GeoJournal 5.4 315-322/1981 © Akademische Verlagsgesellschaft • Wiesbaden

315

Local Mobi l i t y and the Spat ia l D y n a m i c s

o f Measles in a Rural A r e a o f K e n y a *

Ferguson, Alan, Department of Geography, Northwestern University, Evanston I L 60201, USA and Leeuwenburg, Johan, Medical Research Centre, Nairobi, Kenya

Abstract: Population mobility at different scales is important in the analysis of contagious diseases. The role of local mobility among young children is related to spatial and temporal patterns of measles in part of rural Kenya. The dynamics of measles are examined over a period of 3 1/2 years, during which there were two epidemics; the path of the second of these epidemics is studied, using a spatial averaging technique (the centroid). Limited local mobility of children under the age of five, related to low levels of susceptibility provides a probable explanation of the slow diffusion of measles epidemics.

Local Mobi l i t y and t he Spat ia l D y n a m i c o f Measles in a Rural A r e a o f K e n y a

Population mobility is a key factor in the analysis of con- tagious diseases, particularly where a spatial dimension is explicit. The role of mobility in the diffusion of disease may be considered at several scales. Prothero (1977, p. 264) makes a logical division of mobility in tropical Africa between migration (where movement away from the place of residence is permanent) and circulation (where there is an eventual return to the place of residence). Prothero then sub-divides circulation into four types based on the period of absence from the place of residence: daily, periodic, seasonal, and long-term.

Each type of movement will tend to be associated with different spatial phenomena. The farthest movements are associated with international or interregional spread of disease and the shortest movements with the local spread or saturation.

In this article we relate the role of local mobility in young children in a rural part of Kenya to the spatial and temporal patterns of measles. In most of the developed world, complex mobility patterns have been the result of

* This paper is reprinted from RuralAfricana, Spring 1981, with the kind permission of the Editors.

national and personal affluence and the regularities in the spatial series of contagious diseases have tended to be obscured. This is true even of the comparatively less-mobile younger groups most susceptible to measles. Thus, the British geographers Cliff and Haggett have turned their attention from measles epidemics in southwest England (Cliff et al., 1975) to those in the more isolated island community of Iceland (Cliff et al., forthcoming 1981).

Transport facilities in many African countries are being improved rapidly. High rates of permanent and semi-per- manent migration are concomitant with rapid urbanization and have increased rural-urban interaction. However, the day-to-day circulation of people in most rural areas, though doubtless increasing, remains low, especially amongst women and children. It is this type of mobility we in- vestigate here.

The Study Area

The Joint Project Machakos (JPM) was established in 1974 by the Medical Research Centre, Nairobi, under the auspices of the Royal Tropical Institute, Amsterdam. Its purpose is an investigation of factors affecting the health of mothers and children in an area of 87 km 2 in the Northern Division of Machakos District, Kenya. As part of the project a sur-

316 GeoJournal 5.4/1981

To Nairobi

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Fig la Study Area - -Main Features

Fig l b Study Area - Distribution o f Dwellings

GeoJournal 5.4/1981 317

veillance of measles has been continuing since April, 1974. e . . . . The epidemiology of measles in the area has been described by Voorhoeve et al. (1977) and a preliminary subregional 4o analysis by Leeuwenburg et al. (1979).

The study area is shown in Fig 1 (a). The area is divided physically, ecologically and administratively into two dis- tinct parts. The higher, more fertile and more densely- 30 populated western area of Matungulu Location is separated from the lower, drier and more sparsely-populated Mbiuni Location by the Kanzalu Escarpment which is virtually impassable for most of its length. The Matungulu side has 2o better connections with the outside world, particularly to Nairobi (60 km) and Machakos (35 km) than the Mbiuni side. Within the study area the main road loops round the north of the escarpment connecting the two parts. The road lO is an earth one and may be impassable for several days during the rainy seasons. The north and east of the study area is bounded by the Kalala and Athi rivers across which there is little contact. The study area is divided into five e sublocations of which two, Kambusu and Kingoti, have most access to the outside world. The two sublocations, Ulaani and Katitu, which make up Mbiuni Location, are the most remote.

