New Research In
Physical Sciences
Social Sciences
Featured Portals
Articles by Topic
Biological Sciences
Featured Portals
Articles by Topic
 Agricultural Sciences
 Anthropology
 Applied Biological Sciences
 Biochemistry
 Biophysics and Computational Biology
 Cell Biology
 Developmental Biology
 Ecology
 Environmental Sciences
 Evolution
 Genetics
 Immunology and Inflammation
 Medical Sciences
 Microbiology
 Neuroscience
 Pharmacology
 Physiology
 Plant Biology
 Population Biology
 Psychological and Cognitive Sciences
 Sustainability Science
 Systems Biology
Criteria for the control of drugresistant tuberculosis

Edited by Robert May, University of Oxford, Oxford, United Kingdom, and approved May 5, 2000 (received for review March 9, 2000)
Abstract
Antibiotic resistance is a growing impediment to the control of infectious diseases worldwide, tuberculosis (TB) being among them. TB kills two million people each year and foci of multidrugresistant TB (MDRTB) have been identified in Eastern Europe, Africa, Asia, and Latin America. A critical question for health policy is whether standardized shortcourse chemotherapy for TB, based on cheap firstline drugs, can prevent and reverse the spread of drug resistance. Here we use mathematical modeling, in conjunction with treatment results from six countries, to show that bestpractice shortcourse chemotherapy is highly likely to bring strains resistant to either of the two key drugs isoniazid and rifampicin under control and to prevent the emergence of MDRTB. However, it is not certain to contain MDRTB once it has emerged, partly because cure rates are too low. We estimate that approximately 70% of prevalent, infectious MDRTB cases should be detected and treated each year, and at least 80% of these cases should be cured, in order to prevent outbreaks of MDRTB. Poor control programs should aim to increase case detection and cure rates together for three reasons: (i) these variables act synergistically; (ii) when either is low, the other cannot succeed alone; and (iii) the secondline drugs needed to raise MDRTB cure rates are few and extremely costly. We discuss the implications of these results for World Health Organization policy on the management of antibiotic resistance.
Multidrugresistant tuberculosis (MDRTB) is among the most worrisome elements of the pandemic of antibiotic resistance (1) because TB patients that fail treatment have a high risk of death. TB is the second largest cause of death from an infectious agent after HIV/AIDS, and in developing countries, Mycobacterium tuberculosis is one of the most important opportunistic infections associated with HIV (2). MDRTB now has been found on all continents, with especially high rates in countries of the former Soviet Union (3).
The World Health Organization currently recommends, for all new cases of TB, standardized shortcourse chemotherapy (SCC) based on a regimen of four firstline drugs taken for 6–8 months (4). MDRTB is produced by the selection of MDR strains (resistant to at least isoniazid and rifampicin) in patients who fail to complete chemotherapy with the correct combination of drugs. MDRTB cases will continue to arise this way as long as drugsusceptible (DS) and other drugresistant (DR) strains persist anywhere, and as long as some patients fail treatment. Even if some countries manage to eliminate TB, the risk of disease, and drugresistant disease, will persist through immigration.
Cases of MDRTB generated by inadequate treatment can transmit infection to others. Interrupting the transmission cycle is the limiting factor in MDRTB control, because the cure rates of MDR strains are significantly lower than those of DS or DR strains (5). In other words, it is easier in any setting to prevent MDRTB from arising in the first place than to stop transmission by curing it.
Although treatment failure can have grave consequences for individual patients, it will not necessarily generate epidemics of MDRTB through the transmission cycle. Epidemiological theory states that an outbreak of MDRTB requires a cure rate below some threshold, which will be <100%. Our goal in this paper is to try to identify that threshold by using mathematical modeling in conjunction with the latest treatment results from MDRTB patients in six countries (5). Our approach is to establish a set of epidemiological criteria for MDRTB elimination and to determine whether these criteria can be met by the best possible application of SCC. The alternative will be to resort to a limited number of secondline drugs, which are expensive and comparatively toxic. Data describing the global spread of antibiotic resistance are relatively good for TB (3); therefore, both the methods and results of the present analysis may hold lessons that can be applied to the control of other infectious diseases.
Methods
Mathematical Model of Tuberculosis.
