Lagged effects of rainfall on malaria: a case study of Meghalaya


 Background: Meghalaya contributes about twenty per cent of India's total malaria death and is one of the high malaria endemic states in India, very susceptible to malaria transmission mainly due to favorable climatic conditions that mostly facilitate the transmission. In the relationship between malaria and meteorological factors, existing studies mainly focus on the interaction between different climatic factors, while interaction within one specific climatic predictor at different ag times has been largely neglected. This paper aims to explore the interaction of lagged rainfalls and their impact on malaria incidence.
Methods: The district monthly malaria records from Jan 2005 to December 2017 was collected from the Department of Health Services (Malaria), Government of Meghalaya. The district monthly meteorological records from Jan 2005 to December 2017 was collected from the Directorate of Agriculture, Government of Meghalaya, in which average temperature (℃), humidity (%) and rainfall (mm) had been recorded. Monthly malaria cases and three climatic variables of 4 districts in Meghalaya from 2015 to 2017 were analysed with the varying coefficient-distributed lag non-linear model. The missing climatic values were imputed using Kalman Smoothing on structural time series using the package imputeTS in R.
Results: During the period 2005-2017, a total of 309133 malaria cases were reported in all the districts under study. The monthly average rainfall ranges from a minimum of 181.79 mm in South Garo to a maximum of 367.87 in Jaintia. Also, South Garo and East Khasi are the hottest and the coolest place understudy with 26.96 and 16.86 degrees Celsius respectively. Rainfall levels in the first-month lag affect the non-linear patterns between the incidence of malaria and rainfall at each lag time. The low rainfall level at the first-month lag may promote malaria incidence as rainfall increases. However, for the high rainfall level at the first-month lag, malaria incidence decreases as rainfall increases.
Conclusion: The interaction effect between lagged rainfalls on malaria incidence was observed in this study, and highlights its importance for future studies to better understand and predict malaria transmission.

incidence as rainfall increases. However, for the high rainfall level at the first-month lag, 1 malaria incidence decreases as rainfall increases. Conclusion: The interaction effect between lagged rainfalls on malaria incidence was observed 4 in this study, and highlights its importance for future studies to better understand and predict 5 malaria transmission.  Background 10 Epidemiology describes malaria transmission in Meghalaya as perennial and persistent across 11 the states and across the border with both Plasmodium falciparum and Plasmodium vivax found 12 across the states (1). Meghalaya contributes about 20% of India's total malaria death (1) and is 13 one of the high malaria endemic states in India, very susceptible to malaria transmission mainly 14 due to favourable climatic conditions that mostly facilitate the transmission (2). The region 15 received an average annual rainfall of over 2000 mm, and Cherrapunji, located on the 16 Meghalaya plateau 50 Km south of Shillong, receives the highest rainfall in the world with a 17 mean annual rainfall of 11,418.7 mm (3). 18 Apart from socio-economic conditions and agricultural practices, meteorological variables are 19 the main drivers of malaria transmission (4) biologically speaking, weather conditions affect 20 malaria incidence mainly through their effects on both the malaria vectors and the extrinsic 21 incubation period of malaria parasites inside the mosquito vectors (5). The deposition of 22 mosquito eggs and their maturation into larvae and then into adults required a suitable aquatic 23 breeding site and is, therefore, dependent on rainfall and temperature. In cooler environments, 24 the increase in temperature shortens the parasite's life-cycle within the vector, enhancing 1 mosquito biting rate and thus increasing the transmission before the mosquito vector dies (6,7). 2 The existing relationship between meteorological variables and malaria failed to consider the 3 lag effect (4) but the issues of lag and the non-linear pattern are key when exploring the effect 4 of meteorological variables on malaria (5); for instance, a study in Meghalaya, observe a sudden 5 rise in malaria cases during May-July after the commencement of rainy season during April 6 but record low cases during Jan-April which corresponds to dry/low rainy season (1). On the 7 other hand, most time-series studies have established a relationship between meteorological 8 variables and malaria at a single fixed lag of 0, 1, or 2 months (6). However, the single lag 9 effect was not sensible enough to explain the relationship at a population level. The lag effect 10 was biologically divided into three stages, such as the development of mosquitoes from larvae 11 to adults, the extrinsic incubation period of parasites within the mosquito, and the incubation 12 of parasites within the human body (5). The extrinsic incubation period (EIP) describe as the 13 time it takes for the parasites to develop in the mosquito till the stage a mosquito becomes 14 infectious usually last on an average of 10 days and the development from larvae to the adult 15 stage usually last from 10 to 45 days. At each stage, the lag time may vary based on the changes 16 in climatic conditions. Evidence from existing studies suggests that lag and non-linear patterns 17 are essential, and a distributed lag non-linear model proves to be an appropriate method to 18 explore the effect of meteorological variables on malaria (8).

