Heterogeneity in tuberculosis transmission and the roleof geographic hotspots in propagating epidemicsDavid W. Dowdya,b,1, Jonathan E. Goluba,b, Richard E. Chaissona,b, and Valeria Saracenic

aDepartment of Epidemiology, The Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205; bCenter for Tuberculosis Research, The JohnsHopkins University School of Medicine, Baltimore, MD 21231; and cMunicipal Health Secretariat, Rio de Janeiro, RJ 22441-030, Brazil

Edited by Burton H. Singer, University of Florida, Gainesville, FL, and approved May 1, 2012 (received for review February 28, 2012)

The importance of high-incidence “hotspots” to population-leveltuberculosis (TB) incidence remains poorly understood. TB inci-dence varieswidely across countries, butwithin smaller geographicareas (e.g., cities), TB transmission may be more homogeneousthan other infectious diseases. We constructed a steady-state com-partmental model of TB in Rio de Janeiro, replicating nine epidemi-ological variables (e.g., TB incidence) within 1% of their observedvalues.We estimated the proportion of TB transmission originatingfrom a high-incidence hotspot (6.0%of the city’s population, 16.5%of TB incidence) and the relative impact of TB control measurestargeting the hotspot vs. the general community. If each case ofactive TB in the hotspot caused 0.5 secondary transmissions in thegeneral community for each within-hotspot transmission, the 6.0%of people living in the hotspot accounted for 35.3% of city-wide TBtransmission. Reducing the TB transmission rate (i.e., number ofsecondary infections per infectious case) in the hotspot to that inthe general community reduced city-wide TB incidence by 9.8% inyear 5, and 29.7% in year 50—an effect similar to halving time todiagnosis for the remaining 94% of the community. The impor-tance of the hotspot to city-wide TB control depended stronglyon the extent of TB transmission from the hotspot to the generalcommunity. High-incidence hotspots may play an important role inpropagating TB epidemics. Achieving TB control targets in a hotspotcontaining 6%of a city’s population can have similar impact on city-wide TB incidence as achieving the same targets throughout theremaining community.

infectious disease transmission | theoretical models | urban population |epidemiology | communicable disease control

Tuberculosis (TB) remains a leading infectious cause of mor-bidity and mortality, with over 8.8 million cases and 1.4 million

deaths annually worldwide (1). TB is known to cluster in hyper-endemic “hotspots” often characterized by crowding (2), poverty(3), HIV infection (4), and other social determinants (5). However,compared with other infectious diseases [e.g., sexually transmitteddiseases (6) and vector-borne diseases (7)], where 20% of the pop-ulation may generate 80% of transmission (7), TB transmissionappears relatively more homogeneous. As a result, though spatialtargeting is often advocated as an efficient method for achievingcontrol of diseases such as malaria (8), the degree to which hot-spots contribute to community-wide transmission of TB remainsuncertain. The concept of geographically defined hotspots drivingTB transmission has biological plausibility. Preventing TB cases inhigh-transmission areas (e.g., crowded urban slums, poorly venti-lated hospitals) may avert many more secondary transmissionsthan similar efforts in low-transmission areas. Similarly, cases inhigh-transmission areas are more likely to represent recent in-fection (which is more amenable to intervention) than reactiva-tion of latent disease (9). Prior explorations of heterogeneity inTB transmission (10–12) have studied the relative importance ofTB reinfection vs. reactivation, but have not explicitly evaluatedthe contribution of hotspots to broader TB epidemics and theircontrol. Rio de Janeiro boasts substantial geographic heteroge-neity in TB incidence, high-quality surveillance data, and, due tothe upcoming Olympics and World Cup, active efforts to disrupt

the social underpinnings (e.g., drug trade) contributing to TBtransmission (13). Thus, we constructed a mathematical model ofTB transmission in Rio de Janeiro to explore the importance ofgeographic hotspots to community-wide TB control.

ResultsIn this simplified model of TB transmission in Rio de Janeiro(Fig. 1), a subpopulation (hotspot) comprising 6.0% of the city’spopulation accounted for a disproportionate amount of ongoingTB transmission. If each case of active TB in the hotspot caused0.5 secondary transmissions in the general community for eachsecondary transmission within the hotspot (i.e., a randomly se-lected resident of the hotspot was 32× more likely to be infectedby a case of active TB in the hotspot than a randomly selectedresident of the general community), the hotspot accounted for35.3% of all TB transmission in the city (Fig. 2). When the relativerisk of transmission within the hotspot relative to the generalcommunity was lowered from 32 to 20, ongoing transmission inthe community became dependent on the hotspot (i.e., R0 <1 inthe community). Under these conditions, reducing rates of TBtransmission in the hotspot to those in the general community wassufficient to eliminate TB from the population in the long term.By contrast, when no transmission events were assumed to occurbetween the hotspot and the general community, the hotspotaccounted for 19.4% of ongoing TB transmission (Fig. 2). Thecommon modeling assumption of geographic homogeneity in TBtransmission (i.e., relative risk of 1.0 on the x axis of Fig. 2) wasgrossly untenable; if hotspot-to-community transmission is evenone-sixth as likely as hotspot-to-hotspot transmission, the hotspotaccounted for all TB transmission in the community.Under the baseline scenario (0.5 hotspot-to-community trans-

missions for each hotspot-to-hotspot transmission), TB controlinterventions carried out only in the hotspot (6% of residents)had a similar impact on city-wide TB rates as the same interven-tions deployed to the remaining 94% of the population in thegeneral community (Fig. 3). For example, we considered an in-tervention resulting in a 50% reduction in time to treatment (e.g.,household case-finding that detects all TB cases twice as quicklyas passive case-finding). Carried out in the hotspot alone, thisintervention reduced city-wide TB incidence by a mean 1.6% peryear over the first 5 y, and by 25.4% by the end of year 50 (Fig. 3,light blue line). By contrast, when applied to the remaining 94%of the population, the intervention reduced city-wide TB in-cidence by 2.5% per year over the first 5 y, and 28.5% by year 50(Fig. 3, red line).Reducing TB transmission rates in the hotspot to those in the

general community (Fig. 3, green line) reduced city-wide TB

Author contributions: D.W.D., J.E.G., R.E.C., and V.S. designed research; D.W.D. per-formed research; D.W.D. and V.S. analyzed data; and D.W.D., J.E.G., R.E.C., and V.S. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: ddowdy@jhsph.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1203517109/-/DCSupplemental.

