.Soc. Sei. Med. Vol. 26. No. 1. pp. 5-13. 1988 0277-9536188 $3.00 + 0.00

Printed in Great Bntain Copyright c 1988 Pergamon Journals Ltd

TIME-SPACE CLUSTERING OF I/IBRIO CHOLERAE 01 IN MATLAB, BANGLADESH, 1970-1982

MARIAN CRAIG

Department of Community Medicine, United Medical and Dental Schools of Guy’s and St Thomas’ Hospitals, St Thomas’ Campus, London SE1 7EH, England

Abstract-Growing evidence for the existence of an aquatic reservoir of Vibrio cholerae has led some observers to postulate the existence of two distinct modes of disease transmission: primary and secondary. In primary transmission vibrios pass from the aquatic reservoir to humans via edible aquatic flora or fauna, or drinking water. Secondary transmission consists of faecal-oral transmission from person-to- person and may spawn epidemics. Cholera outbreaks are particularly well documented for the Matlab area of Bangladesh, where a field station has been run since 1963, at which patients from a study population of nearly 200,000 are treated for diarrhoeal diseases and monitored in a longitudinal demographic surveillance system. This paper seeks to illuminate the process of secondary transmission by presenting preliminary results of an analysis of the time-space distribution of cholera cases in Matlab for the period 1970-1982. It is argued that the detection of time-space clusters of cases resulting from secondary transmission requires locational data below the level of the village, that is at the level of the bari, or patrilineally-related household group because this is where inter-personal contact is greatest. The mapping of the study area at the bari level is described briefly and it is argued that the proportion of all asymptomatic infections and cases which can be mapped is great enough to enable inferences about transmission processes to be drawn. Results of the analysis of time-space interaction using the Knox method are presented and provide some support for within-bari clustering of cases resulting from secondary transmission. Further analysis of time-space clustering of cholera cases in Matlab must restrict comparisons to epidemics of the same biotype, occurring within periods for which similar proportions of cases may be mapped.

Key words-cholera transmission, mapping, bari, Bangladesh

INTRODUCTION

In the light of evidence for an aquatic reservoir for I/. cholerae Miller et al. [l] have proposed the exis- tence of two forms of cholera transmission: primary and secondary, and sketch the spatial pattern of outbreaks to be expected if this model applies in Bangladesh, where cholera is endemic. They suggest that “scattered, localised outbreaks would be ex- pected. Each outbreak would be associated with a primary transmission event from a local aquatic reservoir, followed by a cluster of secondary cases”.

Matlab is an administrative district (upazilla) in rural Bangladesh, about 45 km from the capital, Dhaka (see Fig. 1). It is an area of low-lying flood plain in the delta of the Ganges and Meghna rivers, with many small tidal rivers and canals and a monsoon climate. Employment is mainly fishing and agriculture. Since 1963, the Intemhtional Centre for Diarrhoeal Disease Research, Bangladesh (ICDDR,B, formerly the Cholera Research Labora- tory) has run a field station in Matlab. The centre carries out research on the epidemiology of diar- rhoeal diseases and the related subjects of nutrition and fertility, and conducts demographic surveillance of a population of nearly 200,000. Many studies of cholera have been carried out in this endemic area.

As Feachem noted in 1982 [2], no serious time- space study of the Matlab mini-outbreaks of cholera had then been carried out. Two studies of cholera in Matlab have since addressed the time-space distribu- tion of hospitalised cases. Glass ef al. [3] reviewed the

geographic distribution of cases from Matlab, be- tween 1968 and 1977, and identified a “dis- tinguishable pattern of high and low risk areas”, high rates occurring in villages near the hospital, which may reflect ease of access of care. Cases were hospi- talised with greater frequency from villages which were Hindu, not adjacent to the main river, and which had daily bazaars. They “tried to identify clustering of cases by time and place” and found that “each year cases began almost simultaneously at distant points in the Matlab area”. Outbreaks affecting entire extended families or villages “help account for the high incidence of cholera in some of the villages which were distant to the hospital”.

In 1983 Glass et al. [4] reported on the analysis of phage types isolated from various Matlab patients and family contacts, reporting the nearly simulta- neous isolation of six different phage types in distant villages. They were unable to document the routine reappearance of a single phage type in the same villages during a period of two years. Both of these studies consider the distribution of cholera at the village level. The authors conclude that their findings are compatible with an aquatic reservoir for V. cholerae in the light of the simultaneous emergence of strains of different phage types which are too far apart to be secondary cases. They state that the phage-typing evidence is compatible with simulta- neous, independent primary transmission events in different villages in the Matlab area, in contrast to diffusion within the area from a single source.

