The Potential of Rapid Diagnosis for Controlling Drug-Susceptible and Drug- Resistant TB in High Prevalence Communities

Transcription

1 JCM Accepts, published online ahead of print on 18 March 2009 J. Clin. Microbiol. doi: /jcm Copyright 2009, American Society for Microbiology and/or the Listed Authors/Institutions. All Rights Reserved The Potential of Rapid Diagnosis for Controlling Drug-Susceptible and Drug- Resistant TB in High Prevalence Communities Pieter W. Uys 1,2 *, Robin Warren 1, Paul D. van Helden 1, Megan Murray 3 and Thomas C. Victor 1 MRC Center for Molecular and Cellular Biology, DST/NRF Centre of Excellence for Biomedical Biomedical TB Research, Faculty of Health Sciences, Stellenbosch University, P O Box 19063, Tygerberg 7505, South Africa, 1 DST/NRF Centre of Excellence for Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Western Cape, South Africa, 2 PSOH, Harvard, USA 3 Corresponding Author*: Pieter W Uys, Division of Molecular Biology and Human Genetics, Faculty of Health Sciences, Stellenbosch University, P O Box 19063, Tygerberg, 7505, South Africa. Tel: ; Fax: ; edserve@iafrica.com Running title: The Potential of Rapid Diagnosis for Controlling TB 1

2 ABSTRACT The long-term persistence of Mycobacterium tuberculosis in communities with high tuberculosis prevalence is a serious problem aggravated by the presence of drug-resistant tuberculosis strains. Drug resistance in an individual patient is often discovered only after a long delay, particularly if the diagnosis is based on current culture-based drug sensitivity testing methods. During such delays the patient may transmit tuberculosis to his or her contacts. Rapid diagnosis of drug resistance would be expected to reduce this transmission and hence decrease the prevalence of drug-resistant strains. To investigate this quantitatively, a mathematical model was constructed, assuming a homogeneous population structure typical of high incidence communities in South Africa. Computer simulations performed with this model show that current control strategies will not halt the spread of multidrug-resistant tuberculosis in such high incidence communities. Simulations show that the rapid diagnosis of drug-resistance can be expected to reduce the incidence of drug-resistant cases provided the additional measure of screening within the community is implemented. Word count: Abstract: 159; Main Text: 3880 (Appendix: 450) MeSH Headings: Drug Resistance Early Diagnosis Infection Control Mass Screening Models, Biological Models, Theoretical Mycobacterium tuberculosis 42 Tuberculosis 2

3 INTRODUCTION Multi-drug resistance in Mycobacterium tuberculosis poses a threat to the success of tuberculosis (TB) control programs and creates an enormous financial burden in high-prevalence regions. The current WHO DOTS TB control strategy recommends passive case detection and diagnosis by sputum smear microscopy. TB patients are first detected when they seek help for symptomatic disease, rather than being identified through active screening. Since there is often a long delay between the onset of infectiousness and the time a patient presents, this means that patients are frequently diagnosed only after they may have transmitted infection to others. Once identified, TB suspects then undergo sputum smear microscopy to detect acid fast bacilli. Smear positivity correlates well with the bacterial burden in the lungs as well as with levels of transmissibility and thus, this approach ensures the identification of the most infectious cases of TB. Nonetheless, recent data demonstrate that smear negative patients are also able to transmit TB 3 and since they are not rapidly detected we propose that they may transmit for a longer period than the more infectious smear positive cases. In high incidence settings, once a patient is diagnosed with TB by smear microscopy, due to resource limitations no further microbiological tests are performed and instead diagnosis is primarily done by microscopy. In South Africa culture and drug susceptibility testing on solid medium is routinely done only for retreatment cases. These test results are not available for a minimum of three weeks and may take as long as ten weeks in high throughput laboratories (average 1000 samples per week) 11. A full description of the setting in which this investigation is conducted, with an emphasis on the exact way in which TB patients are evaluated and treated is provided in Verver

