Simple Linear Regression

            More districts significantly correlated with average yearly mean temperature than with total yearly precipitation for simple linear regressions with both SPR and API.  The following table shows the number of districts that significantly correlated for the given monthly mean temperature or monthly precipitation and API or SPR.  The monthly mean temperatures that had the highest number of districts that significantly correlated (p < 0.10) for both SPR and API were January, April, May, and December lagged one year.

Number of Districts With Statistically Significant (p < 0.10) Correlations between Malaria Prevalence Rates and Monthly Mean Temperature and Monthly Precipitation

            Link here for tables of the R² values and the correlation coefficients for the statistically significant regressions for mean temperature for the months with the greatest number of correlations.  Although mean temperature for January, April, May, lagged November temperature, and lagged December temperature, each correlated significantly with SPR and API, the average across districts for R² values for January mean temperature were the highest.

Mean Temperature Physical Model

            The specific monthly mean temperature that had the largest number of statistically significant correlations with high R² values are not random, but can be explained in terms of the seasonal climate of Karnataka.  April and May are typically the two hottest months of the year and January and December are the two coldest months.  One would expect variation in these months to strongly affect malaria.  To illustrate, if the cold months are too cold or the hot months too hot, vectors and parasites cannot survive.  Diurnal temperature range is not so large in Karnataka (Guha, 2000, personal communication).  Therefore, although minimum and maximum temperatures could lead to a better understanding of the role of extreme temperatures in prediction of malaria rates, using mean temperature was sufficient for this analysis.

            Despite this physical explanation of the high number of correlations with specific months, the coefficients of all of the linear regressions between mean temperature and API or SPR were negative.  This implies that increases in mean temperature in all months corresponded to decreases in malaria for all monthly mean temperatures.  The fact that an increase in temperature was related to a decrease in malaria prevalence in both the cold and the hot months discredits the hypothesis explained above, because an increase in temperature in the cold months should have resulted in an increase rather than a decrease in malaria rates by curbing the increase in malaria due to higher temperatures.  Despite the fact that there are differing magnitudes for the correlation coefficient, the fact that they are negative for all districts for all months is puzzling. 

            Although it is difficult to explain this finding, there are a few possible explanations.  The best explanation based on my findings, is the degree to which mean temperature in cold months is correlated with mean temperature in hot months.   This correlation would indirectly affect malaria rates by increases in cold monthly temperatures being associated with increases in hot monthly temperatures which are too hot for vector and parasite survival.  To test this idea, I calculated the Pearson’s correlation coefficients between mean temperature in December and January with mean temperature in April and May.  I found that both January and December mean temperature were positively correlated with the mean temperature in the next April and May in all districts.  The specific correlation values are illustrated in the table below. This implies that hotter Januarys and Decembers corresponded to hotter Aprils and Mays.  Therefore, with increasing mean temperatures in cold months, the hot month temperatures also increased.

Correlation between Cold and Hot Monthly Mean Temperatures

            Another possible explanation for the negative relationship between mean temperature in cold months and malaria, is the relationship between temperature and precipitation within a month.  Mean temperature and precipitation can affect each other.  For example, when the monsoon arrives, it modifies any natural increase in temperature in the summer months.  Precipitation brings with it increased cloud cover which can decrease the amount of incoming sunlight and therefore decrease mean temperature (Webb, 2000, personal communication). 

            I found negative Pearson's correlation coefficients between mean temperature and precipitation in January, April and May, which are listed in the table below.  These results imply that when mean temperature increased, precipitation decreased.  Therefore, if January mean temperature increased, precipitation decreased, causing fewer breeding grounds for malaria vectors and presumably less malaria transmission.

Correlation between Mean Temperature and Precipitation by Month

However, I found a positive Pearson correlation between mean temperature and precipitation in December.  This result contradicts the finding above and makes the argument not as strong that the relationship between mean temperature and precipitation explains the negative coefficients.  The negative correlations for April and May mean that an increase in mean temperature was correlated with a decrease in precipitation, and vice versa.  This increase in mean temperature was related to a decrease in precipitation, which may have limited malaria rates by reducing the amount of surface water for vector breeding.  Analysis of monthly malaria rates would further clarify whether this correlation is very strong.

