although important differences are described in the appendix. We assume a hypothetical population of constant size in which the treatment success rate has reached 85%. This population was brought to equilibrium (defined as a change in total TB incidence of < 0.001 case per million from one year to the next) with a CDR of 0%, which represents the period before effective TB treatment became available. TB case detection was then increased under two scenarios: (i) rapid expansion from 0% (absolute increase of 10% per year for up to 8 years), followed by stabilization at a constant CDR; and (ii) gradual expansion from 0% over a prolonged period (absolute increase of 1% per year over 90 years). The former scenario may more accurately represent the “best possible” response to DOTS implementation, whereas the latter better fulfils model assumptions of a steady state.35
Fig. 1. Compartmental difference-equation model of a TB epidemica
The model runs were performed in two hypothetical populations. The first was assumed to be entirely HIV-negative; the second was assumed to have a constant incidence of HIV infection sufficient to generate a stable 22% prevalence of such infection among incident TB cases (representative of the WHO African Region) at a TB CDR of 61%.27 HIV-infected and uninfected individuals have different rates of TB progression, reactivation, smear positivity and mortality (Table 1). For simplicity, we assumed only two HIV states, without further parameterization according to CD4+ cell counts and/or antiretroviral therapy status.
Definitions and case detection rate
The TB CDR is actually a ratio defined as follows:
(number of diagnosed TB cases) / (number of total incident TB cases) x 100
By convention, we used “case detection rate” to denote the sputum smear-positive CDR; the sputum smear-negative CDR was calculated by assuming that diagnostic sensitivity for smear-negative TB was a constant fraction of the diagnostic sensitivity for smear-positive disease (Table 1). The CDR is reported by WHO as the number of registered TB cases divided by an estimated denominator. Thus, occasionally the result is an estimated CDR of > 100%.8 Because in the present model we measured incidence directly, we were able to calculate the CDR exactly without an estimated denominator.
We defined a diagnostic attempt as any independent diagnostic effort by a health-care worker who can register and treat a patient with TB; such an attempt will often span multiple clinic visits. Diagnostic attempts may either result in appropriate diagnosis and initiation of TB treatment (“successful” attempt) or failure to diagnose TB (“unsuccessful” attempt). The diagnostic sensitivity, defined as the proportion of successful diagnostic attempts, encompasses the physician’s index of suspicion for TB, the sensitivity of available laboratory techniques (e.g. sputum smear microscopy), and the losses to follow-up before treatment initiation. Since patients with more severe disease (e.g. HIV-positive patients) are likely to present for diagnosis more often than those with less severe disease, we defined the quantity r as the number of diagnostic attempts per death from TB. In the present model, we solved for the CDR numerically by varying the value of r in increments of 0.01.
Effect of case detection on TB incidence
To estimate the effect of changes in case detection on TB incidence, we created decision points at six pre-defined levels of baseline case detection: 0%, 20%, 40%, 60%, 70% and 80%. At each decision point, the CDR was immediately stabilized and held constant for 10 years, and TB incidence was measured annually. For the scenario of gradual expansion in case detection, we also evaluated the effect of continuing to increase the TB CDR by 1% per year and of accelerating this to 2% per year. Finally, we considered the scenario in which the CDR increased immediately from 0% to 70% and remained constant thereafter.
Model validation and uncertainty analysis
To verify that the baseline population provided reasonable estimates of TB incidence, we compared model output to the 2005 WHO estimates of TB burden in 22 high-burden countries.18 Uncertainty analysis was performed by varying each parameter across the range specified in Table 1 and stabilizing the CDR at 70% for 10 years. At the end of those 10 years we measured the per cent annual change in TB incidence between years 10 and 11. We also considered a “best-case” and “worst-case” scenario by setting all parameters to the values that gave the highest and lowest annual reduction in TB incidence at that time.