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incidence by a mean 2.0% per year over the first 5 y, or a 9.8%reduction by year 5 (95% uncertainty range: 6.9%, 11.4%). Byyear 50, TB incidence was reduced by 29.7%, reflecting a 62.8%reduction in incidence in the hotspot and a 23.1% reduction in theremaining community. Corresponding reductions in city-wide TBmortality were slightly lower: 7.8% reduction by year 5, and 29.1%by year 50. This impact was relatively robust to changes in para-meters other than TB transmission rates (Fig. 4). Assigning allsuch parameters to their least-favorable values resulted in a

projected 5-y reduction in TB incidence of 4.7%; the corre-sponding best-case scenario achieved a 22.2% reduction. Re-moving HIV from themodel increased the 5-y incidence reductionto 13.2%, and splitting the single hotspot into three non-communicating hotspots did not change the projected reduction inincidence, to within 0.1%.The contribution of the hotspot to city-wide TB transmission

was most sensitive to hotspot size, hotspot intensity (relative rateof hotspot-to-hotspot vs. community-to-community transmission),and level of cross-transmission (relative rate of hotspot-to-hotspotvs. hotspot-to-community transmission). Fig. 5 shows the 5-y re-duction in TB incidence projected from normalizing a hotspot(i.e., reducing its per-case TB transmission rates to those of thegeneral community), according to these parameter values. Nor-malizing a geographically isolated, low-intensity hotspot (6% ofthe city’s population, per-case TB transmission rate 2.1× that inthe community, and no cross-transmission) reduced city-wide TBincidence by only 4.3%. By contrast, normalizing a nonisolated,high-intensity hotspot of the same size (per-case transmission rate3.5× the community rate, generating one hotspot-to-communitytransmission for every hotspot-to-hotspot transmission) reducedcity-wide incidence in year 5 by 16.3% (Fig. 5, white circles). Bothof these scenarios were consistent with the observed hotspot andcommunity-wide TB incidence rates in Rio de Janeiro.

DiscussionThis simple model of TB transmission in Rio de Janeiro usesplausible conditions to demonstrate that a disproportionate shareof community-wide TB transmission likely occurs in small, geo-graphically defined hotspots. In our baseline scenario, a hotspotcontaining 6% of the city’s population and 16.5% of its TB in-cidence generated 35.3% of all ongoing TB transmission events.Because the burden of TB transmission in such hotspots is greatereven than the burden of TB incidence, TB control efforts focusingon these areas are likely to have greater-than-anticipated impacton community-wide TB control. Equalizing TB transmission ratesbetween our modeled hotspot and the general community

Fig. 1. Compartmental model of TB epidemic in Rio de Janeiro. The pop-ulation is divided into two geographic compartments: the general popula-tion (94% of the total population) and a TB hotspot (6% of the totalpopulation, accounting for 16.5% of TB incidence). TB transmission occurswithin and, to a lesser extent, across geographic compartments. In eachgeographic compartment, individuals fall into one of five TB states. Notshown here, but also included in the model, are two HIV states (HIV infectedand uninfected), with HIV prevalence also higher in the hotspot. Each geo-graphic compartment has its own births and deaths; for simplicity, migrationbetween compartments is not explicitly modeled, but can be conceptualizedas one mechanism of cross-compartment infection.

Fig. 2. Proportion of TB transmission events in Rio deJaneiro arising from cases in the hotspot. The x axis describesthe relative risk of transmission from an active TB case in thehotspot to a randomly selected resident of the generalpopulation, compared with a random hotspot resident. Be-cause the general population is 0.94/0.06 = 15.7× larger thanthe hotspot, a relative transmission risk of 1/15.7 = 0.064assumes that a TB case in the hotspot generates as manysecondary transmissions in the general population as in thehotspot. The baseline scenario in the text assumes one-halfthis rate of cross-transmission (i.e., two hotspot-to-hotspottransmissions for every hotspot-to-community transmission).Under this assumption, the hotspot generated 35.3% of alltransmission events, compared with 19.4% if cross-trans-mission were disallowed.

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reduced city-wide TB incidence by 2.0% per year over the first 5 y,and nearly 30% over a 50-y time horizon—an impact similar tohalving time to treatment among the remaining 94% of thecity’s population.This modeling exercise shows that, though TB may not follow

the “80/20 rule” typical of some other infectious diseases, epi-demics of TB may nonetheless depend on a core group, definedby conditions (e.g., crowding, poor access to health care) thatengender high rates of ongoing transmission (7). Prior geospatialmapping in Brazil has demonstrated the existence of geo-graphically defined incidence clusters that correlate with lowsocioeconomic status (14). Control strategies (e.g., contact in-vestigation, reducing socioeconomic disparities) that target such

clusters may have disproportionate impact, whereas those thatignore these hotspots will have a ceiling to their effectiveness. Theplausibility of this argument is easily demonstrated; our modelfitting suggests that a case of active TB in the hotspot generates2.6× as many secondary infections as a similar case in the generalcommunity (e.g., because the hotspot case is exposed to crowdedconditions and encounters individuals with greater susceptibility toTB). Thus, over two rounds of secondary transmission, preventingone hotspot case could have 2.6 × 2.6 = 6.8× greater impact onfuture TB incidence than preventing one community case. Thisequation is an oversimplification of actual dynamics, in whichpopulations reach new equilibria (and is not assumed in ourmodel). For example, hotspot cases may “saturate” their contacts

Fig. 3. Impact on TB incidence of hotspot-focused vs. population-based interventions. The upper solid line reflects the equilibrium assumption used to fit themodel, in the absence of any intervention. The light blue and red lines correspond to 50% reductions in the mean infectious period (e.g., through active case-finding or improved diagnosis) of cases residing in the hotspot and general community, respectively. The purple line shows a reduction of 50% in thetransmission rate of TB cases (i.e., number of secondary infections per infectious person-year) residing outside the hotspot. By comparison, the green lineshows “normalization” of the hotspot (reduction in TB transmission per infectious hotspot person-year to the mean level in the general population). Thisscenario generates a mean 2.0% annual reduction in TB incidence per year over the first 5 y, or 9.8% reduction in TB incidence by the end of year 5 (29.7% byyear 50). In general, interventions targeting the 6% of people living in the hotspot have similar impact to interventions targeting the remaining 94% of thepopulation.