Fig 1 (b) shows the distribution of the 4,000 odd dwellings in the study. These dwellings house a population of some 25,000. The pattern is a typically dispersed one although the higher population densities in Kambusu and Kingoti can be seen. The scarp slope of the Kanzalu range is clearly marked by the absence of houses.

The study area therefore provided a fairly diverse background against which to consider the dynamics of measles.

The Dynamics o f Measles

Fig 2 shows the profile of measles cases in the whole study area for a period of 3 1/2 years. Two epidemics are obvious, the larger one lasting from May 1976 -October 1977. The collection of data is by fortnightly "rounds". Each house- hold is visited in rotation every two weeks by a field worker and any suspected measles case is diagnosed during a sub- sequent visit by a J PM physician. The full method of data collection is described in Voorhoeve et al. (1977).

The epidemics shown in Fig 2 are slow to pass through such a small population. This, and the lack of fade-out ex- cept in three of the 93 rounds covered in Fig 2, point to the lack of closure of the study area. The constant importa- tion of measles from Nairobi and other areas lowers the susceptibility levels and keeps the disease "ticking over." The average susceptibility level for children under fifteen years of age between April 1974 and March 1976 was estimated by Voorhoeve et al. (1977, p. 433) to be 28 %. Leeuwenburg et al. (1979, p. 318) estimate the secondary

¸

1974 1975 1976

.... ~ . . . . iN 1977

Fig 2 Study Area - Profile of Measles Cases Two-weekly periods April 1974 - November 1977

attack rate within households between April 1974 - Oc- tober 1977 to be 54 %. The high proportion of measles cases which can be considered secondary, plus the low velocity of the epidemics suggest low levels of mobility in a susceptible population which is already relatively small because of the continuous reintroductions of the disease. In the typology of Bartlett (1957, p. 50), therefore, the study area hovers between a Type I (endemic) and Type II (regular epidemics) area.

Fig 3 shows that when the data are disaggregated to sublocation level there are contrasting measles profiles between the different areas. This covers the period March 1976 - November 1977 (rounds fifty-one to ninety-three), the span of the second epidemic. Peaks are recorded at different times in different sublocations although only in Ulaani is there a single, distinct peak. The densely-populated areas (Kambusu and Kingoti) have very few fade-outs although several peaks are distinguishable. In the three smaller sublocafions, outbreaks are sporadic.

These results are contradictory to the idea that the velocity of an epidemic will be positively related to popula- tion density. Kambusu has 536 persons/km 2, Kingoti 355 and Ulaani 112. However, the greater isolation on the eastern side of the escarpment may allow the proportions of sus- ceptibles to build up to higher levels than in the more densely settled part. Ulaani, for example, had only seventy- two measles cases down to round fifty, a rate of around thirty-seven cases a year. Assuming the conservative birth- rate of 3.5 %, the corresponding increase in new susceptibles would be around 160 per annum. It is possible that the build-up of susceptibles in Ulaani also triggered the peaks

318 Geodoumal 5.4/1981

Cases

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November 1977 by Sublocation

in some adjacent areas although the lack of isolation of the study area makes this difficult to ascertain with certainty.

Fig 4 shows the distribution of measles cases during three local peaks in the epidemic at rounds 59, 78 and 85. Local concentration of outbreaks can be seen fairly clearly although it is noticeable that in none of the three rounds portrayed is the spatial concentration complete.

In order to have a more complete picture of the path of the second epidemic throughout the study area a spatial averaging technique - the centroid - was employed.