Projected TB epidemic at baseline
Among HIV-negative individuals, the projected annual TB incidence in the study population at baseline (no TB control programme) was 513 per 100 000, with a point prevalence of 1233 per 100 000 and a TB-specific annual mortality rate of 182 per 100 000. Among those with HIV infection, the projected annual TB incidence (705 cases per 100 000) and TB-specific annual mortality rate (317 per 100 000) were 37% and 43% higher, respectively; the increase in point prevalence (1518 per 100 000) was less marked (23%). By immediately scaling up TB control efforts to a case detection rate of 70% and a treatment success rate of 85%, we observed the TB incidence in the HIV-negative population drop by 42% (38% in the HIV+ population) in the first year and by 74% (67%) after 10 years, an effect equivalent to an annual decline of 13.5% (11.2%) per year over 10 years.
Effect of CDR on TB incidence
When TB case detection – at an assumed treatment success rate of 85% – was increased from 0% to 70% over 7 years (an absolute 10% increase per year) and then held constant in the absence of HIV infection, the effect on TB incidence was similar: a 72% decrease after 10 years was noted. However, once case detection stabilized at a constant level, projected TB incidence also stabilized. After holding case detection constant for 10 years, TB incidence rates fell by no more than 1.0% per additional year, regardless of the CDR at which stabilization occurred (Fig. 2). A similar result was found when the TB CDR was increased at a more gradual rate of 1% per year to a target rate and then held constant for 10 years (Fig. 3). However, if the case detection rate increased to 70% and then continued to increase by 1% annually, TB incidence continued to fall by 2.9–3.2% per year over 10 years; if the annual increase in the case detection rate was accelerated to 2%, the fall in TB incidence was 4.6–5.2% per year (Fig. 3). Although HIV co-infection increased TB incidence, it had relatively little effect on case detection (Fig. 3 and Fig. 4).
Fig. 2. Annual decline in TB incidence under stable case detectiona
Fig. 3. Projected TB incidence in a population without HIV infection when CDR is gradually increaseda
Fig. 4. Projected TB incidence in a population with co-endemic HIV infection when CDR is gradually increaseda
A CDR ≥ 72% (≥ 74% in the presence of HIV co-infection) was required for TB elimination, defined as an equilibrium TB incidence of less than 10 cases per 100 000 population per year. This state corresponds to a basic reproductive rate (the epidemiological parameter R0) of < 1. At a CDR of 70%, R0 was 1.1. The case-detection threshold for TB elimination was highly sensitive to the effective contact rate, defined as the number of secondary TB infections per smear-positive person-year. When the effective contact rate was reduced to 6.0, a CDR of ≥ 30% was required for TB elimination; increasing the effective contact rate to 15.0 raised the CDR threshold for elimination to ≥ 80%. When the base-case contact rate of 11.9 was used, a constant CDR of 80% resulted in an equilibrium annual decline in TB incidence of 1.2% per year.
Uncertainty analysis revealed that, 10 years after stabilizing the CDR at 70%, the annual decline in TB incidence was always between 0.25% and 1.4%, regardless of the variation in any single parameter across the range specified in Table 1. The decline in TB incidence at 10 years was most sensitive to the effective contact rate (0.4–1.4%) and the proportion of new TB infections progressing to active TB among HIV-negative individuals (0.3–1.3%). When we set all parameters to their most favourable values, we made TB incidence decline by 2.7% during year 10 after CDR stabilization; the corresponding “worst-case scenario” caused a 2.6% increase.
Effect of diagnostic interventions on the CDR
Fig. 5 shows the CDR as a function of three parameters: diagnostic sensitivity, diagnostic frequency (expressed as r, the ratio of diagnostic attempts to TB deaths), and presence or absence of continuous active TB case-finding (modelled as one additional diagnostic attempt every 2 years for each individual in the population). The effect of active case finding on CDR is greatest at low diagnostic frequency (i.e. the lower sections of Fig. 5 and Fig. 6 differ more than the upper sections). CDRs > 70% are more easily achievable by increasing diagnostic frequency than sensitivity. For example, at a smear-positive diagnostic sensitivity of 65% and an r of 7 (for a CDR of 70.0%), increasing diagnostic sensitivity to 100% yields a CDR of 78.6%, while a 50% increase in baseline diagnostic frequency plus active case finding yields a CDR of 81.0%. However, interventions that increase diagnostic frequency and those that increase diagnostic sensitivity have a greater effect on the CDR when applied in combination (e.g. movement from the circle in Fig. 5 to the right-hand square in Fig. 6) than sequential interventions that increase only diagnostic frequency or sensitivity alone (e.g. movement from the circle in Fig. 5 to the upper square in Fig. 6).