            The interrelationships between temperature, evaporation, and relative humidity may also have played a role.  Increasing temperature causes increased evaporation, which can decrease the relative humidity, thus limiting vector survival and behavior (Webb, 2000, personal communication).  January is one of the least humid months of the year in India (Takahashi and Arakawa, 1981).  Therefore, during years with higher mean January temperature, January would be even drier and evaporation would increase, thus decreasing the amount of surface water in which the vectors could breed, and also lessening vector survival by decreasing relative humidity.  In addition, for a given amount of water in the air, if the temperature increases, the relative humidity decreases.  Therefore, if the amount of water vapor in the air does not change much throughout the day, changes in temperature throughout the day cause most of the variability in relative humidity measurements (Ahrens, 1985).  This means that if temperature increases, and the amount of water in the air stays the same, then relative humidity decreases.  As stated earlier, if relative humidity falls too low, the Anopheles mosquito is not able to survive.  However, because I did not have access to relative humidity data for this study, it was difficult to assess to what extent this hypothesis is valid in explaining the negative coefficient between mean temperature in cold months and malaria rates.

Precipitation Discussion

            April and November precipitation had the greatest number of districts that significantly correlated with SPR and API.  This link takes you to tables of the p-values, R² values, and correlation coefficients for all statistically significant correlations for April, November and lagged November precipitation and API and SPR.

            The majority of the correlation coefficients between malaria rates and precipitation were positive.  An increase in precipitation was correlated with a decrease in malaria prevalence.  However, the correlation coefficients for regressions between malaria rates and precipitation in Kolar for all months were negative.  Tumkur also had a negative correlation coefficients for some months and positive ones for others.  Only the regressions for May precipitation (positive) and and November precipitation (negative), however, were statistically significant.  Therefore, an increase in May precipitation was related to an increase in malaria prevalence, but an increase in November precipitation corresponded to a decrease in malaria prevalence in Tumkur.  This could be related to the specific vector(s) and specific ecology within Tumkur. 

            The magnitudes of the correlation coefficients for all districts with precipitation, however, were not very large, all within ±1.  Therefore, although monthly precipitation significantly predicted the malaria rate, only large increases or decreases in precipitation were related to increases or decreases in malaria prevalence.

            The fact that April and November precipitation correlated with API and SPR in a large number of districts and these regression models also had high R² values is logical.  In Karnataka, April is usually the month before the monsoon arrives and November is the month after the monsoon has retreated.  Therefore, precipitation in these two months is more likely to vary due to an early onset or a late retreat of the monsoon in some years.  Collins et al. (1990) documents that both of the primary vectors in Karnataka, An. culicifacies and An. fluviatilis, breed in the dry months and that a change in the timing of the monsoon affects when breeding occurs.  This variability in precipitation could have caused a higher or lower likelihood that there was more surface water for vector breeding that would have increased or decreased the potential for malaria transmission.  An increase in precipitation facilitates breeding of vectors in fast flowing rivers and a decrease in precipitation can help vectors that breed in stagnant water by slowing rivers and creating pools of water in the floodplains (Sharma, 1996b).  Therefore, the fact that the correlation coefficient was close to zero could have been caused by the counteracting effects of increased breeding of one species and decreased breeding of another.

            November precipitation correlated more with the current year’s malaria rates than with the next year’s, which is interesting.  November precipitation is not highly correlated with April precipitation, which does not help to explain this result.  The range is from –0.31 in Belgaum to 0.39 in Bidar.  Possibly there was some increase in malaria prevalence during November or December that was related to the increase in precipitation in November of that year.  Analysis of monthly malaria rates would provide more information into the effects of precipitation on monthly malaria rates.