To establish criteria for MDRTB control, we have developed a compartmental model of the dynamics of pulmonary MDRTB in adults over 15 years of age which account for more than 95% of infectious cases (Fig. 1). The model works with persons infected, rather than with pathogen gene frequencies; it is thus epidemiological rather than genetic. It joins a growing family of compartmental models for TB (6–11), but has been tailored (from ref. 11) to investigate the above questions about antibiotic resistance (see Appendix). New pulmonary cases are of two types, infectious and noninfectious. Prior infection with M. tuberculosis, whether of DS or DR strains, provides partial protection against reinfection and is therefore an obstacle to the spread of disease. Case detection removes infectious cases from the prevalent pool. If cases are not detected and treated, they will either die or selfcure. Of those cases treated with drugs, a proportion is cured, with a very low chance of relapse, which is assumed to be zero. Treatment failures are all cases that are not permanently cured, including cases that remain sputum smearpositive after 5 months of treatment and cases that become temporarily smearnegative and relapse some months later. Failures are presumed to be less infectious on average than are new smearpositive cases. The basic case reproduction number, R_{0}, is the number of secondary cases arising from one primary case introduced into a fully susceptible population (12). Here, R_{0} = bcτ, the product of parameters determining susceptibility (b), contact rate (c), and the duration of infectiousness (τ) (Table 1). We define R_{θ} as the case reproduction number modified to allow for chemotherapy, so that R_{θ} ≤ 1 must be satisfied to prevent an outbreak of, or to eliminate, the disease. R_{0m} (without treatment) and R_{θm} (with treatment) are the equivalent case reproduction numbers for MDRTB, and R_{θm} ≤ 1 is required to interrupt the MDRTB transmission cycle. We measure the rate of decline of MDRTB under chemotherapy by the time taken to achieve a 10fold reduction in incidence from the point of intervention, determined by simulation (see Appendix).
Sources and Analysis of Data.
To calculate case reproduction numbers, we have relied on epidemiological studies of DSTB in large populations (13). There have been significant outbreaks of MDRTB in institutions such as hospitals (14, 15) and prisons (16) where the contact rate or susceptibility to disease, especially in HIVinfected persons, could be greater. This analysis therefore is intended to apply to the general population, and our criteria for containment may be insufficient to prevent outbreaks in these special cases. Model parameter values are for adult (>15 years old) TB (ref. 11 and Table 1). The per capita contact rate, c, was estimated to be 14 ± 4 per year (ref. 13 and C. J. L. Murray, unpublished data), and then adjusted for the fraction of persons over 15 years of age in a typical highly endemic country (i.e., India, 0.7). MDR strains probably generate fewer secondary infectious cases than do DS strains, because MDRTB has not become common without drug pressure whereas DS strains have. There is direct evidence both from animal experiments (17) and from epidemiological studies (18) that certain isoniazidresistant strains have lower relative fitness than do DS strains. No such data exist for MDR strains, and any cost of resistance could be small (19, 20) and temporary (21, 22). Based on refs. 18 and 20, we cautiously set modal c_{m} = c, but giving relative fitness c_{m}/c range 0.7–1 in uncertainty and sensitivity analyses (see Uncertainty and Sensitivity Analysis). Treatment success rates reported from six countries are the fractions of cohorts of patients whose sputum smears became negative for acidfast bacilli after 6–8 months of treatment, plus a small fraction who completed treatment without a final smear examination (5).
Uncertainty and Sensitivity Analysis.
We used Monte Carlo simulation to calculate the probability that R_{θm} < 1, using 5,000 iterations for each of 24 × 21 combinations of case detection and cure. R_{θm} was calculated as described in the Appendix. Parameter values were assumed to follow independent, triangular distributions with modes and lower and upper limits given in Table 1. The same distributions were used to put bounds (5th and 95th centiles) on estimates of R_{θm} and in multivariate sensitivity analysis.