Fig. 4. One-way sensitivity analysis showing thereduction in transmission at year 5 from eliminatinghotspots. Values on the x axis represent the relativereduction in city-wide TB incidence achieved at theend of year 5 after normalizing the hotspot (see textand Fig. 3, green line). Relative transmission acrossgeography is varied from 0.01 to 0.063 (one hot-spot-to-community transmission for each hotspot-to-hotspot transmission; Fig. 2); other parametersare varied to produce a 25% change in the corre-sponding epidemiological parameter (Table 1).The top three parameters were subsequently variedin multiway sensitivity analysis that also includedhotspot size (Fig. 5), whereas the remainingparameters were simultaneously varied in best-caseand worst-case uncertainty analysis (see text formore information).

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after a given time (10), or transmission rates may be so high thata prevented transmission event is quickly followed by anothertransmission event (15). However, in the absence of completegeographic isolation, hotspots should contribute a greater pro-portion of ongoing community-wide TB transmission than wouldbe estimated by comparing relative incidence rates alone.It has been well-demonstrated that reducing TB transmission in

hyperendemic hotspots is far more difficult than in the generalcommunity (16). Preventing a case of TB in a resource-poorhotspot is almost certainly more difficult and costly than pre-venting a case in the general community. However, our modelpredicts that in the long term [and similar to other diseases, in-cluding malaria (8) and sexually transmitted infections (6)], thecommunity-wide impact of preventing hotspot cases is likely to bedisproportionately large. In our model, achieving TB control tar-gets (e.g., 50% reduction in time to detection) in a hotspot com-prising 6% of the population had similar community-wide impactas achieving the same target in the remaining 94%. Thus, even ifthe hotspot-based target was 10× more expensive to achieve ona per-capita basis, its impact on TB incidence per dollar spentwould be greater than the hotspot-exclusionary target. This findinghas particular relevance as national TB control programs considerhow best to scale-up novel diagnostic interventions [e.g., XpertMTB/RIF, a cartridge-based, automated diagnostic test that canidentify Mycobacterium tuberculosis (MTB) and resistance to ri-fampicin (RIF) (17, 18)]; our model suggests that targeting suchinterventions—and the necessary infrastructure for reporting andtreatment (19, 20)—to hotspots of high TB transmission may bea more cost-effective use of resources, even if fewer units can bedeployed than when targeted to the general population.The projected impact of hotspot-targeted interventions

depends strongly on the rate of TB transmission from cases in thehotspot to members of the general community. Such cross-trans-mission events may be common in the setting of nosocomialtransmission, incarceration, migration/transportation, and occu-pational exposures. Prior studies have shown that the amount oftransmission that occurs in the household may be small (21, 22),but other transmission events (e.g., at social events) (23) may befar more likely to occur within geographically defined boundariesthan across them. This may also be true of hotspots (e.g., town-ships in Cape Town, South Africa) (24) that are geographically

isolated from low-incidence areas. By contrast, the areas of highestTB incidence in Rio de Janeiro are centrally located and in closegeographic proximity to commercial districts and other residen-tial areas, making them potentially more important to ongoingcity-wide TB transmission. Similar findings, in which the majorityof cases attributed to recent transmission are not geographicallyaggregated, have been reported in Baltimore (25) and Harare,Zimbabwe (26). Although molecular epidemiology studies areunlikely to be undertaken on a sufficient scale to ascertain therelative rates of transmission within vs. across hotspots on a popu-lation level (10), further modeling and mapping studies may shedlight on this question, which is of critical importance in deter-mining the appropriate prioritization of hotspot-centered inter-ventions in TB control.As with any mathematical model, our analysis has important

limitations. First, for purposes of conducting a parsimonious ex-periment, we adopted a deterministic framework with two geo-graphically defined compartments. Though this method allows usto investigate geographic heterogeneity in transmission with mini-mal reliance on extraneous parameter estimates, more complexmodels (e.g., agent-based models) would be necessary to elucidateimportant relationships on a finer scale, including social networksand household structure. Furthermore, our summation of threepopulation clusters into a single transmission hotspot may be overlysimplistic, although a model with three separate hotspots gaveidentical results. Second, as a proof-of-concept study, we did notevaluate the absolute impact of any specific TB control inter-vention. Thus, our numerical estimates of potential impact shouldbe interpreted with caution. Third, we chose to model the pop-ulation of Rio de Janeiro as a site with known geographic het-erogeneity in TB incidence and existing high-quality surveillancesystems. Though we believe the concepts elucidated by this modelmay be broadly applicable, caution should be exercised in gener-alizing specific estimates (e.g., the size or intensity of the trans-mission hotspot) to other epidemiological situations. Finally, thequality of our surveillance data may be lower in hotspots than inother districts of the city (e.g., underdetection of cases in hot-spots); to the extent this is true, our data may underestimate thecontribution of hotspots to ongoing city-wide TB transmission.In conclusion, geographic heterogeneity in TB transmission

results in hotspots that may play a disproportionate role in

Fig. 5. Projected reduction in city-wide TB incidence after normalizing hotspots, according to size and intensity of hotspot. Values of contour lines show theproportional reduction in city-wide TB incidence at the end of year 5 achieved by lowering TB transmission in hotspots to the mean value in the rest of the city(Fig. 3, green line). Box A assumes complete geographic isolation of the hotspot (i.e., no cross-transmission from hotspot to community), box B assumes 0.5transmission events from hotspot to community for every hotspot-to-hotspot transmission, and box C assumes one hotspot-to-community transmission forevery hotspot-to-hotspot transmission. The baseline scenario in the text corresponds to box B, with a relative transmission rate of 2.6 and hotspot size of 0.06(9.8% reduction). Other scenarios that replicate the TB incidence seen in Rio de Janeiro hotspots are a relative transmission rate of 2.1 in box A (4.3% re-duction) and 3.5 in box C (16.3% reduction). These scenarios are shown with open circles.

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propagating TB epidemics. Under plausible conditions, a hotspotcontaining 6% of a city’s population can be responsible for 35% ormore of its ongoing TB transmission. Achieving given TB controltargets in a hotspot of this size may have similar impact on long-term, community-wide TB incidence as achieving the same targetsin the remaining 94% of the population. To achieve maximumcommunity-wide impact, TB control programs should focus theirefforts disproportionately on the areas of highest transmission,even if it is more resource-intensive on a per-capita basis to do so.