In the aquatic reservoir model the primary trans-

5

6 MARIAN CRAIG

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mission event may consist of eating contaminated shellfish or aquatic plants or drinking contaminated water. Secondary cases would result from person-to- person transmission directly or via water. The clus- tering of secondary cases following such a primary transmission event is likely to be greatest where inter-personal contact is maximised. Although there will be most contact within nuclear families living in the same house, contact between family members may not be significantly greater than between bari members. (Baris are proximal, patrilineally-related groups of households situated on mounds of earth raised above the level of the flood plain. Villages are essentially collections of baris.) If this is so a greater proportion of secondary cases can be expected to occur in the same bari than would be predicted on the basis of bari size alone. It is important to be clear about terminology here. Secondary cases are usually defined as those cases occurring in the same family as the index case. However, in terms of the distinction between primary and secondary transmission in the aquatic reservoir model, secondary cases would pre- sumably not be restricted to those occurring in the same family as the initial primary transmission event.

The possibility of detecting clusters will depend on the spatial and temporal units for which data is available and the completeness of data coverage. Cholera outbreaks are unusually well documented for

Matlab. Although reported cases represent a small proportion of all community infections (the impli- cations of this are discussed below), they have the advantage of being bacteriologically confirmed. Given the reputation of the Matlab field hospital, it is probable that an unusually high proportion of infected individuals are hospitalised (as in-patients or out-patients). Furthermore, hospital data afford a picture (albeit partial) of the distribution of cases throughout the study area over a period of years. This paper presents maps of the distribution of cholera cases in Matlab at a more local scale than the village. It discusses the problem of drawing inferences about transmission processes from patterns of distri- bution of mapped hospitalised cases. Data are presented on the time-space distribution of cholera using the method of Knox [S] for counting all possible pairs of cases within critical distance and time limits.

MAPPING THE MATLAB STUDY AREA

Data for hospitalised cases from the Matlab study area have hitherto been available for highly aggre- gated spatial units-villages, or highly disaggregated units-households. Relative locational data have been available at the village level from a sketch map of the field study area, as shown in Fig. 2, but not at the household level. It was therefore decided to map

Time-space clustering of V. cholerae 7

- --

Fig. 2. Sketch map of the Matlab study area, showing village boundaries and boundary of field study area.

the Matlab study area at a scale enabling the location of cases at the bat-i level.

RATIO OF COMMUNITY INFECI’IONS TO MAPPED HOSPITALISED CASES

Since primary and secondary transmission events The team of 120 female village workers in Matlab may both result in inapparent infections and symp-

used a combination of tracings of aerial photographs tomatic cases, our ability to test hypotheses about the and land revenue maps (which enabled the initial scale at which secondary cases cluster following a entry of several reference baris by referring to land primary transmission event, using data on the distri- plot numbers known to bari heads), to enter 1974 bution of cases for smaller spatial units than villages, census numbers of all households in their areas of will depend on how representative the map is of the responsibility [6,7]. The author and field supervisors total spatial distribution of cholera. To assess this an cross-checked 10% of household locations, and by estimate of the ratio of inapparent infections to referring to census data attempted to ensure that a community to hospitalised to mapped hospitalised location had been recorded for every household. cases must be made. Table 1 sets out these ratios for Eight percent of household locations have not been the Classical and ElTor periods in Matlab, beginning mapped because they occur in villages where aerial in July 1970, from which time household location was photographs taken in the dry season did not enable available for most individuals, thereby enabling the identification of households in the much changed mapping of hospitalised cases at the bari scale. (The monsoon topography. Classical biotype of V. cholerae was responsible for

A computerised spatial database for cholera was set up. Laser-Scan Laboratories Ltd digitised house- hold jocations and the river system, using existing software to scale and orientate the household coordi- nates from each digitised fieldworker sheet to a master grid of the study area. Several censuses of the Matlab study population have been carried out. Before assigning coordinates to every case culture- positive for V. cholerae 01 reporting to the Matlab field hospital between 1970 and 1982. it was necessary to assign an equivalent 1974 census number to all cases occurring before the 1974 census. Cholera (statistical) and household (locational) data could then be linked by matching household and village identification codes.

