Indian Journal of Ophthalmology

: 1967  |  Volume : 15  |  Issue : 5  |  Page : 165--171

A simple catalytic model in trachoma epidemiology

NR Parthasarathy 
 National Trachoma Control Programme, Aligarh, India

Correspondence Address:
N R Parthasarathy
National Trachoma Control Programme, Aligarh

How to cite this article:
Parthasarathy N R. A simple catalytic model in trachoma epidemiology.Indian J Ophthalmol 1967;15:165-171

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Parthasarathy N R. A simple catalytic model in trachoma epidemiology. Indian J Ophthalmol [serial online] 1967 [cited 2020 Jul 5 ];15:165-171
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 1. Introduction

1.1. Mathematical Models

Simple mathematical models of epi­demiological processes have been made use of in the formulation of simple hypothesis in accordance with the observations, to study the charac­teristics of the disease and also to guide the future line of investigation. The model provides the clues as to the mode of action of the disease and points out to the epidemic or endemic character of the disease, differences in age or sex incidence and reliability in identifying the infection etc. even if the nature of the disease has not been per­fectly understood. These models have also been used as a tool for measur­ing the force of infection. Hugo Muench (1959) has developed catalytic models for studying the epidemiology of diseases and also for useful inter­pretation of the constants in his models when the epidemiological picture of the disease is well known.

1.2. Its Applicability to Trachoma

Trachoma has been reckoned to be on the increase in the world in recent years and extensive control projects are striving hard to control the disease, in many countries. In India, it is highly endemic in the North and North-West­ern parts. An attempt is made in this paper to provide a simple catalytic model to the agewise prevalence of trachoma (all stages), which may help in further advancing the study on the epidemiology of the disease and to bridge the gaps in our knowledge which still exist.

 2. Materials

The material obtained from the country-wide survey on geographical distribution of trachoma has been made use of in this study. This survey has been conducted and supervised by the Trachoma Control Pilot Project (Indian Council of Medical Research) on behalf of Govt. of India, in collabo­ration with W.H.O. and with UNICEF assistance during the activities of the Project from 1959 to 1963.

The areas covered in this survey were all the States of India compris­ing the rural population, except those which are centrally administered. The design of the sample survey adopted was a two-stage one. In the first stage, villages were selected from districts with probability proportional to their population and with replacement. In the second stage, 20 households were selected from the selected villages following systematic sampling with a random start.

The field study was carried out in the rural areas of all the 15 States by 20 mobile units. All the medical offi­cers employed for this survey received short term training from the head­quarters staff to enable them to ob­serve uniform diagnostic criteria in all the States and eliminate some limita­tions such as the bias in diagnosis. But, as it often happens in epidemiological studies conducted by different person­nel of this kind, personal bias could not be completely eliminated, despite the earnest desire to do so.

Information collected from the ex­amination of 1,77,863 persons inhabit­ing rural areas of fifteen states of India has been used. The findings were recorded on the household cards spe­cially designed for the purpose. All parts of the conjunctiva, cornea and the anterior chamber of the eyes were examined in detail with the help of binocular loupe and torch as a source of light.

 3. Method

The method adopted here to con­struct a simple catalytic curve for tra­choma is on the pattern of HUGO MUENCH. In the field of chemistry, the original molecule may be subjected to come in contact with molecules of a catalyst the contact implying the crea­tion of a new substance. The rate at which this conversion takes place de­pends upon the relative number of molecules of a catalyst and the num­ber of contacts made per unit time. Applying this analogy to the epidemiology of trachoma, one may compare the general population to the original molecule and the trachomatous patient to the catalyst. The forces of trachoma infection acting on the population can be measured in terms of effective con­tacts per unit time, where the effective contact is defined as the contact suf­ficient to produce infection if the subject is susceptible.

Various assumptions have been made in the transfer of this catalytic process to a model of infection while projecting on the population.

(1) The population is entirely suscep­tible to infection at birth.

(2) The constant force of infection to be measured in terms of effective number of contacts.

(3) Evidence to show that the infec­tion has taken place the estimate of which may be obtained based on clinical examination results.

(4) Migration is negligible in the population.

(5) Forces of infection have not varied greatly over a period of time.

(6) Immediate and later complication due to the infection is negligible.

(7) Evidence of exposure to infection is definite and remains so during life or at least through the oldest age band used in this study.