Materials and MethodsUsing ordinary differential equations, we developed a compartmental modelof the TB epidemic in Rio de Janeiro. Because our aim was to explore theimplications of heterogeneity in TB transmission (i.e., not to evaluate specific

interventions), we strove for simplicity in model structure. We sought to in-corporate sufficient complexity to reflect available epidemiological inputs witha minimum of additional assumptions. We therefore adopted a parsimoniousmodel of five TB states (Fig. 1), assigning cases of active TB the weighted av-erage of infectiousness among smear-positive pulmonary, smear-negativepulmonary, and extrapulmonary cases. Latently infected and recovered indi-viduals were assumed to be noninfectious. Population compartments werealso defined by HIV status (positive vs. negative), with HIV-infected individualshaving higher susceptibility to TB, greater risk of progression to active TB,higher general and TB-specific mortality, and lower TB infectivity. Furtherdetails of the model structure are given in SI Materials and Methods.

To fit the model to the population of Rio de Janeiro, we used data fromongoing, high-quality passive surveillance systems for TB, HIV, and mortality.These surveillance systems, which have been described elsewhere (27), collectdata at the level of bairros, geographically defined regions with population

Table 1. Model parameters

Epidemiologicaldata point

Value, Riode Janeiro Value, model

Correspondingmodel parameter Value in model

Sensitivityanalysis range Source

TB incidence, per 100,000per year

95.3 95.3 Number of transmissions per case ofactive TB per year, community

3.71 2.36–4.59 (1)

Proportion of TB incidencein the hotspot

16.5% 16.5% Number of transmissions per case ofactive TB per year, hotspot

9.74 7.93–11.40 (1)

HIV/TB incidence, per 100,000per year

10.7 10.7 Rate of rapid progression afterrecent infection, HIV-positive,per year

0.31 0.15–0.82 (2)

Rate of slow progression afterremote infection, HIV-positive,per year

Held at 25% the rateof rapid progression

(3, 4)

TB mortality, per 100,000/y 5.0 5.0 TB mortality rate, HIV-negative,per year

0.031 0.016–0.047 (2)

HIV/TB mortality, per 100,000/y 0.7 0.7 TB mortality rate, HIV-positive,per year

0.074 0.041–0.111 (2)

TB prevalence, per 100,000 103.1 103.1 TB detection and treatment rate,HIV-negative, per year

0.87 0.79–0.99 (5)

TB detection and treatment rate,HIV-positive, per year

Held at twice theHIV-negative rate

Reflects relativemortality rates

HIV prevalence, per 100,000 390 390 HIV incidence, per year 1.5 × 10−4 1.0–2.1 × 10−4 (2)HIV mortality, per 100,000/y 16.0 16.0 HIV mortality rate (non-TB)

per year0.026 0.001–0.5 (2)

Proportion of retreatmentcases

27.4% 27.4% TB relapse rate per year 0.0083 0.0063–0.0187 (2)

Additional parameters notfit to epidemiological data

Relative infectivity of HIV/TBcases

0.68 0–1 (6)

Partial immunity to reinfectionif latently infected

0.56 0.42–0.70 (7, 8)

Duration of recent infection phase 5 y 4.2–6.2 y (9)Rate of rapid progression duringthis phase, HIV-negative, per year

0.03 0.026–0.036 (9)

Rate of slow progression of remoteTB infection, HIV-negative, per year

0.0005 0.0002–0.0011 (4)

Life expectancy 73 y 40–100 (10)Relative HIV incidence in hotspotvs. community

2.13 1.0–5.0 (2)

1. Municipal Secretary of Health and Civil Defense. Rio de Janeiro Infectious Diseases: Information and Epidemiological Data on AIDS and Tuberculosis. Available at http://www.rio.rj.gov.br/web/smsdc/exibeconteudo?article-id=126082. Accessed February 5, 2012.

2. Municipal Secretary of Health and Civil Defense (2008) Epidemiological Bulletin (Coordination of Infectious Diseases: AIDS, Tuberculosis, Leprosy) (City of Rio de Janeiro, Rio deJaneiro).

3. Gilks CF, et al. (1997) Recent transmission of tuberculosis in a cohort of HIV-1-infected female sex workers in Nairobi, Kenya. AIDS 11:911–918.4. Horsburgh CR, Jr., et al. (2010) Revisiting rates of reactivation tuberculosis: A population-based approach. Am J Respir Crit Care Med 182:420–425.5. World Health Organization (2011) Global Tuberculosis Control: WHO Report 2011 (WHO, Geneva).6. Golub JE, et al. (2007) The impact of antiretroviral therapy and isoniazid preventive therapy on tuberculosis incidence in HIV-infected patients in Rio de Janeiro, Brazil. AIDS 21:

1441–1448.7. Sutherland I, Svandová E, Radhakrishna S (1982) 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 63:255–268.8. Cohen T, Lipsitch M, Walensky RP, Murray M (2006) Beneficial and perverse effects of isoniazid preventive therapy for latent tuberculosis infection in HIV-tuberculosis coinfected

populations. Proc Natl Acad Sci USA 103:7042–7047.9. Vynnycky E, Fine PEM (1997) The natural history of tuberculosis: The implications of age-dependent risks of disease and the role of reinfection. Epidemiol Infect 119:183–201.10. Municipal Secretary of Health and Civil Defense. Rio de Janeiro Vital Statistics. Available at http://www.rio.rj.gov.br/web/smsdc/exibeconteudo?article-id=871476. Accessed February

5, 2012.

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sizes ranging from 180 to 202,000 individuals. We identified three geographicclusters of bairros with TB incidence that was two- to fourfold higher thanthat of the general population of Rio de Janeiro. These clusters correspond to(i) the largest slum (favela) in the city (Rocinha), (ii) the city center, and (iii) asecond favela (Manguinhos) that borders an aging and industrial area of thecity (Bonsucesso). Together, these three clusters accounted for 6.0% of thepopulation of Rio de Janeiro in 2009, but reported 16.5% of all incident TBcases. To facilitate a simple description of transmission dynamics, we thendivided our model population into two subpopulations: the general com-munity and a single, artificially defined TB transmission hotspot with a pop-ulation size and TB incidence equal to that of the combined population of thethree high-transmission clusters of bairros. To evaluate the effect of simpli-fying model structure into a single hotspot, we conducted a structural sen-sitivity analysis in which the hotspot was broken into three separate hotspotswithout cross-transmission.