Results
Best estimates of model parameters give R_{0m} = 1.60 (5th and 95th centiles, 1.02 and 2.67, respectively) in the absence of chemotherapy and when MDRTB is invading a population where 30% of the population already is infected with M. tuberculosis. With a reproduction number of this magnitude, MDRTB incidence doubles every 5.3 years while the epidemic is growing exponentially. A 10fold increase takes 18.6 years. R_{0m} would rise to 1.98 (1.29–3.62) if MDRTB were spreading through a fully susceptible population, i.e. no one infected with DS or other DR strains except the index case. As a rough check on the value of R_{0m}, we used the approximation R_{0m} ≈ 1/(s* + x(1 − s*)), in which s* is the fraction of people uninfected with M. tuberculosis at equilibrium and x is defined in Table 1. For the approximately stable, endemic disease seen in many developing countries (2), s* ranges from 30% to 50% and R_{0m} is <2.
Point estimates of R_{θm} over a wide range of case detection and cure rates are shown in Fig. 2a, where case detection is expressed more intuitively as its reciprocal, the duration of infectiousness. This value is the approximate number of months to treatment, or to retreatment for those that fail the first course. The righthand axis indicates the cure rate of new, infectious MDRTB cases; the cure rates of retreatment cases were assumed to be 38% (range 15–62%) lower (5). The contours on this map join points of equal R_{θm}, and the contours become flatter as R_{θm} increases. At very low rates of cure, more active case finding can even increase R_{θm}. This pattern arises because there is formally an interaction between case detection and cure such that case finding is less effective, pro rata, when the cure rate is low (see Appendix, Eq. A15). If patients take drugs intermittently, if they default from treatment, or if they are given the wrong drugs, a high proportion will remain persistently infectious, no matter how promptly they are treated (23). R_{θm} = 1 is the most important contour in Fig. 2a: Any combination of infectious duration and cure rate lying above that line will interrupt the transmission cycle of MDRTB. If DS, DR, and MDR strains have equal average fitness, then R_{θm} ≤ 1 interrupts the transmission cycles of all strains, and all will eventually be eliminated, including MDRTB.
To make a more careful assessment of the impact of control, we calculated the probability that R_{θm} ≤ 1 (rather than making point estimates of R_{θm}) by using Monte Carlo methods to carry out multivariate uncertainty analysis (Table 1 and Fig. 2b). Interruption of the transmission cycle of MDRTB is most likely in the upper lefthand corner of the graph. The vertical line on this map marks the duration of infectiousness (17 months) corresponding to an annual detection rate of 70% of prevalent infectious cases. The horizontal lines mark the range of cure rates for MDRTB patients observed under SCC in six countries, from Ivanovo Oblast in Russia (treatment success rate 11%), through the Dominican Republic, Italy, Korea, and Peru, to Hong Kong (treatment success rate 60%). The wide gap between these lines indicates that the quality of case management varies enormously among countries. In the best cases, Hong Kong and Peru, the probability that R_{θm} ≤ 1 would be 80%, assuming an annual case detection rate of 70%. The probability will be lower if some MDRTB patients deemed to be “cured” after 5 months of uninterrupted treatment later relapse. Multivariate sensitivity analysis shows that these results are most responsive to parameters p and c but are insensitive to incidence rate at the time of intervention.
The cure rates of patients carrying fully susceptible bacilli, or bacilli resistant to either rifampicin or isoniazid, are much higher than 60%—approximately 80% in Hong Kong and Peru (5). Reconstructing Fig. 2b for nonMDR strains (with higher relative fitness given by c instead of c_{m}) indicates that the probability of preventing an outbreak of, or eliminating, disease caused by these strains (R_{θ} ≤ 1) is better than 90% (data not shown). This result is correct even when allowing for the fact that approximately 10% of rifampicinresistant cases may later relapse (24). Ultimately, these high cure rates should eliminate all forms of TB (see Appendix).
If the incidence of MDRTB is likely to decline, we need to know how long it will take to achieve a significant reduction. Fig. 2c shows the number of years needed to reduce MDRTB incidence by a factor of 10. Even for Hong Kong this period would be over 40 years with 70% case detection. Moreover, the gradient of the surface is very steep in this region of the graph, indicating that small changes in the treatment interval and cure rate would dramatically affect the rate of decline of MDRTB. Thus, the transmission cycle would never be interrupted if the cure rate fell just 10% from 60% to 50%. Fig. 2c suggests that the cure rate should be at least 80% to be confident of a 10fold reduction in the incidence of MDRTB within 20 years. The cure rate would need to be higher than 80% where less than 30% of people are already infected with DS or DR strains.