For each round between July 1976 (round 59) and August 1977 (round 86) with the exception of two rounds (74 and 81 ) which had less than ten cases each, the epidemic centroid was calculated. The method used was based on a simplified form of the algorithm developed by Kuhn and Kuenne (1962) which estimates the two cartesian co- ordinates of the centroid by an iterative procedure, gradual- ly moving the centroid into an optimum position. The estimates of the two coordinates are give by UK and VK which are calculated as:

n n

E g j = l j = ,

and

fl n

V K : Z dj ,K-1 Z

j = l j = l

where

(uj/dj,K- 1)

(v j /d j ,~ _ 1)

n = number of measles cases in the given round dj, K - 1 = distance between household "j" and centroid

calculated at iteration ( K - 1 ) uj, vj = coordinates of household 'j'

The procedure is terminated at the Kth iteration when both ^ ^

(0K--13K-- 1) and (VK--VK_I) are less than 100 m. To produce the exact location for the centroid (and the maps on Fig 1 (b) and Fig 4) each household in the study area had to be measured on a six-digit coordinate. Calculation of the centroids took between two and thirteen iterations, beginning with a random position at the outset and setting the initial values of UK and VK to the centroid of the pre- vious round for subsequent calculations. The movement of the ecpidemic centroid is shown in Fig 5.

From a position centered in Ulaani in round 59 (Fig 4), the epidemic tracks south and west into the more populous areas and then circulates back and forth between Kambusu and Kingoti. At the highest peak of the epidemic (round 84) the centroid is just north of the Kambusu-Kingoti boundary. Reference to Fig 3 confirms that after round 66 there are only a few sporadic cases east of the escarpment and that the epidemic is marked by a system of local peaks in Kam- busu,Kingoti and Katheka.

It should be emphasized that the lines joining successive centroids should not necessarily be interpreted as infection paths, although in a closed community such an interpreta- tion would have some validity. In this application the centroids are used to show simply the different centers of concentration during the course of the epidemic (for example, in Kambusu in rounds 77, 78 and 79).

We now turn to examine the movements of the sus- ceptible population and try to relate them to some of the patterns we have described here.

Local Mobi l i ty

Voorhoeve et al. (1977, p. 433) provide an age-specific breakdown of measles cases in the study area for the period April 1974 - March 1976 which shows that almost 80 % of

GeoJournal 5.4/1981 319

Fig 4 Measles Case Locations Rounds 59, 78, 85 (A, B, C,)

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75

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320 GeoJoumal 5.4/1981

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Fig 6 Movement Patterns by Function and Distance -- Children up to 5 Years

the cases occurred in children under five years old. The highest attack rate is amongst children between one and two years old and the median age was found to be thirty months. To link local mobility with spread patterns of measles we must therefore look primarily at the "action spaces" of the very young children in the area.

Between February 1 4 t h - 28th 1979 the movements of a sample of 176 children in the area were investigated. The sample consisted of children up to five years old and was stratified by age and sublocation. Each evening mothers were asked by the fieldworker where the child had gone that day. At the end of the period there was a set of 176 x 14 "child-days" to provide information on local mobility. There were no noticeable differences in the action spaces of children in different areas but some important ones between younger and older children. The mobility information is presented in two different ways in Fig 6.

In diagrams A and B, the movements of the children in the sample are presented in eight functional categories with the sample split between the under-threes (111 children) and the over-threes (65 children). In diagrams C and D the maximum physical distances moved from the home com- pounds have been calculated for each child-day and the more familiar "distance-decay function" plotted for the two subsamples.

The most obvious feature of these diagrams is the large proportion of child-days when no movement outside the home compound is recorded. Even allowing for some degree of under-reporting by mothers, the extremely low level of mobility is striking. In 61% of child-days in the under-three sample and in 42 % of the over-threes the children do not move outside the home compound. They may, of course, be visited by children from other compounds.

Comparing diagrams A and B, the movement patterns of the youngest children correspond basically to the activi- ty of the mothers, as one would expect. Hence, more time is spent at home and a greater proportion of time is spent in markets and outside the study area. The outstanding difference between the two age-groups is the attendance at nursery school of some of the older children. Just over half of the sample of older children attended a nursery school which, typically, has between thirty and forty children. Attendance at nursery school may be an important factor in the local circulation of measles, more so than with pri- mary schools, given the higher susceptibility of the younger children.

The age-specific differences are reflected in differences between the two distance-decay functions in diagrams C and D. Both demonstrate the limited action-spaces of young children, but the distance-decay function is much steeper for the younger group, reflecting principally the greater amount of time spent at home and the low proportions of under-threes attending nursery schools.