4 Several recent operational studies have found that even after diagnosis of drug resistant TB, further delays are often experienced before patients receive appropriate second line drug regimens 1. During such delays, further transmission events may take place 6 thereby potentially amplifying or perpetuating the epidemic, or ensuring that MDR-TB remains endemic. The potentially serious consequences of a delay in appropriate treatment for MDR-TB have already been recognized 10,14. Drug susceptibility testing using molecular techniques can enhance tuberculosis diagnosis 11 and various rapid molecular tests for drug resistance are available but have not been implemented in high-tb-burden settings. Currently the two main diagnostic tests available commercially are the INNO-LiPA TB test (Innogenetics) 12 and the MTBDRplus kit (Hain Lifescience) 15. These assays have recently been approved by the World Health Organization as a tool for rapid MDR-TB diagnosis 27. Recently, the MTBDRplus kit was tested in a busy routine diagnostic laboratory in Cape Town, South Africa 2. This commercially available molecular line-probe assay for rapid detection of rifampicin and isoniazid resistance was assessed and provided the following measurements: Overall, 97% of smear-positive specimens gave interpretable results within 1-2 days using the molecular assay. Sensitivity, specificity, and positive and negative predictive values were 98.9, 99.4, 97.9, and 99.7%, respectively, for detection of rifampicin resistance; 94.2, 99.7, 99.1, and 97.9%, respectively, for detection of isoniazid resistance; and 98.8, 100, 100, and 99.7%, respectively, for detection of multidrug resistance compared with conventional results 2. The results show that this molecular assay is an accurate screening tool for MDR-TB, and has the potential to reduce diagnostic delay. 4

5 In order to examine the potential benefits of rapid diagnosis of multi-drug resistant TB, we developed a mathematical model of TB to simulate trajectories of the course of the epidemic under continued application of current strategies and under the application of rapid diagnostic tools. To place this analysis in realistic context, we calibrated the model to epidemiologic data reported for a high incidence region in South Africa. MATERIALS AND METHODS In a community where TB is prevalent, at any given time, an individual could be in any one of a number of different states with regard to TB (Figure 1). These states include: (1) Actively diseased and infectious (2) Diseased and undergoing therapy (3) Recovered after undergoing therapy (4) Developing resistance while undergoing therapy (5) Latency (6) Re-activation (7) Re-infection (8) Immunity Either susceptible disease treatable by first-line drugs or resistant disease involving drugresistant bacteria is possible. In order to properly analyze the effect of time delays in treating TB cases, all the possible sequences of these various states must be taken into account. This must be done both for first- 5

6 line drug susceptible and resistant TB cases. Some of the simpler scenarios are listed in table 1. A schematic flow diagram depicting the various states and transitions among them is shown in figure 1. Note that a patient infected with a first-line drug-resistant strain of TB would (under current practice) be started on regular therapy as for a susceptible TB case. Only later would it be determined that resistant TB was involved so that appropriate therapy for drug-resistant TB could be started. Similarly, patients who develop resistance during regular therapy would experience a delay before their new condition would be diagnosed. Delays incurred before diagnosis of an actively diseased, and hence infectious, patient, allow transmission events to take place. The number of such events could be reduced if rapid diagnostic strategies were instituted. These delays therefore form an important integral part of the dynamics of the epidemiological process. There are several other delays that also affect this process. A patient with MDR-TB disease and who is receiving therapy for drug susceptible disease remains infectious and could infect others. The delay prior to diagnosis of the true condition therefore affects the dynamics of TB in the community. The same applies to patients acquiring resistance whilst undergoing a course of therapy for drug susceptible TB. Detailed descriptions of the epidemiological principles incorporated in the mathematical model used can be found elsewhere 13. Only some of the main considerations are repeated here: 1. The essential mechanism underpinning many of the dynamic processes is the principle of mass action whereby the rate of infection is proportional to the number of infectious cases and also to the number of non-immune persons. 2. It is assumed that when therapy is completed, the status of a newly cured patient returns to that of being disease-free. Such patients may experience re-infection followed by a further episode of active disease, termed exogenous disease. This type of event is evident among the 6

7 case histories observed in our data set. Indeed, it is not uncommon for persons to experience several disease episodes, each time with a different strain of TB 17. Instead of active disease resulting from an infection or reinfection event, it is possible that a person may experience a relapse of a previous disease episode. Such cases are not uncommon. Finally, it is also possible that a patient may suffer a disease episode as the result of reactivation of a longstanding latent infection. 3. As with Vynnycky 25, we have assumed that the infection and reinfection rates are the same. We have however assumed that infection rates are not age dependent 13 since the focus of this investigation is to determine the benefits of rapid diagnosis. 4. Whether a person who has been infected shortly thereafter develops active disease or remains latent with the potential to develop disease much later can for present purposes be regarded as largely a matter of chance. For a population such random factors average out to probabilities. Thus we have a probability of infection, a probability of re-activation or a probability of developing resistance. These probabilities can be treated as rates. The probability of an infection progressing to disease varies according to the time elapsed since the infection event We assume the presence of MDR strains that have the same level of fitness and present the same annual risk of infection (ARI) as the average for susceptible strains A core capability of the model is the way it represents the acquisition of drug resistance by patients undergoing treatment for susceptible TB. A model for TB has to account for all the different states that an individual could be in as well as the transitions of persons between states. Several of these transitions are predominantly 7