The contribution of hotspots to community-wide TB transmission dependson the relative rate of TB transmission from the hotspot to the generalcommunity vs. within the hotspot. We therefore set three independent TBtransmission rates: hotspot-to-hotspot, community-to-community, and therelative rate of cross-population (compared with within-population) trans-mission. A focused review of the literature (SI Materials and Methods) sug-gested that 30–50%of recent TB transmission at the city level is geographicallyclustered (25, 26, 28), but a small study in a Rio de Janeiro hotspot (29) founda higher rate of geographic aggregation (70%). Thus, for our baseline sce-nario, we estimated that a case of active TB in the hotspot would generate 0.5secondary transmission events outside the hotspot for every transmissionevent occurring within the hotspot—a scenario that would lead to 67% geo-graphic clustering among secondary cases if linked to the index case. Becausethe general community was 16× larger than the hotspot, the relative cross-transmission rate (i.e., rate of transmission to a randomly selected personin the other subpopulation vs. a randomly selected member of the samesubpopulation) was 0.5/16 = 0.03. We performed sensitivity analyses for theextremes of complete geographic isolation (i.e., relative cross-transmissionrate of zero) and one hotspot-to-community transmission event for everyhotspot-to-hotspot transmission event (relative rate of 1/16, leading to 50%geographic clustering).

Model parameters were fit using epidemiological data from Rio de Janeiro(Table 1). We mapped model parameters to epidemiological data points inone-to-one fashion, using an iterative routine (30) to fit the model to theepidemiology of TB in Rio de Janeiro in 2007–2009, the last years for whichcomprehensive data were available. For simplicity in illustration and

mathematical rigor, we assumed an equilibrium (steady-state) epidemic atbaseline, defining equilibrium as <1% relative (or 1 per 100,000 absolute)change in any epidemiological data point in Table 1 over 5 y, and adequatemodel fit as matching each data point in Table 1 to within 1% of its recordedvalue. In Rio de Janeiro, both HIV and TB incidence have remained within a±10% range over the last 4 y for which data are available, supporting theconcept of near equilibrium (31).

After the equilibrium model was constructed, we introduced hypotheticalcontrol interventions as described in Results. Our primary outcome was theprojected reduction in TB incidence at 5 y after reducing the rate of TBtransmission per active case in the hotspot to the mean rate in the generalpopulation. Because we did not seek to evaluate specific control inter-ventions, the mechanism of achieving this reduction in transmission (e.g.,general improvement in living conditions vs. TB-specific control measures)was not specified.

We performed one-way sensitivity analyses on all model parameters bydetermining the parameter value that would generate a 25% change (in-crease or decrease) in its corresponding epidemiological data point afterreaching a new equilibrium (defined as the passage of 50 y). Because modelsensitivity to parameters describing TB transmissibility was qualitativelygreater than to other parameters, we performed an a priori three-waysensitivity analysis on the size of the hotspot, intensity of the hotspot (i.e.,relative rate of hotspot-to-hotspot vs. community-to-community trans-mission), and relative cross-population TB transmission rate (i.e., hotspot-to-community vs. hotspot-to-hotspot). To estimate the remaining uncertaintyrelated to the values of other model parameters, we performed best- andworst-case scenario analysis on the primary outcome, simultaneously settingall nontransmissibility related parameters to their most- and least-favorablevalues, respectively. We compared these results to those of probabilisticuncertainty analysis, where we simultaneously (using Latin hypercube sam-pling) varied all parameters other than the relative TB transmission rate overa β distribution (α = 2) defined by the range in Table 1, taking the most likelyvalue as the mode. We report the 95% uncertainty range as the 2.5th and97.5th percentile of results from 10,000 such simulations. We assessedstructural uncertainty by comparing results of our model to those of parallelmodels incorporating three separate, noncommunicating hotspots as above,and also by excluding compartments related to HIV coinfection.

ACKNOWLEDGMENTS. This work was supported in part by the Bill andMelinda Gates Foundation Grant 19790.01, Consortium to Respond Effec-tively to the AIDS/TB Epidemic.

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8. Bousema T, et al. (2012) Hitting hotspots: Spatial targeting of malaria for control andelimination. PLoS Med 9:e1001165.

9. Wang JY, et al. (2007) Prediction of the tuberculosis reinfection proportion from thelocal incidence. J Infect Dis 196:281–288.

10. Cohen T, Colijn C, Finklea B, Murray M (2007) Exogenous re-infection and the dy-namics of tuberculosis epidemics: Local effects in a network model of transmission.J R Soc Interface 4:523–531.

11. Colijn C, Cohen T, Murray M (2007) Emergent heterogeneity in declining tuberculosisepidemics. J Theor Biol 247:765–774.

12. Schinazi RB (2003) On the role of reinfection in the transmission of infectious diseases.J Theor Biol 225:59–63.

13. Devi S (2010) Innovation and education improve health in Rio’s favelas. Lancet 376:83–84.

14. Maciel EL, et al. (2010) Spatial patterns of pulmonary tuberculosis incidence and theirrelationship to socio-economic status in Vitoria, Brazil. Int J Tuberc Lung Dis 14:1395–1402.

15. Uys P, Marais BJ, Johnstone-Robertson S, Hargrove J, Wood R (2011) Transmissionelasticity in communities hyperendemic for tuberculosis. Clin Infect Dis 52:1399–1404.

16. Kritzinger FE, et al. (2009) No decrease in annual risk of tuberculosis infection inendemic area in Cape Town, South Africa. Trop Med Int Health 14:136–142.

17. Boehme CC, et al. (2010) Rapid molecular detection of tuberculosis and rifampin re-sistance. N Engl J Med 363:1005–1015.

18. Boehme CC, et al. (2011) Feasibility, diagnostic accuracy, and effectiveness of de-centralised use of the Xpert MTB/RIF test for diagnosis of tuberculosis and multidrugresistance: A multicentre implementation study. Lancet 377:1495–1505.

19. Evans CA (2011) GeneXpert—a game-changer for tuberculosis control? PLoS Med 8:e1001064.

20. Dowdy DW, Cattamanchi A, Steingart KR, Pai M (2011) Is scale-up worth it? Chal-lenges in economic analysis of diagnostic tests for tuberculosis. PLoS Med 8:e1001063.

21. Verver S, et al. (2004) Proportion of tuberculosis transmission that takes place inhouseholds in a high-incidence area. Lancet 363:212–214.

22. Guwatudde D, et al. (2003) Tuberculosis in household contacts of infectious cases inKampala, Uganda. Am J Epidemiol 158:887–898.

23. Classen CN, et al. (1999) Impact of social interactions in the community on thetransmission of tuberculosis in a high incidence area. Thorax 54:136–140.

24. Murray EJ, et al. (2009) A multidisciplinary method to map potential tuberculosistransmission ‘hot spots’ in high-burden communities. Int J Tuberc Lung Dis 13:767–774.

25. Bishai WR, et al. (1998) Molecular and geographic patterns of tuberculosis trans-mission after 15 years of directly observed therapy. JAMA 280:1679–1684.