A total of 3876 cases were hospitalised between 1970 and 1982, of which 2205 (57%) were mapped. Certain cases cannot be mapped because of: the exclusion of villages from the Demographic Surveil- lance System in 1978 (approximately one-third of the population [S]); inadequate field survey during the construction of the map; failure to link the identification number of the household of origin of the case to the equivalent 1974 number; or, for a small proportion of cases, out-migration and internal migration of the families of cases since hospi- talisation.

Maps of the distribution of hospitalised cases in two of the five major epidemics which have occurred since 1970 are shown in Fig. 3.

Period

Table I, Incidence, hospitalisation and mapped hospltahsauon rakes* for cholera in Matlab

Community asymptomatic Community symptomatic+ Hospitalised Mapped hospitaked

Classical 7/7@-12172 12: (10) 3 (12, 13) 1.3 (3) 0.4

El Toor l/73-8/82 lOS-300$ (IO) 3 (12, 13) 2.9 (3) 1.3 (l/73-8/82)

2.0 (9/78-8/82)

Classical/El Toor S/82-6/83

*Infections or cases/l000 per year.

ND ND 9.2 6.5

tThcse figures apply to limited parts of the Classical period. SBased on a 4: I ratio of inapparent infections to community cases. §Based on a 35 to 100: I ratio of inapparent infections to community casts. Figures in parentheses denote references.

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Time-space clustering of V. cholerae 9

most cases of cholera occurring in Matlab before 1973 From 1973 onwards the El Tor biotype was predominant until September 1982 when Classical reappeared [9].) Data in the table are restricted to studies carried out in Matlab.

The data for the incidence of community asymp- tomatic infections come from Bart et aZ.‘s [lo] sero- epidemiological studies during a simultaneous epi- demic of El Tor and Classical I/. choierae in 1968. They indicate a much higher rate of infection per 1000 population in the El Tor period compared to the Classical period. However, a study carried out in Dhaka by Khan and Shahidullah more recently (cited in Feachem [2]) showed that El Tor cholera appeared to be reverting to a pattern similar to Classical cholera with a case/infection ratio higher than that typically reported for the El Tor biotype.

observable in the total group of community asymp- tomatic and symptomatic cases. It is reasonable to suppose that levels of host immunity, for example, will be distributed randomly in the study population, to the extent that members of different age strata are distributed randomly. More systematic factors influence hospitalisation rates, the most obvious being distance or travel time to hospital, cost of travel to hospital and perceptions of the effectiveness of hospitalisation. However the sphere of influence of the Matlab field hospital now extends 40 miles, well beyond the boundary of the study population, so the effect of distance will be diminished to some extent.

De Zoysa and Feachem (111 have identified two studies which record incidence rates for symptomatic infections in the Matlab community. Both report three episodes per 1000 per year for all ages [ 12, 131. This would seem low when compared to hospi- talisation rates in Matlab reported by Glass et al. [3]. They analysed hospital records for all surveillance area patients culture-positive for I/. cholerae 01 be- tween 1966 and 1982 and found a hospitalisation rate of 1.3 patients/1000 per year in the Classical period and of 1.9 patients/1000 per year in the El Tor period. The difference may partly reflect changing perceptions of the effectiveness of the hospital.

Finally we must consider the proportion of hospi- talised patients for which we can locate households on the bat-i map. Figure 4 shows the monthly distri- bution of cholera cases in Matlab for the period 1970 to 1982, from data for all hospitalised and all mapped hospitalised cases. The proportion of mapped cases increases steadily throughout the period, the lower values prior to 1978 mainly reflecting the decrease of almost a third in the size of the surveillance area in 1978.

The influence of factors affecting the decision to seek hospital care for a diarrhoea case is likely to exaggerate the existence of clusters in the observed spatial distribution of cholera cases, in that a milder case, which may not otherwise have been thought to need hospitalisation may accompany a more severe case from the same bari or household. This would increase the likelihood of detecting clusters of mild and severe cases, and increase the possibility of overlooking a cluster of mild cases. Conclusions about the significance of any observed clustering should err on the side of caution in view of this. In other words, if clustering is observed at, say, the bari level: either it is an artefact of the selection of cases which appear on the map, and results from the tendency of an individual from a given bari to seek hospital treatment if another person from the same bari does so; or it reflects the greater likelihood of secondary cases among members of the same bat-i; or it results from a combination of both.