Fig. 5. TB CDR, according to diagnostic sensitivity and ratio of diagnostic attempts to deaths, under the assumption of no active case-finding efforts for TBa
Fig. 6. TB CDR, according to diagnostic sensitivity and ratio of diagnostic attempts to deaths, under the assumption of ongoing active TB case-finding covering the population once every 2 yearsa
This mathematical model of a TB epidemic in a hypothetical population corroborates earlier projections1,36 that rapid scale-up of TB control efforts to a case detection rate of 70% and a treatment success rate of 85% can reduce TB incidence by an average of 10% per year for 10 years (equal to a 65% decrease over 10 years). However, gradual improvement in case detection leads to more gradual declines in TB incidence (a 3% annual decline in TB incidence when the TB case detection rate increases by 1% per year). Furthermore, once target levels of case detection are achieved, TB incidence stabilizes within 10 years unless case detection continues to improve. CDRs > 70% are most attainable by increasing the frequency of diagnostic attempts. Our findings suggest that current goals for TB control are unlikely to be met without continued improvements in case detection beyond current target levels. Such improvements should be pursued vigorously.
The present model explains two empirical observations. First, in areas with relatively low HIV infection prevalence and high CDRs (e.g. the WHO Western Pacific Region), TB incidence is declining at approximately 1% per year,8 a rate consistent with model projections. Second, among countries with a high TB burden, the annual change in TB incidence is not correlated with absolute CDR (r²= 0.03; P = 0.45, among 22 high-burden countries in 2006),8 in keeping with the contents of Fig. 2. By contrast, this model predicts a substantial decline in TB incidence during any period in which TB CDRs are increasing. However, TB incidence increased between 1990 and 20067,8 despite the achievement of a 61% smear-positive case detection rate under DOTS.6,8 This discrepancy may reflect offsetting increases in TB incidence from other causes (e.g. HIV infection), improved reporting without concomitant improvements in actual diagnosis, or overly optimistic model assumptions about the effect of DOTS. In all of these cases, however, TB incidence is still predicted to stabilize if continued improvements in case detection are not made.
The concept that a sustained, high CDR will result in a constant annual decline in TB incidence is intuitively appealing but implies mathematically that TB will ultimately be eradicated if current targets for case detection and treatment success are maintained. A seminal model by Blower et al.37 demonstrated that > 75% of cases must be treated for eradication to occur, even for a “mild” TB epidemic. We found a similar threshold at a 72% CDR in the absence of HIV infection. Below this threshold for TB elimination, a constant annual decline in TB incidence is a mathematical impossibility. Even at a CDR of 80% (which is likely to be above the threshold for elimination), our model suggests that long-term annual declines in incidence of greater than 2.0% are unlikely in the absence of further interventions or other external forces (e.g. the decline in the effective contact rate in western Europe during the 20th century19). Initially these results appear to conflict with those of Dye et al.,2 who estimated that achieving a 70% CDR with a DOTS success rate of 85% could reduce TB incidence by 11% per year. However, this apparent discrepancy reflects the fact that Dye et al. used a 20-year time horizon to evaluate the immediate effect of DOTS, whereas the present model studied the effect of DOTS over a longer time scale. Our model projects a 13.6% annual reduction in TB incidence over 10 years after full-scale DOTS expansion (Fig. 3), or a 7.1% annual reduction if averaged over 20 years. These estimates do not fall far outside the corresponding uncertainty range (8–12%) quoted in the initial model by Dye et al.2; the small additional discrepancy is largely due to our model’s provision of partial infectivity in smear-negative patients, who are difficult to diagnose if under DOTS.