26. Easterbrook PJ, et al. (2004) High rates of clustering of strains causing tuberculosis inHarare, Zimbabwe: A molecular epidemiological study. J Clin Microbiol 42:4536–4544.

27. Miranda AE, et al. (2009) Tuberculosis and AIDS co-morbidity in Brazil: Linkage of thetuberculosis and AIDS databases. Braz J Infect Dis 13:137–141.

28. Alland D, et al. (1994) Transmission of tuberculosis in New York City. An analysis byDNA fingerprinting and conventional epidemiologic methods. N Engl J Med 330:1710–1716.

29. Mendes JM, et al. (2008) Molecular diversity of Mycobacterium tuberculosis strains ina slum area of Rio de Janeiro, Brazil. J Bras Pneumol 34:1063–1068.

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Supporting InformationDowdy et al. 10.1073/pnas.1203517109SI Materials and MethodsPopulation Selection.The city of Rio de Janeiro is divided into 160geographic regions called bairros, each of which has a populationbetween 180 and 202,000. These bairros are aggregated into 10larger planning areas. The population and incidence of tuber-culosis (TB) of each bairro is reported by the city’s Departmentof Health and Civil Defense on an annual basis. The last year forwhich data are available is 2009. In that year, city-wide TB in-cidence was 95.3 per 100,000.We identified hotspots as those areas fulfilling three criteria: (i)

geographically and administratively contiguous; (ii) TB incidenceat least twice the city-wide average; and (iii) at least 120 incidencecases of TB in 2009 (i.e., 2% of the city’s total). Three areasfulfilled these criteria (Fig. S1).Planning Area 1 (AP 1.0, red) consists of the city center, with a

population of 248,908 and TB incidence of 219 per 100,000 (545cases). Manguinhos and Bonsucesso (blue) are geographicallycontiguous with AP 1.0, but administratively distinct; they are alsoseparated from AP 1.0 by a large highway. Manguinhos is largely aslum (favela), and Bonsucesso contains an aging, industrial pop-ulation. These areas had a combined 2009 population of 55,647(Manguinhos 37,544; Bonsucesso 18,103), with a TB incidence of313 per 100,000 (174 cases). Rocinha (green) is Rio de Janeiro’slargest favela, with a 2009 population of 70,600 and TB incidenceof 382 per 100,000 (270 cases). Taken together, these three pop-ulations contain 6.0% of Rio de Janeiro’s population (6.29 mil-lion), but 16.5% of its notified incident TB cases in 2009 (5,993).Because reporting of TB cases relies on a passive surveillancesystem, the relative contribution of these hotspots to TB incidencein the city is likely underestimated (as passive case reporting islikely less complete in these areas than in the city as a whole).

Model Selection.Because our aim was to demonstrate the potentialimportance of heterogeneity on TB transmission as a proof ofconcept—not to evaluate specific interventions—we sought tocreate the most parsimonious model that would incorporate (i)geographic heterogeneity in recent TB transmission and (ii)existing epidemiological data from surveillance systems in Rio deJaneiro and/or Brazil. We identified nine potentially relevantdata points (also listed in Table 1):

TB incidence, city-wideTB incidence, hotspot areas (see above)TB prevalenceTB mortalityProportion of incident TB represented by retreatment casesHIV prevalenceHIV mortalityTB/HIV incidenceTB/HIV mortality

Themost parsimoniousmodel that could incorporate all of theseparameters, aswell asgeographicheterogeneity in transmission(vs.reactivation of latent disease), would use four TB compartments(susceptible, latent infection, active disease, and recovered/cured),twoHIVcompartments (HIV-negativeandHIV-positive), andtwogeographic compartments (hotspot and general population). Weexpanded the number of TB compartments to five (splitting latentinfection into a recent and remote compartment), as this funda-mentally requires no more assumptions than a four-compartmentmodel that allows both fast and slow progression, and likely rep-resents the riskof progression to active diseasemore appropriately.

Certain assumptions governing model equations (e.g., that meantime spent in a compartment is equal to 1/rate) are formally validonly at equilibrium/steady-state (i.e., rate of flow into each com-partment is equal to the rate of flow out of that compartments).Furthermore,neitherHIVnorTBincidencehasvariedbymore than10% over the past 4 y. Thus, wemodeled the baseline population asbeing at equilibrium. Our primary results do not vary to a substan-tive degreewhen small variations fromequilibrium (e.g., 5%declinein TB incidence year over year) are introduced into the model.

Estimating the Relative Rate of Hotspot-to-Hotspot vs. Hotspot-to-Community TB Transmission. Empirical data on this relative trans-mission rate are sparse, owing to the limitations of existingmethods(e.g., molecular epidemiology) in estimating the proportion of TBdue to recent transmission (1, 2) as well as the expense of con-ducting population-based molecular epidemiological studies. Toinform an estimate of the relative transmission probability withinvs. across geographical hotspots, we conducted a focused review ofthe literature in PubMed on April 13, 2012, using the terms (tu-berculosis AND geograph* AND [“molecular epidemiology” ORfingerprint*]). We identified 69 titles initially, and searched thereference lists of relevant articles for further citations. Resultsfrom population-based molecular epidemiological studies withappropriate geographical data to inform this estimate are sum-marized here.Only one study was identified that overlapped with the present

population (3). This study evaluated 10 transmission clusters(mostly of two patients each) within the district of Manguinhos,one of the hotspots in this analysis. The authors found that threeclusters linked patients in distant favelas, whereas seven clusterslinked patients in the same or nearby favelas. If one assumes thatthe relative rate of hotspot-to-community vs. hotspot-to-hotspottransmission follows this same ratio, then 3/7 = 0.43 hotspot-to-hotspot transmissions would occur for every hotspot-to-commu-nity transmission. However, the authors did not evaluate trans-mission outside this district; thus, the relative rate of transmissionoutside the hotspot could not be assessed.We identified three other population-based molecular epide-

miological studies carried out at the city level and presentinggeographical information (4–6). In Baltimore, from 1994 to 1996,16 of 28 patients (57%) in documented transmission clusters withknown epidemiological links showed significant geographic ag-gregation; among those in molecularly similar transmission clus-ters without a known epidemiological link, only 11 of 58 patients(19%) showed such clustering (4). The mean intracluster distancewas 1.72 km in the first group and 3.10 km in the second group;the largest of our three hotspots has a square area of 8.4 km2