The interaction between case detection and cure is revealed more fully in Fig. 3. It is better to increase the detection rate of new cases rather than of treatment failures, especially when the cure rate is high (Fig. 3a). Likewise, it is better to improve the cure rate of new cases rather than of treatment failures, though the differential advantage of curing new cases over treatment failures almost is independent of the rate of case finding (Fig. 3b). Thus, where control programs are poor, efforts should be made to improve both case detection and cure rates, especially of new cases, because these two variables act synergistically.
Conclusions
Three conclusions about the control of antibiotic resistance emerge from these comparisons of model and data. First, to be sure of preventing MDRTB epidemics under present assumptions, secondline drugs will be needed to raise MDRTB cure rates above the maximum that can be achieved by SCC. To be cautious about the management of MDRTB, we have chosen values of the relative fitness of MDR strains that probably err on the high side. If MDR strains are in the future found to be less transmissible (lower c) or less virulent (lower b or τ), then lower rates of case detection and cure will be needed to prevent an epidemic. The analytical framework set out in this paper could be used to interpret any new data on the relative fitness of MDRTB. The essence of the problem is to calculate the basic case reproduction number for MDRTB; in this context, our estimates of R_{0m} are lower than suggested by an earlier analysis (6, 7) mainly because we have set the average duration of infectiousness for untreated patients realistically to 2 years (13) instead of to more than 4 years. In this instance, accurate parameter estimates are more important than are some structural details of the model.
Second, we already know that it is easier to prevent MDRTB from arising through inadequate treatment than to bring an established epidemic under control. The present analysis suggests that bestpractice SCC, by achieving cure rates over 80%, can control epidemics of isoniazid or rifampicinresistant disease and can prevent the emergence of MDRTB, provided the interval from becoming infectious to treatment is not excessive. It is vital that control programs achieve the best possible results with firstline drugs, thereby preventing the selection of MDR strains, before attempting to interrupt the transmission cycle with secondline drugs (4).
Third, a new strategy to treat MDRTB cases more promptly is highly desirable, making case detection more active than passive. We estimate that approximately 70% of prevalent, infectious MDRTB cases should be detected and treated each year, and at least 80% of these cases cured, to interrupt the transmission cycle. Poor control programs should aim to increase case detection and cure rates together because these variables act synergistically and because, when either is low, the other cannot succeed alone. One way of improving case detection is to target those individuals known to be at high risk of carrying drugresistant TB, such as the homeless or those in hospitals and prisons (14, 16, 18, 24, 25).
A further step in devising a rational approach to the containment of drug resistance will be to quantify the costs of unit increases in case detection and cure rates, for resistant strains of various types. A course of secondline drugs for MDRTB treatment costs at least 100 times as much as SCC ($2,000–5,000 U.S. for drugs alone), so there is a high premium on balancing drug choice with rapid case finding and improved case management.
Acknowledgments
We thank M. Espinal, T. Frieden, N. Nagelkerke, and M. Raviglione for helpful comments.
Appendix
Mathematical Model of TB.
The following system of differential equations (with S^{⋅} = dS/dt, etc.) describes the dynamics of infection and pulmonary disease in adults.
Uninfected: A1 Latent (slow breakdown to disease): A2 Latent (fast breakdown to disease): A3 Infectious: A4 Noninfectious: A5 Treatment failure (F_{i}, i = 1 to 3): A6 A7 A8 Selfcure: A9 Cure (by treatment): A10 Definitions and values of parameters and control variables come mostly from previous work (11) and are given in Table 1. The basic case reproduction number, assuming no chemotherapy, is R_{0} = bcτ, in which c is the rate of contact per unit time between an infectious case and others in the population, and b is the proportion of infections that leads to infectious cases, A11 Without treatment, the average time a case remains infectious, τ, is A12 where p_{N} is the proportion of cases that selfcures and later relapses to infectious disease, A13
Impact of Chemotherapy.
SCC reduces the average duration of infectiousness. Here we use R_{θ} to denote R_{0} modified to allow for chemotherapy. Then R_{θ} = bcτ_{θ}, and R_{θ} ≤ 1 guarantees, in a deterministic model, the elimination of disease or the prevention of outbreaks. With the introduction of casefinding and treatment comes the possibility of treatment failure, so τ in Eq. A12 must be replaced by τ_{θ}, the sum of the components τ_{1}–τ_{4}.