8 deterministic and involve a specific time lag. An example would be that of regular therapy provided to a patient with susceptible disease for a period of six months and having a successful outcome. The patient would be in the therapy state for precisely that period at the conclusion of which the status of that patient would become that of disease-free. It should be noted that during the period of treatment and from within a week or so of the commencement of such treatment, the patient will not be infectious. Other transitions are probabilistic. Two examples are the probability of death or the probability of the transition from the state of being infected to that of being actively diseased. Within the context of the community the later transition is also density dependent. Thus for an individual, the transition from merely infected to actively diseased is effectively a random event with a certain probability, while for the cohort of persons that are infected, the number becoming diseased is that same probability multiplied by the number of infected people. No single specific time lag or delay can be associated with this kind of transition event. In mathematical terms a model of this nature can be expressed as a system of simultaneous differential equations governing the number of people in each state. These equations are presented in the appendix. Straightforward standard numerical methods are available for the solution of such systems. These methods enable simulations mimicking the course of an epidemic and can be implemented quite readily on a spreadsheet such as MS Excel. Excel also has a feature (indexing of arrays) that makes it possible to incorporate the modeling of timedelays. These time-delays may differ from one differential equation to another and Excel can accommodate this as well. Moreover, the indexing feature in Excel allows the user to specify particular values for such delays before each simulation is performed. In this way, the effect, for instance, of a reduction from the time of onset of illness to the correct diagnosis of susceptible or 8

9 resistant TB, as the case may be, can be ascertained by performing suitable simulations with appropriate values set for the time delay parameters The model was calibrated so as to yield simulations matching as closely as possible the conditions historically observed in a study area in the Western Cape Province of the Republic of South Africa where the population is low-income and has an incidence that exceeds 700/100,000 pa 20,21. A recent survey of 366 new adult smear-positive tuberculosis cases (2000 to 2002) in this epidemiological field site showed that 10% of the tuberculosis cases were HIV positive 2. The HIV prevalence in this community thus has been and is still relatively low, so modeling the epidemiology of TB here is free of the complications of having to consider the effects of HIV. This model therefore does not include any HIV effects and can only be applied to communities with low HIV prevalence. This community has been the subject of careful local and international investigations over the past decade with the result that considerable data has been accumulated. A relatively good standard of health care delivery to TB patients has been in place over the same period and this has been carefully monitored. Thus this community presents an ideal case study for the application of a mathematical model. This community has a population of about , but all the parameter values have been normalized to correspond to a population of In addition, since the population has remained fairly constant over a decade and there is minimal immigration or emigration we may assume that the birth rate and the average death rate are approximately equal to each other. The data used for calibrating the model, that is, to determine the various parameters used in the model, are listed in table 2. 9

10 The aim of this particular study was to ascertain the extent of the reduction of the epidemic of drug resistance that could be achieved by earlier diagnosis of drug resistance. The potential benefits of screening contacts were also investigated. A time frame of twenty years was used 8. A longer period of time would imply many assumptions about future conditions that could render the predictions highly speculative. Several simulations were performed in order to compare various strategies for the control of the TB epidemic. The first simulation assumed that the present strategy continued unchanged. The second simulation assumed rapid detection of resistance was in place. A third simulation assumed a situation of proactive case finding in addition to rapid diagnosis. Variations of these basic simulations were performed to ascertain the sensitivity of the predictions to the parameters being varied. This helps identify those factors that play the major roles in any effort to control a TB epidemic. The total treatment costs for drugs only were calculated during the running of each simulation. RESULTS The main results obtained from the simulations are set out in table 3 and are discussed as follows. The model predicts that if the present control strategies remain unchanged then by the end of a twenty-year period, the incidence of MDR-TB cases will have increased from two per month to eleven cases per month (per ). With rapid diagnosis (see table 2) in place, the increase will still be high at 9.6 cases per month even if the rapid diagnosis method has a 90% sensitivity i.e. 90% of positive cases are identified. If the diagnosis method has a sensitivity rate of 97%, then the model predicts that the incidence will still increase, but from two per month to only 2.4 cases per month. The projected incidence of 11 per month would thus have been reduced to only 2.4 cases per month. This shows that it is important that the diagnostic technique 10