(http://portalgeo.rio.rj.gov.br/bairroscariocas/index_ra.htm), cor-responding to a radial distance of 1.64 km using a circular ap-proximation. Thus, themean presumed distance of transmission inBaltimore was larger than the approximated radius of the largesthotspot in Rio de Janeiro. Taken together, these data suggest thatin Baltimore, at least half of all TB transmission occurred outsideof geographically defined regions the same size as hotspots in thepresent study.InNewYorkCity from1989 to 1992, 39patientswere identified in

12 documented transmission clusters. Of the 34 with availablegeographic data for mapping, 16 (47%) occurred within a singlegeographical regionapproximately the samesize (1.5-milediameter)as our largest hotspot. This again suggests that a substantial pro-portion of recent transmission occurs across geographical regions,

Dowdy et al. www.pnas.org/cgi/content/short/1203517109 1 of 4

but the lackof cluster-specific geographicdata precludes an estimateof within- vs. across-hotspot transmission.An analysis of 187 patients in Harare, Zimbabwe, revealed a

remarkably high rate of transmission clustering: 147 patients wereconfirmed to be part of a transmission cluster (6). Of these, only36% of patients with a shared spoligotype (and fewer with sharedtandem-repeat pattern) were geographically aggregated at thelevel of the city district, again suggesting that over half of alltransmission occurs across geographical boundaries of similar sizeas those of the hotspots in the present study.These findings are corroborated by data from larger geo-

graphical catchment areas, which showed that 47% of all trans-mission clusters in England spanned geographical regions the sizeof London (7), and that the largest transmission cluster in Thai-land (n = 13 patients) spanned five full provinces, with no oneprovince containing more than six (46%) patients (8).Taken together, these studies suggest that only 30–50% of

recent TB transmission, as detected by population-based mo-lecular epidemiology, is geographically aggregated at a levelsimilar to that of the hotspots in this model. Nevertheless, theone study performed in a Rio de Janeiro favela suggests thatgeographic aggregation may be higher (up to 70%) in this set-ting. Thus, for our baseline scenario, we estimated that a case ofactive TB in the hotspot would generate 0.5 secondary trans-mission events outside the hotspot for every transmission eventoccurring within the hotspot—a scenario that would lead to 67%geographic aggregation among secondary cases if linked to theindex case. However, we performed sensitivity analysis across awider range of parameter values, as shown in the text, including ascenario in which one hotspot-to-community transmission wouldoccur for every hotspot-to-hotspot transmission (i.e., 50% geo-graphic aggregation).

Model Description and Equations. The model consists of five TBcompartments: (i) Shg, susceptible; (ii) L1hg, latently infected,recent; (iii) L2hg, latently infected, remote; (iv) Ahg, active TB;and (v)Rhg, recovered/treated. Each of these five compartments issubdivided into two HIV compartments (subscript h = 0 if HIVuninfected, 1 if infected), and two geographic compartments(subscript g = 0 if general population, 1 if resident of hotspot).Rates of flow between compartments are governed by the

following differential equations. The first five equations are theprimary model equations; the subsequent three equations de-scribe parameters used in the primary equations. The values of allparameters are given in Table 1 with their symbolic represen-tation in Table S1. The model was programmed in R (R Projectfor Statistical Computing), and the source code for the model isavailable from D.W.D. on request.Susceptible (S):

dShg=dt ¼�mortgh

�−�λg þ μ0 þ μh

�∗ Shg þ

�hivhg ∗ Shg

�; [S1]

where mortgh (Eq. S7) is the sum of all mortality in geographicregion g (to keep the population constant), λg (Eq. S6) is theforce of infection in geographic region g, μ0 represents thebackground mortality rate, μh represents the HIV-related mor-tality rate (0 if h = 0 and μ1 if h = 1), and hivhg (Eq. S8) rep-resents HIV incidence.Susceptible individuals enter through birth (held equal to all

mortality in the corresponding geographic region, to maintaina constant population in each subpopulation) and exit through TBinfection and mortality. HIV infection causes transfer of indi-viduals from the HIV-negative to the HIV-positive compartment.Migration between the subpopulations does not occur.Latent, recently infected (L1):

dL1hgdt

¼ λg ∗�Shg þ L2hg ∗ ð1− pÞ þ Rhg

�

− ðηþ ζh þ μ0 þ μhÞ ∗L1hg þ�hivhg ∗ L1hg

�;

[S2]

where λg (Eq. S6) is the force of infection in geographic region g,p is the degree of partial immunity to reinfection if latently infected,η = [1/(duration of recent infection phase)], ζh is the rate ofprimary progression per year, μ0 represents the background mor-tality rate, μh represents the HIV-related mortality rate (0 if h = 0and μ1 if h = 1), and hivhg (Eq. S8) represents HIV incidence.Latent, recently infected individuals enter through infection of

the susceptible, latent (remote), and recovered populations. Thelatent compartment exhibits partial immunity from rapid pro-gression after reinfection, which is modeled as a reduction in therate of flow from the remotely infected to recently infectedcompartment. Latent (recent) infections exit through progressionto remote infection via passage of time, progression to active TB(rapid/primary progression), and mortality (at the same rate asthe TB-uninfected population). HIV infection causes transferof individuals from the HIV-negative to the HIV-positivecompartment.Latent, remotely infected (L2):

dL2hg=dt ¼ η ∗ L1hg −�λg ∗ ð1− pÞ þ υh þ μ0 þ μh

�∗ L2hgþ�

hivhg ∗L2hg�;

[S3]

where η = [1/(duration of recent infection phase)]; λg (Eq. S6) isthe force of infection in geographic region g, p is the degree ofpartial immunity to reinfection if latently infected, υh is the rateof reactivation to active TB per year, μ0 represents the back-ground mortality rate, μh represents the HIV-related mortalityrate (0 if h = 0 and μ1 if h = 1), and hivhg (Eq. S8) representsHIV incidence.Latent, remotely infected individuals enter through pro-

gression of latent (recent) TB infection through passage of time.These individuals exit through reactivation, reinfection (afterconsideration of partial immunity to rapid progression after re-infection), and mortality (at the same rate as the TB-uninfectedpopulation). HIV infection causes transfer of individuals from theHIV-negative to the HIV-positive compartment.Active TB (A):

dAhg=dt ¼�ζh ∗L1hg

�þ �υh ∗L2hg

�þ �ψh ∗Rhg

�

− ½ρh þ μ0 þ μh þ μTBh� ∗Ahg þ�hivhg ∗Ahg

�;

