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Logo of mjafiGuide for AuthorsAbout this journalExplore this journalMedical Journal, Armed Forces India
 
Med J Armed Forces India. 1998 April; 54(2): 107–110.
Published online 2017 June 26. doi:  10.1016/S0377-1237(17)30494-X
PMCID: PMC5531329

A MATHEMATICAL MODEL FOR PREDICTING THE PERSISTENCE AND EFFICACY OF BACILLUS THURINGIENSIS VAR ISRAELENSIS IN RELATION TO WATER POLLUTION

Abstract

In a simulated field trial, the bead formulation of Bacillus thuringiensis var israelensis (Bti) was found to be more persistent in moderately polluted as compared to highly polluted water. A mathematical model was built up to study the influence of time (independent variable) on larval reduction (dependent variable) in relation to degree of water pollution. Two predictive models for different grades of water pollution were developed, which estimated that the larval mortality in moderately polluted water was likely to decline by 3.79 as compared to 5.02 on an average, in highly polluted water with each passing day.

KEYWORDS: Biocide, Mosquito control, Prediction model

Introduction

The efficacy of biocides, especially Bacillus thuringiensis var israelensis (Bti) under field conditions is influenced by the presence of debris, silt, vegetation, water temperature and sunlight [1, 2, 3]. The effect of the degree of water pollution on larval reduction has however not been studied extensively. It is therefore desirable that the effect of water pollution, separately for moderate and high levels of pollution on larval reduction be studied to understand the behaviour of Bti in aquatic environment. The influence of the degree of water pollution on the efficacy and persistence of Bti in terms of larval reduction can be estimated by simple statistical procedures, where for each type of polluted water, the larval reduction over a period of time is recorded and analysed. This type of analysis, however, suffers from the defect that the influence of time as an independent (predictor) variable on larval reduction (dependent variable) as per different levels of water pollution can not be evaluated.

Keeping in view the objective of the study, a mathematical model was built up to assess the degree of correlation between larval reduction and time in days and to work out predictions for the expected larval reduction on the basis of time for the types of polluted water.

Material and Methods

The water samples from different water collections like soak-age pits, seepage from septic tanks, drains etc were chemically analysed. Based on the levels of free and saline ammonia and albuminoid ammonia, water was classified as moderately polluted (free and saline ammonia in the range of 0.05 – 0.5 ppm and albuminoid ammonia 0.1 – 1.0 ppm) and highly polluted (free and saline ammonia > 0.5 ppm and albuminoid ammonia > 1.0 ppm). A simulated field trial was undertaken with 3 replicates and concurrent controls for each type of polluted water (moderate and highly polluted). The trial was conducted in 20L capacity tubs in which 100 field collected third instar Culex quinquefasciatus larvae per tub were released every week starting from day zero, the day of treatment and mortality recorded after 24 hours. Every fresh batch of 300 larvae (three replicates of 100 each) were thus independent measures of the larvicidal capacity of biocide, the larvae of the previous batch either dead or else pupated and emerged as adults. The Bti formulation used was 33 per cent w/w Bti beads, which were activated by the treatment of 3 per cent Nacl for 2 hours.

Statistical Procedure :

Pearson's product moment correlation co-efficient was worked out taking the count data of larval reduction as the dependent (outcome) variable and time (in days) as the independent (predictor) variable. Separate models were then built up each for moderately polluted and highly polluted water and the influence of degree of water pollution on larval reduction estimated.

Results

The results reveal a cent per cent larval reduction on day zero in both the types of water; similar results have also been reported by other workers [4]. A subsequent decline in larval count to 282 and 267 by day 7 in moderately and highly polluted water respectively and thereafter a slow but sustained decline in this parameter till day 21, when the larval reduction reached 237 (79%) and 219 (73%) in moderately and highly polluted water respectively. Subsequently, the decline was quite steep reaching a level of 135 (45%) and 84 (28%) in moderately and highly polluted water respectively at day 42. Between days 21 and 42, the decline in the larval reduction was more marked for water with high degree of pollution as compared to water with moderate pollution. The statistical analysis data presented in Table 1 reveals no significant difference between the two levels of water pollution as regards larval reduction between day 7 to 21st day post-treatment (P>0.05). However, a significant difference was observed at day 7 (P<0.05) and subsequently from day 28 onwards till 42nd day (P<0.01).