11 used should not only be rapid but also highly reliable and sensitive. In this analysis it was assumed that cases were diagnosed within two weeks of having attained such an infectious stage. In the community studied it is unlikely that patients would visit a clinic at so early a stage. Thus screening of the community would have to be in place to locate such cases. However, the model predicts that with the addition of the implementation of screening together with prophylactic treatment of contacts at only a 10% level of success, the incidence of MDR-TB will be reduced to almost zero. This demonstrates the critical importance of rigorous and pro-active implementation of any rapid diagnostic technology. The main results inferred from simulations performed using the mathematical model are summarized in table 3. The point estimates stated need to be qualified by considering the sensitivity to parameter values as shown in table 4. The comparative cost implications are shown in figure 2. These costs were computed during the corresponding simulations by adding at each time step the cost of only the drugs used during that time step. Again, these results must be qualified by referring to table 4. The relative importance of time delays in the control of TB and especially MDR-TB is illustrated in the conceptual diagram figure 3. The effects of different diagnostic sensitivities and delays were investigated. The results are summarised in figures 4 and 5. These results seem to indicate that delay to diagnosis has a relatively small effect on incidence. This may be so for susceptible disease and low diagnostic sensitivity but for resistant disease diagnostic delay has a major effect on incidence (figure 5). In a sense it could be said that low diagnostic sensitivity effectively produces a long delay to diagnosis. A low sensitivity results in patients not being diagnosed at first visit and remaining in 11

12 the infectious cohort. Thus although the delay to the first visit could be short actual successful diagnosis of a TB positive case may take much longer. Conversely, at high diagnostic sensitivities the chances are good that the patient is diagnosed at the first visit and the time to diagnosis is then reduced to the time from onset of symptoms to the actual visit. The model simulations reflect that situation. It will be noted that even with effective control stratgeies in place one can expect incidence of disease to increase for several years before actual declines can be observed (figure 4). This is because the large cohort of latent infected people needs several years to shrink by mortalities and reactivations even when the recruitment rate has decreased. A modelling sensitivity analysis was also performed to ascertain how sensitive the predictions of the model are to parameter values (table 4). The model predictions were not found to be unduly sensitive to uncertainties in any of the model parameters. DISCUSSION Dye 8 found that merely to prevent outbreaks of drug-resistant TB, high rates (70%) of detection of active cases combined with high cure rates (80%) are needed. It was noted that these factors acted synergistically. When either one was low the other cannot succeed alone. Recently Recently Dowdy 8 found that expanded testing of suspects with a diagnostic test with 100% sensitivity and no diagnostic delay could reduce the cumulative incidence of MDR-TB over a 20- year period by 19.9% Using our model, under optimal conditions, the projected incidence of 11 per month is reduced to only 2.4 cases per month. Unfortunately this cumulative figure cannot be directly compared to a monthly incidence figure but both results demonstrate the need for rapid diagnosis with a high senstivity test. Given a situation where drug-resistant TB has already 12

13 become prevalent, we found that an intensively proactive approach is needed to reduce the prevalence of drug resistance. Rapid diagnostic techniques with a high level of accuracy are necessary. Such methods are now becoming available and are practical, highly sensitive and are similar in cost to standard culture methods. In addition, it was found that rapid diagnosis must be supplemented by screening of contacts and that infected persons should be given prophylactic therapy to reduce the burden of disease. Only then is a substantial reduction in incidence rates achieved. It was found that such reductions in incidence would occur even if only 10% of the infected contacts of an infectious person with drug-resistant disease are located and treated. However, any delays in diagnosis or failures to locate at least a significant number of the contacts of patients with drug-resistant disease will allow the incidence of resistant TB cases to increase. It should be noted that simply screening traditional or household contacts may not constitute an effective screening protocol. Regular screening of the entire community may be necessary in order to locate the many possible casual contacts 13. These conclusions are supported by investigations using clinical data in various regions of the world 7,18. It should be noted that the conclusion that we have drawn using this model are subject to the conditions described earlier and in particular apply only to regions where the incidence of TB is high and that of HIV is relatively low. The necessary measures are technically achievable with current rapid diagnostic methods 2. The benefits for individual patients with MDR-TB and also for the community at large are substantial and important. Moreover, enormous savings in therapy costs would be realized compared to the situation that would otherwise develop should current control strategies continue to be used. The greatest challenge will be the institution of a cheap and effective community-wide screening 13