[S4]

where ζh is the rate of primary progression per year, υh is the rateof reactivation to active TB per year, ψ is the rate of relapse peryear, ρh is the rate of diagnosis and treatment (including spon-taneous recovery) per year, μ0 represents the background mor-tality rate, μh represents the HIV-related mortality rate (0 if h =0 and μ1 if h = 1), μTBh represents the TB-related mortality rate,and hivhg (Eq. S8) represents HIV incidence.Individuals with active TB enter through progression of latent

TB infection (both recent and remote), as well as relapse aftertreatment/recovery. These individuals exit through diagnosis andtreatment (or spontaneous recovery), as well as mortality. HIVinfection causes transfer of individuals from the HIV-negative tothe HIV-positive compartment.Recovered/treated (R):

dRhg=dt ¼�ρh ∗Ahg

�−�λg þ ψh þ μ0 þ μh

�∗ Rhg þ

�hivhg ∗Rhg

�;

[S5]

where ρh is the rate of diagnosis and treatment (includingspontaneous recovery) per year, λg (Eq. S6) is the force of in-fection in geographic region g, ψ is the rate of relapse per year,

Dowdy et al. www.pnas.org/cgi/content/short/1203517109 2 of 4

μ0 represents the background mortality rate, μh represents theHIV-related mortality rate (0 if h = 0 and μ1 if h = 1), and andhivhg (Eq. S8) represents HIV incidence.Recovered/treated individuals enter through diagnosis and

treatment (or spontaneous recovery) of active TB and exit throughrelapse, reinfection, and mortality. HIV infection causes transfer of

individuals fromtheHIV-negative totheHIV-positivecompartment.The following equations are used to calculate quantities in the

above primary model equations:Force of infection (λ):

λg ¼�βg=zg

�∗�Ag0 þ ri ∗Ag1

�þ�βg′=zg′

�∗ rt ∗

�Ag′0 þ ri ∗ Ag′1

�;

[S6]

where βg is the transmission parameter for geographic region g, zgrepresents the proportion of the total population living in regiong (i.e., density-dependent transmission), ri represents the relativeinfectiousness of HIV-infected (vs. HIV-uninfected) TB cases(e.g., lower proportion of smear-positive disease), and rt repre-

sents the relative transmission of TB across (vs. within) geo-graphic regions. In this equation, g′ represents the oppositegeographic region. Thus, in evaluating the force of infection forthe hotspot (λ1), g = 1 and g′ = 0.Summed mortality:

where μ0 is the baseline mortality, μ1 is the HIV-associated

mortality, and μTBh is the mortality associated with TB accordingto HIV status.HIV infection

hivgh ¼ φ if g ¼ 0 and h ¼ 0;¼ −φ if g ¼ 0 and h ¼ 1;¼ rh ∗ φ if g ¼ 1 and h ¼ 0;¼ −rh ∗ φ if g ¼ 1 and h ¼ 1;

[8]

where φ is the HIV incidence rate and rh is the relative HIVincidence in the hotspot vs. the general population.

1. Glynn JR, Vynnycky E, Fine PE (1999) Influence of sampling on estimates of clusteringand recent transmission of Mycobacterium tuberculosis derived from DNA fingerprintingtechniques. Am J Epidemiol 149:366–371.

2. Murray M, Alland D (2002) Methodological problems in the molecular epidemiology oftuberculosis. Am J Epidemiol 155:565–571.

3. Mendes JM, et al. (2008) Molecular diversity of Mycobacterium tuberculosis strains ina slum area of Rio de Janeiro, Brazil. J Bras Pneumol 34:1063–1068.

4. Bishai WR, et al. (1998) Molecular and geographic patterns of tuberculosis transmissionafter 15 years of directly observed therapy. JAMA 280:1679–1684.

5. Alland D, et al. (1994) Transmission of tuberculosis in New York City. An analysis by DNAfingerprinting and conventional epidemiologic methods. N Engl J Med 330:1710–1716.

6. Easterbrook PJ, et al. (2004) High rates of clustering of strains causing tuberculosis inHarare, Zimbabwe: A molecular epidemiological study. J Clin Microbiol 42:4536–4544.

7. Love J, et al. (2009) Molecular epidemiology of tuberculosis in England, 1998. Int JTuberc Lung Dis 13:201–207.

8. Rienthong D, et al. (2005) Restriction fragment length polymorphism study ofnationwide samples of Mycobacterium tuberculosis in Thailand, 1997-1998. Int J TubercLung Dis 9:576–581.

mortgh ¼ μ0 ∗�Sg0 þ Sg1 þ L1g0 þ L1g1 þ L2g0 þ L2g1 þ Ag0 þ Ag1 þ Rg0 þ Rg1

�þ μ1 ∗

�Sg1 þ L1g1 þ L2g1 þ Ag1 þ Rg1

�þ μTB0 ∗Ag0 þ μTB1 ∗Ag1;[S7]

Fig. S1. Map of Rio de Janeiro bairros. This map shows all 159 bairros of Rio de Janeiro. The bairros corresponding to the three TB transmission hotspots areshown in color, as described in SI Materials and Methods. Map courtesy of the government of the City of Rio de Janeiro.

Dowdy et al. www.pnas.org/cgi/content/short/1203517109 3 of 4

Table S1. Model parameters and their symbolic representation

Parameter Description Value

β0 Number of transmissions per active TB per year, community 3.71β1 Number of transmissions per active TB per year, hotspot 9.74rt Relative rate of transmission, hotspot-to-hotspot vs. hotspot-to-community 0.03z1 Proportion of total population residing in the hotspot 0.06ζ1 Rate of rapid progression after recent infection, HIV-positive, per year 0.31υ1 Rate of slow progression after remote infection, HIV-positive, per year 0.08μTB0 TB mortality rate, HIV-negative, per year 0.031μTB1 TB mortality rate, HIV-positive, per year 0.074ρ0 TB detection/treatment rate, HIV-negative, per year 0.87ρ1 TB detection/treatment rate, HIV-positive, per year 1.74φ HIV incidence, per year 1.5 × 10−4

μ1 HIV mortality rate (non-TB), per year 0.026ψ TB relapse rate, per year 0.0083ri Relative infectivity of HIV/TB cases 0.68p Partial immunity to reinfection if latently infected 0.561/η Duration of “recent infection” phase 5 yζ0 Rate of rapid progression during this phase, HIV-negative, per year 0.03υ0 Rate of slow progression of remote TB infection, HIV-negative, per year 0.00051/μ0 Life expectancy 73 yrh Relative HIV incidence in hotspot vs. community 2.13

Dowdy et al. www.pnas.org/cgi/content/short/1203517109 4 of 4