Our findings have important practical implications. They highlight the importance of case detection in TB control and suggest that DOTS, combined with a case detection rate of 70% and a treatment success rate of 85%, can reduce TB incidence by 70% by comparison with no TB control. However, they also suggest that maintaining stable case detection levels may not meaningfully reduce TB incidence further where these targets have already been achieved. Case detection targets above 70% must be pursued if elimination of TB is to be attained with existing tools. Such targets are achievable by improving access to care, which in turn increases the frequency of diagnostic attempts.38 Additional efforts to increase diagnostic frequency (e.g. active case finding39) are enhanced by simultaneous improvements in diagnostic sensitivity (e.g. improved diagnostic testing40). Further research into new diagnostic tools and mechanisms to increase diagnostic frequency is sorely needed.
The present model also has important limitations. It uses a simplified TB epidemic structure in a hypothetical population and thus cannot fully represent the epidemiologic situation in any given region. As such, this model provides proof of principle under reasonable assumptions and elucidates the longer-term implications of similar models that generate many key hypotheses (e.g. an annual 5–10% reduction in TB incidence at target case detection and treatment success rates); it does not make explicit predictions about future TB control efforts in any specific population. Furthermore, while uncertainty analysis can estimate the effect of uncertain parameter estimates on key model outputs, it cannot fully account for uncertainty inherent in the model structure or in the ability of a mathematical representation to characterize actual TB control efforts. Moreover, to maintain a parsimonious model, we did not incorporate elements such as drug resistance or alternative treatment regimens, which may strongly influence the effect of DOTS in certain populations. Finally, by focusing on case detection, this model fails to evaluate other essential elements of TB control, including treatment success rates and DOTS coverage.
In conclusion, this novel mathematical model suggests that improved CDRs may have a dramatic effect on TB incidence in the short-term, but that maintaining those rates – even at currently-defined target levels – may not reduce TB incidence by more than 1–2% per year in the long term. CDRs greater than 70% may be achievable by increasing the frequency of diagnostic attempts and exploiting the additive effects of diagnostic frequency and sensitivity. TB control programmes and researchers should vigorously pursue improvements in case detection, regardless of current CDRs. ■
We thank Christopher Dye for his helpful comments on an earlier draft of this manuscript.
Funding: This research is supported by the National Institutes of Health – Medical Scientist Training Program Award (T32 GMO7309 to DWD) and K24 Award (AI 01637 to REC) – and by the Bill and Melinda Gates Foundation through the Consortium to Respond Effectively to the AIDS-TB Epidemic (CREATE).
Competing interests: None declared.
- Styblo K, Bumgarner R. Tuberculosis can be controlled with existing technologies: evidence. The Hague: Tuberculosis Surveillance Research Unit; 1991.
- Dye C, Garnett GP, Sleeman K, Williams BG. Prospects for worldwide tuberculosis control under the WHO DOTS strategy. Directly observed short-course therapy. Lancet 1998; 352: 1886-91 doi: 10.1016/S0140-6736(98)03199-7 pmid: 9863786.
- Forty-forth World Health Assembly. Resolution WHA 44.8. Geneva: World Health Organization; 1991.
- The Global Plan to Stop TB 2006-2015. Geneva: World Health Organization and Stop TB Partnership; 2006.
- Dye C, Maher D, Weil D, Espinal M, Raviglione M. Targets for global tuberculosis control. Int J Tuberc Lung Dis 2006; 10: 460-2 pmid: 16602414.
- Dye C, Hosseini M, Watt C. Did we reach the 2005 targets for tuberculosis control? Bull World Health Organ 2007; 85: 364-9 doi: 10.2471/BLT.06.037580 pmid: 17639221.
- Dye C, Watt CJ, Bleed DM, Hosseini SM, Raviglione MC. Evolution of tuberculosis control and prospects for reducing tuberculosis incidence, prevalence, and deaths globally. JAMA 2005; 293: 2767-75 doi: 10.1001/jama.293.22.2767 pmid: 15941807.
- Global tuberculosis control 2008: surveillance, planning, financing. Geneva: World Health Organization; 2008.