14 system. Thus cheap mass screening technologies need to be developed. Failure to do this will lead ultimately to a daunting problem in the not too distant future Acknowledgements The authors would like thank the South African National Research Foundation (IFR ), the Harry Crossly Foundation and the IAEA (SAF6008; SAF grants) for support. Downloaded from on June 27, 2018 by guest 14

15 References Achonu, C. et al Evidence for local transmission and reactivation of tuberculosis in the Toronto Somali community. Scand.J.Infect.Dis. 38: Barnard, M. et al Rapid molecular screening for multidrug-resistant tuberculosis in a high-volume public health laboratory in South Africa. Am J Respir Crit Care Med 177: Behr, M. A., S. A. Warren, H. Salamon, P. C. Hopewell, L. A. Ponce de, C. L. Daley, and P. M. Small Transmission of Mycobacterium tuberculosis from patients smear-negative for acid-fast bacilli. Lancet 353: Bechan, S. et al Directly observed therapy for tuberculosis given twice weekly in the workplace in urban South Africa. Trans.R.Soc.Trop.Med.Hyg. 91: Beyers, N. et al The use of a geographical information system (GIS) to evaluate the distribution of tuberculosis in a high-incidence community. S.Afr.Med.J. 86:40-41, Brewer, T.F., S.J. Heymann To control and beyond: moving towards eliminating the global tuberculosis threat. J.Epidemiol.Community Health 58: Cronin, W.A. et al Molecular epidemiology of tuberculosis in a low- to moderate-incidence state: are contact investigations enough? Emerg.Infect.Dis. 8: Dowdy, D.W. et al The potential impact of enhanced diagnostic techniques for tuberculosis driven by HIV: a mathematical model. AIDS 20:

16 Dye, C, B.G. Williams Criteria for the control of drug-resistant tuberculosis. Proc.Natl.Acad.Sci.U.S.A 97: Heifets, L.B., G.A. Cangelosi Drug susceptibility testing of Mycobacterium tuberculosis: a neglected problem at the turn of the century. Int.J.Tuberc.Lung Dis. 3: Johnson, R. et al Drug susceptibility testing using molecular techniques can enhance tuberculosis diagnosis. JIDC 2: Morgan M, S. Kalantri, L. Flores, M. Pai A commercial line probe assay for the rapid detection of rifampicin resistance in Mycobacterium tuberculosis: a systematic review and meta-analysis. BMC Infect Dis. 5: Resch, S.C. et al Cost-Effectiveness of Treating Multidrug-Resistant Tuberculosis. PLoS.Med. 3:e Sanchez-Perez, H. et al Pulmonary tuberculosis and associated factors in areas of high levels of poverty in Chiapas, Mexico. Int.J.Epidemiol. 30: Sandgren A, M. Strong, P. Muthukrishnan, B.K. Weiner, G.M. Church, M.B. Murray Tuberculosis Drug Resistance Mutation Database. PLoS Med February 10;6(2):e Schaaf, H.S., K. Shean, P.R. Donald Culture confirmed multidrug resistant tuberculosis: diagnostic delay, clinical features, and outcome. Arch.Dis.Child 88: Van Rie, A. et al Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment [see comments]. N.Engl.J.Med. 341:

17 Van Rie, A. et al Classification of drug-resistant tuberculosis in an epidemic area. Lancet 356: Van Rie, A. et al Transmission of a multidrug-resistant Mycobacterium tuberculosis strain resembling "strain W" among noninstitutionalized, human immunodeficiency virus-seronegative patients. J Infect Dis. 180: Verver, S. et al Proportion of tuberculosis transmission that takes place in households in a high-incidence area. Lancet 363: Verver, S. et al Transmission of tuberculosis in a high incidence urban community in South Africa. Int.J Epidemiol. 33: Victor, T.C. et al Molecular characteristics and global spread of Mycobacterium tuberculosis with a western cape F11 genotype. J Clin.Microbiol. 42: Victor, T.C. et al Spread of an emerging Mycobacterium tuberculosis drugresistant strain in the western Cape of South Africa. Int.J Tuberc.Lung Dis. 11: Victor, T.C. et al Transmission of multidrug-resistant strains of Mycobacterium tuberculosis in a high incidence community. Eur.J Clin.Microbiol.Infect Dis. 16: Vynnycky, E., P.E. Fine The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol.Infect. 119: Warren, R.M. et al Patients with active tuberculosis often have different strains in the same sputum specimen. Am J Respir Crit Care Med 169:

18 World Health Organization Molecular line probe assays for rapid screening of patients at risk of multidrug resistant tuberculosis (MDR-TB). Policy statement. Available:http//

19 Figure legends Figure 1. The boxes represent cohorts of persons in a particular state. Single arrows indicate flows of people from one state to the next according to some probability. Double arrows indicate flows, involving time lags, of people from one state to the next. Broken arrows indicate removal of persons from the indicated state due to death. Suffices s and r refer to susceptible and resistant strains respectively of TB. Endogenous refers to reactivation of an earlier infection to produce an actual episode of disease. Double borders signify a state involving resistant TB. Block arrows indicate a flow of persons at a rate dependent on the time since infection. Figure 2. Annual costs of treating susceptible cases and MDR cases shown as a multiple of the present day annual cost of treating susceptible cases. Although the actual case load for MDR-TB is considerably less than that for susceptible TB, the costs are far greater since the cost of treating a patient with MDR-TB is two orders of magnitude greater than that for susceptible TB. Figure 3. Conceptual chart showing relative numbers (represented approximately by areas of shapes and not to accurate scale) of people in different categories and relative durations (represented by lengths of boxes) of the illness and treatment phases. Note that patients with MDR-TB disease may for a period incorrectly receive treatment for susceptible TB. (Dark shaded box). The situation of resistant disease compared to susceptible disease is asymmetrical by virtue of the one-way flow depicted by the double-arrow from the box representing patients undergoing therapy for susceptible TB and who develop resistance. The time a TB patient is ill before diagnosis and treatment starts is indicated by the length of the box with diagonally hatched shading. All actively diseased people contribute to further infection events until their 19

20 treatment starts. All flows are directly proportional to not only the numbers in the source categories but also to the length of time before commencement of treatment or the detection of conversion to resistant disease Figure 4. Incidence of susceptible disease for various diagnostic sensitivities and diagnostic delays. Figure 5. Incidence of resistant disease for various diagnostic sensitivities and diagnostic delays. Tables TABLE 1. Examples of partial sequences of states concerning TB. Scenario State 1 Naïve Exposure to infection Immune Death 2 Exposure to infection 3 Primary infection Active disease episode 4 Therapy for susceptible TB 5 Latent 6 Latent Primary infection Latent Death Development of resistance Re-activation (endogenous disease) Re-infection (exogenous disease) Therapy for susceptible TB Resistance diagnosed Diagnosis Diagnosis Disease-free Therapy for resistant TB Therapy Therapy 20

21 TABLE 2. Data used to set the parameter values used in the simulations Description Value Population at beginning of the 20-year period 100,000 Birth rate (number of live births per 100,000 population per annum) 1,500 Average death rate (all causes, per 100,000 population per annum) 1,500 Initial monthly incidence of drug susceptible cases (per 100,000 population) * 63 Initial monthly incidence of MDR cases (per 100,000 population) * 2 Initial annual risk of infection 3.5% Risk of conversion during the treatment period from susceptible to resistant disease 0.1 The risk of progress to disease for an infected person within two years of infection 0.05 Mean number of days for executing diagnosis ( rapid method) 2 Mean number of days for executing diagnosis (culture method) 40 Mean number of weeks for standard treatment 26 Mean number of weeks for treatment of a resistant case 78 Notes: This table uses reported historical data for the study population. The rate of re-infection was assumed to be the same as the rate of infection and such rates were assumed to be the same for susceptible and drug-resistant TB 21,25 *. This value is more conservative than the 5% used by Resch 13. Value determined by making adjustments in order that simulations yielded output corresponding to historical data. This value is less than the value of 0.4 found by Resch 13 for data pertaining to Peru. This is less than the 8% used by Resch. 21