THE TIME-SPACE DISTRIBUTION OF CHOLERA CASES IN MATLAB

Given that only 57% of hospitalised cases can be mapped, the grounds for analysing the time-space pattern of cholera outbreaks on the basis of mapped hospitalised cases rest on two crucial assumptions. First, that the ratio of community asymptomatic infections and cases to hospitalised cases is far greater than the ratio of hospitalised cases to mapped hospi- talised cases. Secondly, that there is no spatial bias in the cases which can be mapped. The data in Table 1 support the first assumption and there is no spatial bias in the cases that cannot be mapped because of changing monsoon topography. The main source of bias is the exclusion of one-third of the population from the surveillance system in 1978. To the extent that inferences about transmission processes may be made on the basis of the distribution of hospitalised cases, this will also be true for mapped hospitalised cases, at least from 1978 onwards.

Analysis of time-space interaction of cholera in Matlab was carried out using the method of Knox [5]. This consists of comparing all possible pairs of cases occurring within a defined geographical area and finite time period, where each pair is specified in terms of a critical time and distance interval. Expected values under a null hypothesis of random distribution in time and space are calculated, which enables a test for any significant association between short dis- tances and short times. The method has been used mainly for diseases whose infectious characteristics are not well established, such as Burkitt’s lymphoma [ 141 or cleft lip and palate [ 151, where significant associations between short distances and short times are taken as evidence for infection or contagion. Significant associations between short times and dis- tances for cholera, which is known to be infectious, would be expected. The purpose of using the method in this context is to look for evidence of within-bat-i clustering and to compare the consistency of this evidence through the study period.

It must also be considered how cases have been The data used in the analysis are summarized in filtered at each link in this chain. If there is any Table 2 below. It shows the total number of hospi- systematic bias in the cases filtered out at each link, talised and mapped hospitalised cases occurring in this will pose problems for interpretation of patterns each of the five major epidemics since 1970. A major of mapped hospitalised cases. There is no u priori epidemic was deemed to be one in which there were reason for supposing that factors influencing the more than 50 cases in any one fortnight. The start development of symptomatic cases from infections and finish of each epidemic was defined on the basis should obscure any clustering effects which may be of steep increases or decreases in the gradient of the

IO MARIAN CRAIG

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Table 2. Numbers of mapped and hospitalised cases for major epidemics since 1970

Map@ Hospitalised Date cases cases

Oct. 1971-Feb. 1972 150 450 Sept.-Dec. 1974 333 692 Aug.-Dec. 1977 673 1134 Sept.-Dec. 1978 422 781 Sept.-Dec. 1982 627 al9

plot of monthly totals of hospitalised cases (see Fig. 4).

Table 3 shows the results of the Knox test for four epidemics since 1974, using ‘critical’ time periods of 1 day from 0 to 10 days, and ‘critical’ space intervals of 250 m from 0 to 2000 m (although values for all distance intervals are not shown here).

The difference between observed and expected

values is significant at the 0.01 probability level for all ‘critical’ time-distance intervals. (Statistical signifi- cance Jevels were calculated using the computed expectation and variance, following Pike and Smith [16] and Pike and Bull [17].) This is as would be expected for an infectious disease. Although lack of space precludes the presentation of results for a greater range of distance intervals, the computation was performed for intervals up to 14 km apart and there were significantly more pairs of cases than expected, up to and including this distance and for all time intervals up to 10 days. In view of the evident clustering in the maps of the 1977 and 1982 epidemics shown in Fig. 3, the greater than expected number of pairs of cases occurring at a distance as great as 14 km (too far apart to be the result of person-to- person transmission) is likely to reflect outbreaks in different parts of the Matlab area occurring simultaneously or close together in time.

Table 3. (i) Cases hospitalised. Sept.-Dec. 1974 (n = 333)

Time (in days)

0.00 < 1.00 c2.00 < 3.00 <4.00 <MO <6.00 <7.00 <a.00 c9.00

< 10.00

0 I7 35 58 70 a5 96

105 107 III 115 121

Time Distance (in metres) observed (in days)

<250 <500 <750 <lOOO.. <2000 27 37 43 48 75 0.00 55 78 89 I04 173 1.00 86 123 154 I81 286 <2.00

I05 I54 200 231 383 <3.00 139 I95 255 298 499 <4.00 163 224 290 337 596 <5.00 179 250 328 389 699 <6.00 188 267 355 428 805 <7.00 205 292 389 471 897 < 8.00 220 319 421 513 993 <9.00 234 346 458 557 1086 < 10.00

