Concepts of diffusion theory and a graphic approach to the description of the epidemic flow of contagious disease.

Concepts used to analyze sociological, geographic, and economic processes were adapted to an examination of the diffusion of contagious disease. The example used in applying these concepts was an epidemic of variola minor which continued for 12 months in an area of 1,006 square kilometers centered on the city of Bragança Paulista, Sao Paulo State (Brazil). A graphic procedure is proposed that depicts aspects of the epidemic flow of person-to-person transmission. Spatial, temporal, and sociological characteristics of the epidemic flow are disclosed in sequential diagrams. They represent geographic areas as well as schools and agglomerates of households affected by the epidemic at a given time, the mode of diffusion, and the source of the infection. The procedure yielded indirect evidence of the role of school pupils as introducers of variola minor into households and school classes. All subdivisions of the city, six of the seven rural districts, and four of the five elementary schools were affected through hierarchical (between-areas) diffusion. Subsequently, there was neighborhood (within-area) diffusion, and this resulted in new interactions between areas.

Variola minor in Braganca Paulista County, 1956. Flow of the epidemic through the schools of the county.

The characteristics of the 10 elementary, teachers, business and high schools operated in the city capital of the Braganca Paulista County, state of São Paulo, Brazil, during the 1956 epidemic of variola minor (alastrim) are presented. Also shown are the numbers of students with variola and of students without variola but with homemates with variola, by grade and school. Of the total 131 cases recorded among students, 128 occurred in the 4 elementary schools. Of the latter cases, 101 occurred among the students of the JG School and the JT School. The distribution of these cases by age, sex, previous immunity status, school grade and clinical severity of the disease (typed according to Dixon's classification) were remarkably similar in these two schools. Only the ratio of students introducing the disease into their households to students having secondary cases in their households suggestively varied, the JT School having more introductory cases. No student with a previous attack of variola showed any clinical manifestation in any school. Only 2 of the total 101 cases from the JG and JT Schools occurred among students with a previous successful vaccination. Moreover, those two cases apparently resulted from within-household contacts rather than from contacts at the school. No student with current variola showed a severe type (Dixon's types 1 to 5). More than half of the cases typed showed the typical, medium-severity type (Dixon's type 6). More than 2/3 of the cases occurred among students aged 6 to 9 years, particularly among those 7- to 9-year old. The number of cases reached a maximum in the first grade and gradually and definitely decreased with increasing grade.

Variola minor in Bragança Paulista county, 1956. Observations on the clinical course of variola minor and on pregnancy in women with the disease.

Occasional observations on the clinical course of 485 cases of variola minor composing an epidemic are reported. 17% of the cases showed a complication. Otitis was observed in one case. An erythematous rash limited to the upper chest, neck and head appeared, instead of the pock eruption, after the pre-eruptive phase, in a previously vaccinated case. Convulsions, drowsiness, stupor, delusions, dizziness or deafness were observed in 23 patients whose individual characteristics are also presented. One of these cases showed a definite neurologicl syndrome: encephalitis. Neurologic complications were mostly seen in patients with medium to severe variola minor. Neither abortion nor death were seen among 4 pregnant women who developed variola minor, even though one of them delivered, on term, a dead foetus, 4 months after developing variola minor.

Variola minor in Bragança Paulista County, 1956. Distribution of onset of cases in the two schools including most school children with variola.

Class attendance during illness was confirmed for numerous pupils of two schools. Successive generations whose median cases were separated by an interval consistent with the "serial interval" of variola minor were clearly found in the epidemic curve for II of the 29 classes with cases from both schools. Twenty two other classes had no case at all.

Variola minor in Bragança Paulista County, 1956. Respiratory manifestations in cases of variola and in household contacts of cases.

A respiratory complication was recorded for 62 of the 485 cases of variola minor occurring in Bragança Paulista County, Brazil, 1956. The respiratory complication preceded onset of the classical variola minor in 2 cases; lasted only the pre-eruptive phase in 38 cases; lasted only the eruptive phase in 9 cases; lasted both the pre-eruptive phases in 1 case and had an unrecorded relationship to the clinical course in 12 cases. Six of the 17 household contacts with a respiratory syndrome contemporaneous with variola in the household had previously suffered from variola.

Variola minor in Braganca Paulista county, 1956: a trend-surface analysis.

Trend-surface analysis (TSA), a form of polynomial regression used in geology, ecology and geography, was applied to analysis of the spread of an epidemic of variola minor in a small Brazilian city. Cubic surfaces gave a generalized map of the space-time distribution of the epidemic, allowing those parts of the city to be identified where variola minor was spreading rapidly or slowly. The epidemic spread relatively quickly over the core area of the city, especially to the peripherally located household dwellings in a northeast to south-west direction. The dwellings of adults and pre-school children introducing the disease into their households broadly followed the overall pattern. School child introductory cases from a southern-located school yielded a saddle-shaped contour pattern, centered about the school; but this pattern was not repeated for the school serving the northern half of the city, which showed a ridge-shaped pattern dipping toward the west. Cubic surfaces for the influence of certain household and individual characteristics were investigated, but showed only week trends. The nearest match to the bowl-shaped overall pattern of introductory dates was provided by the vaccination level of the households. From this application, it appears that TSA permits the identification of regional trends in an objective manner and gives a quantitative measure of the importance of these regional trends in terms of the overall variation in the spatial pattern.

Contour mapping of the temporal-spatial progression of a contagious disease.

A methodology for contour-map study of contagious-disease epidemics is presented. Its application is exemplified in a smallpox epidemic occurring in a small Brazilian town. Computer-controlled contour-mapping of dates of introduction of variola minor into 169 households and the coordinates of the affected dwellings did not show a single contour pattern, but a group of subareal patterns of within-household outbreaks. Introduction by adults and pre-school children were distributed throughout the whole city area. However, introduction by school children formed two groups of contours and of affected dwellings. Each group was included in a discrete area corresponding to the zone of pupil recruitment of the two schools enrolling 91% of the school-child introductory-cases. The latter were responsible for introduction of the disease into 45% of the city's affected households. Altogether, both zones practically covered the whole city area. In either zone, several patterns surrounded the corresponding school. Even though no time value was entered for any school, contour maps clearly evidenced the influence of those two schools on spread of the epidemic. An estimated rate of linear spread of variola minor was 1.35 m per day in a city subarea.