22 TABLE 3. Predicted epidemiological outcomes over a twenty-year period. Strategy Average number of cases diagnosed in one month at the end of the twenty-year period Susceptible Current Rapid diagnosis of resistance 90% sensitivity Rapid diagnosis of resistance 97% sensitivity Screening of contacts as well as rapid diagnosis of resistance Screening of contacts but with 4 week delay in detecting development of resistance Resistant Note: At the commencement of each simulation, the average monthly incidence of susceptible and resistant TB cases was set at 63 and 2 respectively. This corresponds to a caseload during the early stages of the simulation of the order of 750 and 36 respectively. The point estimates shown need to be qualified by taking into account their sensitivity to parameter values given in Table 4. TABLE 4. Model sensitivity analysis Susceptible Disease Resistant Disease Incidence incidence Mortality rate Rate of progress to infectious disease Rate of infection Rate of reinfection Rate of reactivation Rate of conversion to resistant disease Notes: The percentage increase in disease incidence for susceptible and resistant disease is shown for separate 10% increases in the stated parameters. The sensitivities to the various mortaility rates 22

23 were investigated and only the maximum sensitivities are shown. These data show that the model predictions are not unduly sensitive to parameter value uncertainties. APPENDIX Notational conventions In order to aid the presentation of the model equations, the following notational conventions have been used to denote the parameters used. Table 3 lists all the parameters used and their values: π(a B): Probability during one week of a transition from a state A to the state B. Depending on the particularities of the transition, the actual numbers of individuals involved in the transition may equal π(a B)*A or may additionally entail a further density dependent factor. λ(a B): Number of persons transferring during one week from a state A to the state B and entailing a specific time lag, depending on the pair A and B. λ(a B) requires the simulation program to view the number of persons in cohort A at an earlier time given by the current time minus the time lag λ t. The number of persons transferring to cohort B is a fraction λ f of the number of persons in cohort A at that earlier time. For example, if A is the cohort of patients starting treatment at time t 0 and B is the cohort of cured patients, then the time lag is the duration of the treatment and λ f is the cure rate. µ(a): Per capita weekly mortality rate for cohort in state A. A distinction is maintained between people infected with susceptible and resistant disease and each state is therefore, where applicable, represented by a state comprising people with susceptible disease or a state comprising resistant disease and indexed with a subscript s or r. Throughout, bold upper case letters refer to the number of people in the relevant state. In view of the large number of variables required, it is deemed helpful to resort to the use of short acronyms. The various symbols used for this purpose, in the order of appearance, and their meanings are as follows: 23

24 (Throughout, the index k may take the value s or r to indicate susceptible, or resistant disease respectively). 24

25 Symbols used The following symbols stand for the number of persons in the designated cohort: U: Uninfected, C: Cured, I k : Infected, E k : Total cohort of active disease episode, P k : Primary disease episode, EX rk : Secondary disease episode, latent resistant and re-infected with susceptible or resistant according to the index k, EX sk : Secondary disease episode, latent susceptible and re-infected with susceptible or resistant according to the index k, ST s : Susceptible disease treated with therapy for susceptible disease, ST r : Acquired resistant disease treated with therapy for susceptible disease, L k : Latent, N k : Endogenous (re-activation), RT: Acquired resistance, X sk : Exogenous (secondary) re-infection, latent susceptible and re-infected with susceptible or resistant according to the index k, X rk : Exogenous (secondary) re-infection, latent resistant and re-infected with susceptible or resistant according to the index k, T r : Resistant disease on therapy for resistant disease, RT s : Resistant disease but commenced with therapy for susceptible disease. 25