TABLE 1
Comparison of larval densities in moderate and high water pollution

It is evident from the results of the above analysis that larval reduction is significantly more in moderately polluted water till the 42nd day. It can therefore be concluded that the reduction in larvae is likely to be more in moderately polluted water especially during the first week and thereafter from fourth week onwards.

“Goodness of Fit”

The “Goodness of Fit” of the mathematical model was assessed by calculating the predicted larval reduction at different days for the two types of water pollution using the values of intercept and β co-efficients obtained from the mathematical model. The differences between the observed values and those as predicted by the model were calculated. The details are presented in Table 2. It is seen from the table that the actual (observed) values and those predicted by the model were quite similar, there being hardly any difference between the two. The mean difference was only 0.0014 in case of moderately polluted water and 0.0071 in case of highly polluted water.

TABLE 2
Test for “goodness of fit” of the mathematical model

Correlation between larval reduction and time :

Moderately polluted water

A very strong and negative correlation between larval reduction and the time period that elapsed following the biocide treatment was observed as presented in Table 3 and Fig 1. The pearsons product moment correlation co-efficient (r) was −0.98, while the co-efficient of determination (r2) was 0.96. The 95 per cent CI of r was −1.00 to −0.86 thus indicating that the correlation was not only strong but also significant, on regressing the larval reduction (dependent variable) on time (predictor variable). The ß co-efficient was −3.796 with a standard error of 0.35 indicating a highly significant ß co-efficient. The 95 per cent CI of ß co-efficient was −4.49 to −3.10. It is therefore evident that with each passing day, larval reduction in moderately polluted water is likely to come down on an average by 3.79.

Fig. 1
Regression line with 95% CI for moderately polluted water
TABLE 3
Correlation regression analysis for moderately polluted water

Highly polluted water

On regressing larval reduction on time for highly polluted water, it was observed that the findings were almost similar to those observed for moderately polluted water. The value of Y was −0.99, thus indicating an extremely strong and negative correlation between the larval reduction and time (in days). The 95 per cent CI of ‘r’ was −1.0 to −0.94. The β co-efficient was −5.02, with a standard error of 0.306, thereby giving 95 per cent CI of ß co-efficient as −5.62 to −4.42. It is therefore apparent that in highly polluted water, larval reduction is likely to decline by 5.02 with each passing day. The data is presented in Table 4 and Fig 2.

Fig. 2
Regression line with 95% CI for highly polluted water.
TABLE 4
Correlation regression analysis for highly polluted water

Discussion

Though the ß co-efficients for both moderately as well as highly polluted water were highly significant, it was observed that the average decline in larval reduction was more marked in highly polluted water i.e. a drop of 5.02 for each day as compared to moderately polluted water, in which it dropped down by 3.79 for each day.

Equations for predicting the expected larval reduction (LR) in different types of polluted water :

Based on the findings of the present study, the undermentioned predictive equations have been developed for calculating the expected LR in the two types of polluted water.

(a) Moderately polluted water

LR = 309.86 +(−3.796 × Day post-treatment)

Upper and lower limits of this expected prediction can be estimated as follows :-

(i) Upper limit of LR = 309.86 +(−3.10 × Day)

(ii) Lower limit of LR = 309.86 +(−4.49 × Day)

(b) Highly polluted water

LR = 308.57 +(−5.02 × Day post treatment)

(i) Upper limit of LR = 308.57 +(−4.42 × Day);

(ii) Lower limit of LR = 308.57 +(−5.62 × Day).

An extensive search in the same field of study using computerised data base (Med line, ExtraMed) yielded no such predictive models having been developed so far. It is recommended that the parameters obtained from this study may be utilised for making predictions regarding efficacy and persistence of Bti under similar experimental conditions and mathematical models on similar lines may be developed for other influencing factors.

Answer to quiz on pg. 130

REFERENCES

1. Becker N. Factors influencing the activity of BTI treatments. J Am Mosq Control Assoc. 1992;8:283–289. [PubMed]
2. Sheeran W, Fisher SW. The effects of agitation, sediment and competition on the persistence and efficacy of BTI. Ecotoxical Environ Safety. 1992;24:338–346. [PubMed]
3. McLaughlin RE. Effectiveness of BT Serotype H-14 against. An crucians Mosq News. 1982;42:370–373.
4. Balaram K. Field trial of Bacillus thuringiensis H-14 (VCRC B-17) against Culex and Anopheles larvae. Indian J Med Res. 1983;77:38–43. [PubMed]

Articles from Medical Journal, Armed Forces India are provided here courtesy of Elsevier