0 <250 <500 1.38 3.09 4.86 3.92 a.79 13.84 6.50 14.56 22.92 8.92 19.98 31.45

11.42 25.58 40.27 13.94 31.22 49.16 16.48 36.93 58.14 18.96 42.47 66.86 21.44 48.03 75.61 23.79 53.31 83.92 26.26 58.84 92.63

Distance (in metres) exoected I

<750 6.66

18.95 31.39 43.06 55.13 67.31 79.61 91.55

103.53 114.91 126.84

<lOOO. ..<2000 8.49 18.97

24.15 53.95 40.00 89.38 54.88 122.62 70.27 157.00 85.78 191.66

101.47 226.70 116.68 260.69 131.95 295.80 146.45 327.21 161.65 361.17

Table 3. (ii) Cases hospitalised, Aug.-Dec. 1977 In = 67?1

Time (in davs) Distance (in met& observed

Time (in days) Distana (in metm) exoected

0.00 <l.OO < 2.00 <3.00 <4.00 <5.00 <6.00 <7.00 <a.00 <9.00

<IO.00

0 <250 <500 <750 < :lOOO.. < 2000 208 230 271 297 315 397 279 354 429 492 550 794 338 452 563 659 746 1171 416 565 701 819 928 1559 472 641 a04 945 1087 I a90 499 685 a77 1043 1207 2173 527 739 954 II41 1332 2509 544 768 1010 1215 1438 2809 554 794 1055 1283 1536 308 I 576 823 I I07 I362 1639 3342 587 a53 II55 1439 1750 3623

0.00

< 1.00 <2.00 <3.00 <4.00 < 5.00 <6.00 <7.00 <a.00 <9.00

< 10.00

0 <250 <500 <750 <lOOO... <2Otm 5.75 9.46 13.76 la.82 24.36 53.05

15.49 25.49 37.10 50.74 65.66 143.03 25.01 41.17 59.91 81.93 106.02 230.96 34.24 56.35 82.01 112.15 145.13 316.14 43.12 70.98 103.31 141.27 182.82 398.23 51.43 84.65 123.21 168.49 218.03 414.95 59.55 98.01 142.65 195.07 252.44 549.89 68.31 112.43 163.63 223.77 289.57 630.78 76.73 126.28 183.80 251.35 325.26 708.52 85.35 140.48 204.46 279.59 361.81 788.15 93.63 154.10 224.28 306.71 396.90 864.58

Table 3. (iii) Cases hospital&d. Sept.-Dec. 1978 (n = 422)

Time (in days)

0.00 < 1.00 <2.00 <3.00 t4.00 < 5.00 <6X10 <7.00 <a.00 <9.00

<IO.00

0

42 71 98

122 I37 147 I50 162 I70 173 I80

Time Distance (in metres) observed (in days)

~250 <500 <750 <lOOO.... <2000 57 73 80 a7 137 0.00

116 156 176 194 329 I71 237 275 312 566 212 299 345 398 766 237 336 398 478 967 271 390 471 567 1168 288 419 508 617 1312 312 456 564 685 1461 327 484 599 736 1594 344 515 639 792 1741 361 548 682 851 1893

<I.00

< 2.00 <3.00 <4.00 <5.00 < 6.00 <7.00 C8.00 t9.W

< 10.00

0

2.03 6.09

10.07 13.91 17.86 21.90 25.75 29.44 32.87 36.64 40.23

Distance (in metres) expected

<250 <500 <750 <lOOO.... c2OOt.J 4.49 7.80 10.53 13.84 32.75

13.45 23.38 31.57 41.49 98.17 22.26 38.67 52.22 68.63 162.39 30.73 53.40 72.10 94.16 224.22 39.47 68.59 92.61 121.72 288.01 48.39 84.08 113.53 149.22 353.07 56.90 98.87 133.50 175.47 415.18 65.06 Il3.04 152.64 200.62 474.69 72.64 126.22 170.43 224.00 530.02 80.97 140.69 189.97 249.69 590.79 88.91 154.49 208.60 274.18 648.73

12 MARIAN CRAIG

Table 3. (iv) Cases hospital&d, Sept.-Dec. 1982 (n = 627)

Time (in days)

<O.OO

<I.00

t2.00 :3.00 <4.00 <s.OO ~6.00 c7.00 < 8.00 <9.00

< 10.00

0 43 88

114 139 164 193 21s 227 235 244 254

Distance (in metres) observed Time

(in days)

t2so <SO0 <7so <lcalO... t2000 88 126 IS2 190 389 <o.OO

216 332 404 492 1062 < I.00 321 497 607 759 I680 <2.00 421 661 831 I057 2367 <3.00 521 816 1049 1342 3019 <4.00 598 940 1236 IS91 3603 <s.OO 658 1041 1394 1817 415s <6.00 722 II49 IS59 2035 4680 <7.00 772 1241 1688 2232 5174 t8.00 804 1316 1x1s 2414 5680 <9.00 847 1387 1326 2586 6151 < 10.00