26 The model equations du/dt = RecruitmentRate {µ(u) + π(u I r )*E r + π(u I s )*E s }*U + dc/dt dc/dt = λ(st s C) + λ(t r C) E k = P k + EX rk + EX sk (k = s, r) di k /dt = π(u I k )*U*E k { π(i k P k ) + µ(i k ) + π(i k L k )}*I k (k = s, r) dp k /dt = π(i k P k )*I k µ(p k )*P k λ(p k ST k ) (k = s, r) dst s /dt = λ(p s ST s ) µ(t s )*ST s λ(st s C) + λ(n s ST s ) + λ(ex ss ST s ) + λ(ex rs ST s ). dst r /dt = λ(p r ST r ) µ(st r )*ST r λ(st r T r ) + λ(n r ST r ) + λ(ex sr ST r ) + λ(ex rr ST r ). drt s /dt = λ(st r RT) + λ(n r RT s ) + λ(p r RT s ) + λ(x rr RT s ) + λ(x sr RT s ) µ(rt s )*RT s λ(rt s T r ) dl s /dt = π(i s L s )*I s + π(x ss L s )*X ss {π(l s X sr ) + π(l s N s ) + µ(l s )}*L s dl r /dt = π(i r L r )*I r + π(x rr L r )*X rr + π(x sr L r )*X sr + π(x rs L r )*X rs {π(l r X rs ) + π(l r X rr ) + π(l r N r ) + µ(l r )}*L r dn k /dt = π(l k N k )*L k {π(n k T r ) + µ(n k )}*N k (k = s, r) dx kl /dt = π(l k X kl )*L k *(P k + EX sl + EX rl ) µ(x kl )*X kl π(x kl L k )*X kl (k, l = s, r) dex kl /dt = π(x kl EX kl )*X kl µ(ex kl )*EX kl π(ex kl T s )*EX ks (k, l = s, r) dex kr /dt = π(x kr EX kr )*X kr µ(ex kr )*EX kr π(ex kr T rs )*EX kr (k = s, r) dt r /dt = λ(rt s T r ) µ(t r )*T r λ(t r C) As described earlier, the parameters used in the above system of differential equations are listed together with their values, in their order of appearance, in table 3. The various parameter values were determined by running computer simulations and varying parameter values until the simulation output yielded results that correspond to the data in table 2. 26

27 Table 3: Parameter values used in simulations Parameter Value µ(u), µ(i k ), µ(p k ), µ(t k ), µ(st r ), µ(rt s ), µ(l k ), µ(n k ), per week (1) µ(x kl ), µ(ex kl ) π(u I k ), π(x kl EX kl ) per week (2) λ(st s C) λ t = 24 weeks (3), λ f = 0.99 (4) λ(t r C) λ t = 48 weeks (3), λ f = 0.99 (4) π(i k L k ), π(x kl L k ) per week (5) λ(p k ST k ), λ(n k ST k ), λ(ex ss ST s ), λ(ex rs ST s ), λ(ex sr ST r ), λ(ex rr ST r ), λ(st r T r ), λ(st r RT), λ(n r RT s ), λ(p r RT s ), λ(x rr RT s ), λ(x sr RT s ), λ(rt s T r ) Time lag from onset of disease to diagnosis. (weeks) Detection rate. Both varied in simulations (6) π(l k X kl ) per week (7) π(l k N k ) per week (8) π(n k T r ), π(ex kl T s ), π(ex kr T rs ) 0.9 (9) Notes: (1) The simplifying assumption was made that mortality rates were the same for all cohorts. No data is available for most types of cohorts. (2) These are the infection and the re-infection rates respectively and they were assumed to be equal.the value was determined by simulations using the known prevalence as goal. (3) These are the usual therapy duration times. (4) These are the rates of cure, and were varied in simulations to explore the minimum cure rates needed to control an epidemic. (5) Most infection, re-infection events do not lead to disease but rather latency. (6) The time lag from onset of disease to diagnosis was assumed to be the same irrespective of the manner in which the active disease originated. Similarly detection rates were assumed to be the same. Various values for the time lag and the detection rate were explored in simulations. This aspect is the actual focus of this work. (7) This is the re-infection rate for the latent cohort and was varied in simulations (8) We assumed that over a lifetime of 70 years, the probability of latent disease re-activating is

28 (9) This is the sensitivity of the test for the diagnosis of disease. Simulations can be done with various values of this paramenter The solution method The system of differential equations constructed for this model is non-linear and cannot be solved by analytical means. Instead, numerical methods have to be employed. A standard algorithm for doing this is the Euler method with a time step-size of one week being suitable. This can readily be done on a spreadsheet such as MS-Excel. Excel also has a feature (indexing of arrays) that makes it possible to incorporate the modeling of time-delays. Thus, for example, the number of people successfully completing a course of regular therapy during a particular week is not simply related to the total number of people undergoing such therapy at that time. Rather it is found by referring to the number of persons commencing such treatment 24 weeks earlier (24 weeks being the duration of standard therapy), less the number of those same people dying or developing resistance during the same period. Other time delays can be treated in the same way. Simulations representing time periods of several decades were performed. The computer solution comprises values of the various state variables over a sequence of time steps and represents a computer simulation of the progress of the epidemic being modeled. Simultaneously, the cost over the simulation period associated with a specific strategy of diagnosis and treatment can be estimated and compared with the costs of other strategies

29

30

31

32

33