New cases: A14 Treatment failures: A15 Casefinding also intercepts some patients who would otherwise have selfcured, so p_{N} in Eqs. A12 and A13 becomes A16 We confirmed by numerical simulation of equations A1–A10 (Euler method; time step, 0.1 year) that TB incidence increases when R_{θ} > 1 and decreases when R_{θ} ≤ 1.
MDRTB.
Among drugresistant strains of M. tuberculosis, MDR is outstandingly important because treatment success is markedly lower under SCC. Based on the arguments above, we can derive two criteria for MDRTB elimination, one for MDRTB arising from DR strains by mutation and selection and the other to interrupt the MDR transmission cycle. It is clear that MDRTB will arise by mutation and selection as long as DS or other DR strains continue to exist, and as long as some patients fail treatment. R_{θ} ≤ 1 is therefore required to prevent MDRTB emerging in previously treated patients, as well as to break the transmission cycle of nonMDR strains.
The most stringent criterion for interrupting the transmission cycle arises when one infectious case is introduced into a population uninfected with any strain of M. tuberculosis. MDRTB strains are likely to have different relative fitness, because one or more of b, c, and τ_{θ} are different (typically lower, via parameters p, v_{f}, v_{s}, etc.). Here we allow for the potentially lower fitness of MDR strains by replacing contact rate c with c_{m}, so that R_{0m} = bc_{m}τ (no treatment), R_{θm} = bc_{m}τ_{θ} (under treatment), and R_{θm} ≤ 1 is required to prevent an outbreak of MDRTB. If R_{θm} ≤ 1 but R_{θ} > 1, we expect to see MDRTB in previously treated patients, but only rarely in new TB cases. If R_{θm} > 1 but R_{θ} ≤ 1, MDR strains ultimately will replace all others.
In practice, we are more likely to see an infectious case of MDRTB arise in a population where the fraction of individuals already infected, z, is large (typically 1/4 to 1/3) and fairly steady (2). Assuming constant z, Eqs. A1–A10 can be used to model the shortterm dynamics of MDRTB if c in Eqs. A1–A3 is replaced with c_{m}(1 − z + zx) (Fig. 1). With z > 0, MDRTB will spread more slowly, because those infected are partially immune to reinfection. Then, to calculate R_{θm}, a more general expression for b_{m} (replacing Eq. A11) is needed, A17 The longterm rate of decrease is determined by the principal eigenvalue of Eqs. A1–A10 and its corresponding eigenvector. Here we are more interested in the time taken to achieve a 10fold reduction in incidence from the point of intervention, which was determined by simulation using Eqs. A1–A10 and transmission term c_{m}(1 − z + zx). More accurate calculations of the rate of decline can be carried out by extending Eqs. A1–A10 to model simultaneously the dynamics of both drugsusceptible and drugresistant TB.
Footnotes

↵† To whom reprint requests should be addressed. Email: dyec{at}who.ch.

This paper was submitted directly (Track II) to the PNAS office.

Article published online before print: Proc. Natl. Acad. Sci. USA, 10.1073/pnas.140102797.

Article and publication date are at www.pnas.org/cgi/doi/10.1073/pnas.140102797
Abbreviations
 TB,
 tuberculosis;
 MDRTB,
 multidrugresistant TB;
 SCC,
 standardized shortcourse chemotherapy;
 DS,
 drugsusceptible;
 DR,
 drugresistant
 Received March 9, 2000.
 Copyright © The National Academy of Sciences
References
 ↵
 ↵
 ↵
 ↵
 Pio A,
 Chaulet P
 ↵
 ↵
 ↵
 Blower S,
 Small P M,
 Hopewell P C

 Murray C J L,
 Salomon J A
 ↵
 ↵
 Anderson R M,
 May R M
 ↵
 Styblo K
 ↵
 ↵
 ↵
 ↵
 ↵
 Soolingen D,
 Borgdorff M W,
 de Haas P,
 Sebek M M G G,
 Veen J,
 Dessens M,
 Kremer K,
 van Embden J D A
 ↵
 ↵
 ↵
 ↵
 Bjorkman J,
 Hughes D,
 Andersson D I
 ↵
 Styblo K,
 Bumgarner R
 ↵
 Centers for Disease Control
 ↵