Combining the mobility patterns with the low levels of susceptibility provides a highly probable explanation of the slow diffusion of measles epidemics in the study area. The secondary attack rate of 54 % calculated within households again reflects the highly constrained spatial nature of the epidemic. Much of the epidemic may be envisaged as a series of local peaks as infection is diffused amongst the susceptibles in a small community, for example, the catch-

GeoJournal 5.4/1981 321

ment area of a nursery school. The epidemic peaks on endemic troughs seen in Kambusu and Kingoti tend to reflect this type of mechanism. Mobility and susceptibility are too low to allow diffusion of the disease throughout the study area in a short period although, as we have seen, when the level of susceptibility climbs as in Ulaani, the epidemic wave will travel much more quickly and the peak will be more pronounced.

Finally~ circulation of the people within the study area and between the study area and the outside world varies throughout the year. More travelling is done at the end of the month and at holiday periods. The rainy season restricts movements within the study area. However, no seasonality has yet been discovered in the measles records. Given the low absolute levels of mobility in the majority of sus- ceptibles, variations due to holidays, weather and so on must only be marginal and are not translated into any ob- vious spatial or temporal regularities in the measles series.

Conclusions and further Research

In this paper we have attempted to describe the characteri- stics of a measles epidemic in a rural area of Kenya and to relate certain features of the epidemic to local mobility patterns. The constant presence of measles amongst a population of around 25,000 suggests continual importa- tion of the disease. This, in turn, keeps the average level of susceptibility low except in the more remote parts. The low levels of mobility and susceptibility serve to dampen the epidemic peaks, to slow down the velocity of the epidemic and to vary its direction of spread within the area. A spatial disaggregation of the measles data shows the existence of very localized surges of measles cases but these rarely build up into powerful waves.

The next step in this research is an attempt at simulat- ing the spread of measles within the study area. Given the fact that the disea, se is being continually reintroduced by random contacts from the outside, this is clearly a difficult

task. However, when the location of a single infected child has been established it should be possible to replicate the local patterns of spread, given estimates of the susceptibili- ty and mobility parameters. The partial closure of the study area and the internal variation in geographical conditions provide challenging problems in building a simulation model. At present we are working towards a Monte-Carlo simulation model of the spatial diffusion of measles in Machakos. If the model can reproduce the actual patterns to a reasonable extent we should then be in a position to consider the effects of changes in the key parameters of susceptibility and mobility. A better appreciation of the effects of such changes may be beneficial to disease control and public health policies generally and, although the test ground is a small part of Kenya, it is to be hoped that any advances made in this respect would have relevance to much of the rest of rural Africa as well.

References

Bartlett, M.J.: Measles Periodicity and Community Size. Journal of the Royal Statistical Society, A, 120, 1, 4 8 - 59 (1957)

Cliff, A. D., Ord, J. K., Bassett, K. A. and Davies, R. B.: Elements of Spatial Structure: A Quantitative Approach. pp. 8 3 - 106. Cambridge: Cambridge University Press, 1975.

Cliff, A. D, Haggett, P., Ord, J. K. and Versey, G. R.: Spatial Dif- fusion. Cambridge: Cambridge University Press, forthcoming in 1981.

Kuhn, H.W. and Kuenne, R.E.: An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economics. Journal of Regional Science 4, 21 - 3 3 (1962)

Leeuwenburg, J., Omondi Odhiambo and Ferguson, A. G.: Spatial Contagion in Measles Epidemics, Machakos Project Studies XIII, Tropical and Geographical Medicine 31,311 -- 20 (1979)

Prothero, R.M.: Disease and Mobility: A Neglected Factor in Epi- demiology. International Journal of Epidemiology 6, 259 - 67 (197i)

Voorhoeve, A.M., Muller, A.S., Schulpen, T. W. ]., Gemert, W., Valkenburg, H.A. and Ensering, H. E.: The Epidemiology of Measles. Machakos Project Studies III, Tropical and Geographi- cal Medicine 29,428 - 40 (1977)