 4. Results and Discussions

4.1. [Table 1] below shows the results of clinical examination (Trachoma all stages) by age in the rural population of India:

It will be noted from [Table 1] that the prevalence of trachoma (all stages) increases with age in rural India. The question arises as to whether this rise is due to a constant force of infection action on the rural population and, if so, what is the estimated size of this force? In order to get at this informa­tion, a simple catalytic curve as des­cribed by HUGO MUENCH has been fitted to the observed data.

4.2. [Table 2] gives the fraction with trachoma positives found in rural po­pulation samples for the whole of In­dia and the details of calculation done to arrive at the simple catalytic curve.

The simple catalytic model which best fits the observed data is given by y = 0.461 x (1-e -0.1187 t ) where `y' is the expected fraction of trachoma posi­tives and `t' is age.

4.3. The results indicate a force of infection r = 0.119 or 119 effective contacts per 1000 rural population per year. This average contacts include a number of deviations. It may be very well observed that the area covered is wide, and at a given time, the force of infection will be much more than 119 in some places while this may be zero in others. The results also indicate an upper limit of 46% (estimated) in­fected with trachoma.

4.4. In an attempt to elucidate the epidemiologic pattern of trachoma in the highly endemic areas, the simple catalytic pattern as envisaged earlier has been carried out. It will be ob­served from [Table 2] that trachoma (all stages) increases with age. [Table 3] gives the fraction with tra­choma positives found in high ende­mic areas and calculation carried out to arrive at the simple catalytic curve. The catalytic model fitted to the ob­served data is given by the equation y = 0.833 (1-e -0.0925 ) where `y' is the expected fraction of trachoma positives and `t' is age. The results indicate a force of infection r = 0.0925 or 93 effective contacts per 1000 rural popu­lation per year. This average also as stated earlier includes a number of de­viations. In the highly endemic area covered, the force of infection has been found to be 92 as against 119 effective contacts for all the regions combined. The results also indicate the upper limit of 83 per cent (estimated) infect­ed with trachoma.

4.5. The histograms drawn to the observed data alongwith the simple catalytic curve for all the area com­bined and for the highly endemic area are shown in the [Figure 1],[Figure 2]. The histograms representing the fraction of trachoma positives in the population shows a fairly regular upward trend with the increase of age. It is observed that, upto 15 years of age the catalytic curve is just below the observed line, while the increasing trend remains the same. It is possible that the rates are different in younger age-groups i.e. less than 15 years and in the older age-group above 15 years. It may be also possible that a sudden surge of high contact rates had produced epi­demic conditions and may have effect­ed a large section of the younger age ­groups in a short time. Between 15 to 50 years of age, the expected trend being higher than the observed values but beyond 50 years the observed be­ing higher than the expected curve. This implies that there is some fac­tor operating between 15 to 50 years of age producing a sharp increase in risk. This age group is the productive age group consisting of all those who work in the agricultural fields and are open to many infections of the eye due to dust storm, lack of water for clean­ing faces and insanitary environments. These factors have been studied under the epidemiology of the disease. The rate of infection observed is more than the expected in 0-15 years and adults above 50 years, because they are more commonly being diagnosed as tracho­matous as it is generally known that these groups suffer from the disease. Reasons apart from this will have to be investigated based on Age-Sex pre­valence and other population charac­teristics. Many reliable inferences can be drawn when these simple catalytic models are developed for the different regions of endemicity of trachoma, medium and low considered on the basis of age and sex.

 5. Summary

(1) The data obtained from the survey on geographical distribu­tion of trachoma in India has been made use of to construct a simple catalytic model.

(2) It is found that this simple cata­lytic model fits the data on total trachoma by age.

(3) The results show that the esti­mate of force of infection acting on the rural population to be 119 effective contacts annually per 1000 and an upper limit of 46% (estimated) to have been infected with trachoma for all the areas combined.

(4) In the high trachoma epidemic region, the estimate of forces of infection on the rural popula­tion is 93 effective contacts an­nually per 1000 and an upper limit is 83 per cent (estimated) to have been infected with tra­choma.

(5) Some factors seem to operate in the age group 15-50 years as a sharp increase in risk has been observed from the model.[2]


1Hugo Muench, Catalytic Models in Epidemiology, Harvard University Press, Cambridge, Massachusetts, 1959.
2World Health Organisation (1962) SEA/ Trach110 Rev. 1 Add. 2.