- Page KR, Godfrey-Faussett P, Chaisson RE. Tuberculosis-HIV coinfection: epidemiology, clinical aspects, and interventions. In: Raviglione M, ed. Reichman and Hershfeld’s tuberculosis: a comprehensive international approach. New York, NY: Informa Healthcare; 2006. pp. 371-416.
- De Cock KM, Chaisson RE. Will DOTS do it? A reappraisal of tuberculosis control in countries with high rates of HIV infection. Int J Tuberc Lung Dis 1999; 3: 457-65 pmid: 10383056.
- Aziz MA, Wright A, Laszlo A, De Muynck A, Portaels F, Van Deun A, et al., et al. Epidemiology of antituberculosis drug resistance (the Global Project on Anti-tuberculosis Drug Resistance Surveillance): an updated analysis. Lancet 2006; 368: 2142-54 doi: 10.1016/S0140-6736(06)69863-2 pmid: 17174706.
- Blondal K. Barriers to reaching the targets for tuberculosis control: multidrug-resistant tuberculosis. Bull World Health Organ 2007; 85: 387-90 doi: 10.2471/BLT.06.035345 pmid: 17639225.
- Stevenson CR, Forouhi NG, Roglic G, Williams BG, Lauer JA, Dye C, et al., et al. Diabetes and tuberculosis: the impact of the diabetes epidemic on tuberculosis incidence. BMC Public Health 2007; 7: 234- doi: 10.1186/1471-2458-7-234 pmid: 17822539.
- Jha P, Jacob B, Gajalakshmi V, Gupta PC, Dhingra N, Kumar R, et al., et al. A nationally representative case-control study of smoking and death in India. N Engl J Med 2008; 358: 1137-47 doi: 10.1056/NEJMsa0707719 pmid: 18272886.
- Davies PD. The world-wide increase in tuberculosis: how demographic changes, HIV infection and increasing numbers in poverty are increasing tuberculosis. Ann Med 2003; 35: 235-43 doi: 10.1080/07853890310005713 pmid: 12846265.
- Corbett EL, Watt CJ, Walker N, Maher D, Williams BG, Raviglione MC, et al., et al. The growing burden of tuberculosis: global trends and interactions with the HIV epidemic. Arch Intern Med 2003; 163: 1009-21 doi: 10.1001/archinte.163.9.1009 pmid: 12742798.
- Behr MA, Warren SA, Salamon H, Hopewell PC, Ponce de Leon A, Daley CL, et al., et al. Transmission of Mycobacterium tuberculosis from patients smear-negative for acid-fast bacilli. Lancet 1999; 353: 444-9 doi: 10.1016/S0140-6736(98)03406-0 pmid: 9989714.
- Global tuberculosis control 2007: surveillance, planning, financing. Geneva: World Health Organization; 2007.
- Vynnycky E, Fine PE. The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol Infect 1997; 119: 183-201 doi: 10.1017/S0950268897007917 pmid: 9363017.
- Holmes CB, Wood R, Badri M, Zilber S, Wang B, Maartens G, et al., et al. CD4 decline and incidence of opportunistic infections in Cape Town, South Africa: implications for prophylaxis and treatment. J Acquir Immune Defic Syndr 2006; 42: 464-9 doi: 10.1097/01.qai.0000225729.79610.b7 pmid: 16810113.
- Sutherland I, Svandova E, Radhakrishna S. The development of clinical tuberculosis following infection with tubercle bacilli. 1. A theoretical model for the development of clinical tuberculosis following infection, linking from data on the risk of tuberculous infection and the incidence of clinical tuberculosis in the Netherlands. Tubercle 1982; 63: 255-68 doi: 10.1016/S0041-3879(82)80013-5 pmid: 6763793.
- Currie CS, Williams BG, Cheng RC, Dye C. Tuberculosis epidemics driven by HIV: is prevention better than cure? AIDS 2003; 17: 2501-8 doi: 10.1097/00002030-200311210-00013 pmid: 14600522.