Distance (in metres) expected

0 <2so <so0 < 750 <lOOO.. <2tmo 5.00 18.33 31.64 45.41 62.89 ” 159.73

14.06 51.59 89.03 127.78 176.98 449.48 22.83 83.76 144.53 207.45 287.31 729.69 32.38 118.82 20503 294.28 407.57 1035.12 41.42 151.96 262.23 376.38 52 I .28 1323.90 49.90 183.07 315.90 453.41 627.96 1594.85 58.54 214.76 370.60 53 I .92 736.70 1871.02 66.94 245.61 423.83 608.31 842.51 2139.73 74.17 274.32 473.38 679.43 941 .OO 2389.90 82.65 303.23 523.26 7s I .02 1040.16 2641.71 90.28 331.22 571.55 820.34 1136.16 288S.54

As already stated the technique is not designed to compare the relative significance of clustering at different time-space scales in a situation where clus- tering is clearly indicated. In this context the extent to which apparent within-bari clustering varies from one epidemic to another is compared. This com- parison may enable us to assess whether the patterns revealed by maps showing varying proportions of hospitalised cases are consistent. Table 4 shows the proportion of pairs of cases which occur less than 250m apart and which come from the same bari (distance = 0) for time intervals of three and ten days. The lowest proportion of same-bari pairs occurred in the 1982 epidemic (33%); the highest in the 1977 epidemic (74%). For all epidemics the proportion of pairs within the same bari decreased by the tenth day. The 1977 epidemic was the only one where a distinct majority of pairs of cases less than 250m and less than ten days apart occurred within the same bari.

DISCUSSION

In attempting to make inferences about cholera transmission processes from time-space patterns of the distribution of cases beneath the level of the village three things need to be explained or recon- ciled: an unsteady increase through time in the extent of map coverage; an unsteady decrease through time in the degree of within-bari clustering; and a change in biotype in 1982, from El Tor with its low propor- tion of cases to asymptomatic infections, to Classical with its higher case:infection ratio.

It is unlikely that changes in the extent of map coverage would cause artifactual clustering in some time periods because the change is accounted for by the removal of a contiguous part of the Matlab study area. (However data for the Autumn 1983 epidemic in Matlab is currently being analysed, which will extend the time series for which map coverage of

Table 4. Proportions of within 250 m pairs from same bari

Percentage pairs of cases occurring within 250111

which come from same bari

Epidemic Within 3 days

1982 33 1978 58 1977 74 1974 67

Within IO days

30 so 69 s2

more than 75% of hospitalised cases is available.) A priori change in the degree of within-bari clustering would be expected to result from a change in biotype if the biotype change was accompanied by a change in the ratio of asymptomatic cases to infections. Feachem [2] summarises data which shows that the proportion of family members falling ill following a Classical cholera index case is higher than following an El Tor index case. If this is so (as stated above Feachem cites evidence which suggests that El Tor may be reverting to a case:infection ratio similar to Classical), a higher proportion of cases would be expected to occur within the same bari in an epidemic caused predominantly by Classical cholera, than in an E 1 Tor epidemic. The computation of the propor- tions of within-bari pairs has not shown this. This would suggest either that biotype-specific differences in the ratio of asymptomatic -cases to infections. Feachem [2] summarises data which shows,that the revealed by the distribution of hospitalised cases, or that the method, as used here to measure bari clus- tering, is insensitive. It should signal caution in making generalisations about time-space clustering of cholera which apply throughout the period for which spatial data beneath the level of the village is available for Matlab.

Further analysis using the method of Knox [5] or other methods must compare epidemics of the same biotype, and restrict comparisons to periods within which the proportion of cases which may be mapped is consistent.

Acknowledgements--I am grateful to the following for guidance and stimulating discussion; D. J. Bradley, A. D. Cliff, R. G. Feachem, P. G. Smith; and to James Green and Anita Thakore for computer programming. Much of this work was carried out under an Economic and Social Research Council Linked Award. The costs of digitising were met by the 1CDDR.B. Any errors remain the responsibility of the author.

I.

2.

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Time-space clustering of V. cholerae 13

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