- Cohen T, Lipsitch M, Walensky RP, Murray M. Beneficial and perverse effects of isoniazid preventive therapy for latent tuberculosis infection in HIV-tuberculosis coinfected populations. Proc Natl Acad Sci USA 2006; 103: 7042-7 doi: 10.1073/pnas.0600349103 pmid: 16632605.
- Ferebee SH. Controlled chemoprophylaxis trials in tuberculosis. A general review. Bibl Tuberc 1970; 26: 28-106 pmid: 4903501.
- Gilks CF, Godfrey-Faussett P, Batchelor BI, Ojoo JC, Ojoo SJ, Brindle RJ, et al., et al. Recent transmission of tuberculosis in a cohort of HIV-1-infected female sex workers in Nairobi, Kenya. AIDS 1997; 11: 911-8 doi: 10.1097/00002030-199707000-00011 pmid: 9189217.
- Actuarial Society of South Africa. ASSA2003 AIDS and demographic model. Available from: http://www.assa.org.za/aids/content.asp?id=1000000449 [accessed on 30 March 2007].
- 2007 AIDS epidemic update. Geneva: Joint United Nations Programme on HIV/AIDS; 2007.
- Styblo K. Epidemiology of tuberculosis. The Hague: Royal Netherlands Tuberculosis Association (KNCV); 1991.
- Wood R, Middelkoop K, Myer L, Grant AD, Whitelaw A, Lawn SD, et al., et al. Undiagnosed tuberculosis in a community with high HIV prevalence: implications for tuberculosis control. Am J Respir Crit Care Med 2007; 175: 87-93 doi: 10.1164/rccm.200606-759OC pmid: 16973982.
- Keeler E, Perkins MD, Small P, Hanson C, Reed S, Cunningham J, et al., et al. Reducing the global burden of tuberculosis: the contribution of improved diagnostics. Nature 2006; 444: 49-57 doi: 10.1038/nature05446 pmid: 17159894.
- Verver S, Warren RM, Beyers N, Richardson M, van der Spuy GD, Borgdorff MW, et al., et al. Rate of reinfection tuberculosis after successful treatment is higher than rate of new tuberculosis. Am J Respir Crit Care Med 2005; 171: 1430-5 doi: 10.1164/rccm.200409-1200OC pmid: 15831840.
- Pronyk RM, Makhubele MB, Hargreaves JR, Tollman SM, Hausler HP. Assessing health seeking behaviour among tuberculosis patients in rural South Africa. Int J Tuberc Lung Dis 2001; 5: 619-27 pmid: 11467368.
- Menzies D. Effect of treatment on contagiousness of patients with active pulmonary tuberculosis. Infect Control Hosp Epidemiol 1997; 18: 582-6 pmid: 9276242.
- Murray CJ, Salomon JA. Modeling the impact of global tuberculosis control strategies. Proc Natl Acad Sci USA 1998; 95: 13881-6 doi: 10.1073/pnas.95.23.13881 pmid: 9811895.
- Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press; 1991.
- Borgdorff MW, Floyd K, Broekmans JF. Interventions to reduce tuberculosis mortality and transmission in low- and middle-income countries. Bull World Health Organ 2002; 80: 217-27 pmid: 11984608.
- Blower SM, Small PM, Hopewell PC. Control strategies for tuberculosis epidemics: new models for old problems. Science 1996; 273: 497-500 doi: 10.1126/science.273.5274.497 pmid: 8662538.
- Khatri GR, Frieden TR. Controlling tuberculosis in India. N Engl J Med 2002; 347: 1420-5 doi: 10.1056/NEJMsa020098 pmid: 12409545.
- Golub JE, Mohan CI, Comstock GW, Chaisson RE. Active case finding of tuberculosis: historical perspective and future prospects. Int J Tuberc Lung Dis 2005; 9: 1183-203 pmid: 16333924.
- Perkins MD, Cunningham J. Facing the crisis: improving the diagnosis of tuberculosis in the HIV era. J Infect Dis 2007; 196: S15-27 doi: 10.1086/518656 pmid: 17624822.