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Existing studies on the relationship between meteorological variables and malaria primarily 20 focus on the lag effect and interaction between climatic factors (9) but the effect of between 21 lag interactions has long been neglected. Between lag interaction effect is defined as the 22 interaction between one covariate at a different lag time, for instance, the interaction effect of 23 rainfalls four and the five weeks previously on the malaria incidence of the current week, 24 whereas the interaction between various climatic factors are of the same time period and 25 simultaneously affect malaria incidence (10). This concept of interaction between lagged 1 predictors was first used to examine the effect of heat exposure on excess mortality (11). This 2 study investigates the interaction effect between several meteorological factors at different time 3 lags on the risk of developing malaria. To our knowledge, this is the first study in the context 4 of India. Particularly, using the monthly data on malaria cases and climatic variables during varying coefficient was adopted to model the association between malaria cases and rainfall. 7 The findings from the study will help to better understand the complex relationship between  Hills) are taken. The remaining districts are not considered for the analysis due to a lack of 18 information.

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The climate of East Khasi Hills, in particular, is of interest to climatologists as Mawsynram 20 and Cherrapunji, which are reported to be among the wettest places on the planet are located   The non-linear and delayed dependencies can be described by a distributed lag non-linear 12 model (DLNM) (8). A Poisson regression model was employed to model the expected number 13 of malaria counts � � in month j in district i and several climatic variables in previous 14 months as,

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(1) 20 where and are the malaria counts and population in district i in month j respectively; 1 0 is the intercept effect due to i th district. , , ,ℎ , , respectively represent the monthly 2 rainfall, humidity and mean temperature in j th month in i th district.

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Biological knowledge suggests that malaria cases in a particular month can be affected by 4 climatic variables several months earlier for the lag effect in the model and hence, Model (1) 5 estimates the cumulative effects across the whole lag range rather than at a single fixed lag 6 time. Therefore, considering occurrences of malaria cases in a relatively long period i.e. 7 monthly the model considers the lag ranges from the first to sixth month for rainfall and first (1) a second-order natural cubic spline was applied in order to take into account the unimodal 18 nature of climatic variables and parsimony of the model fitted (13). those changes are as shown below, , 13 (2)   Table   7 S1).  The estimated lagged non-linear relationships between malaria incidence and rainfall are 23 shown in Fig 3. The Y-axis represents the logarithmic value of the relative risk of malaria 24 incidence in comparison to the reference value at rainfall 0 mm. The dashed lines indicate a 95% confidence interval of the estimated non-linear effects of malaria incidence (solid lines).

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In the low level of rainfall in the first-month lag, rainfall helps in increasing the incidence of 2 malaria. However, in the high level of rainfall in the first-month lag, there is a negative 3 association between malaria incidence and rainfall. A distinctive difference can be seen in the 4 non-linear patterns between rainfall and malaria incidence at each time lag across the three 5 levels of rainfall. In the case of the medium level of rainfall, a slight increase in the logarithmic 6 value of the relative risk of malaria at first reaching the maximum at approximately 1500 mm, 7 then starts declining sharply. Furthermore, in the high level of rainfall, a positive correlation is 8 observed in the range 0-500 mm between rainfall and malaria incidence. Afterwards, the 9 correlation becomes negative. In the low rainfall level in the first-month lag, rainfall is 10 positively associated with the malaria incidence, and there is a sharp increase in log RR with 11 the increase in rainfall. The third-month lag has the greatest impact on the risk of malaria at the 12 low and medium levels of rainfall whereas, the effect of the second-month lag is greater than 13 that of the fourth-month lag.
14 At low-level rainfall at one month lag, the relative risk of malaria gradually increases and then 15 decreases with an increase in rainfall in two, three and four-month lags. Compared to medium 16 and high-level rainfall, the interaction effect is quite low for low rainfall at one month lag. This  three, and four months lag respectively. In low-level rainfall, the effect of four-month lagged 23 rainfall is more pronounced than the other two. With the increase in rainfall at the fourth-month 24 lag, relative risk increases to a certain level and then declines. After some point, rainfall at fourth-month lag becomes negatively associated with malaria as log RR takes a negative value 1 and decreases sharply. In a medium level of rainfall, the difference is negligible. In high-level 2 rainfall, the rate of increase of risk is low for the fourth-month lag in comparison to two and 3 three-month lags.  between lagged rainfalls on malaria. When the level of rainfall at the first-month lag is low, the 20 malaria incidence increases along with the increase of rainfall, indicating that the increasing 21 rainfall helps malaria transmission when the rainfall level is low at the first-month lag. away or destroyed the mosquito breeding sites, and consequently reducing the mosquito density 2 (18). Specifically, when the level of rainfall at first-month lag is low, abundant rainfall at month 3 t would relieve the effect of low rainfall, so the rainfall would offer more numbers of breeding 4 sites, which then increased the risk of malaria incidence. In contrast, when the level of rainfall 5 at the first-month lag is high, then excessive rainfall at the month t would intensify the effect 6 of excessive rainfall, resulting in mosquitos breeding sites being destroyed and fewer people 7 doing their outdoor activities (10). 8 Also, it is observed that the lagged effect of rainfall on the risk of malaria incidence was highest 9 in the third lag month, compared to the second and fourth lag months. This may be due to the 10 fact that the effect of rainfall occurring during the current month or too long before has a 11 negligible impact on malaria incidence.

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It can be observed from Fig 4 that higher relative risk due to the heavier rainfall results in a 13 shorter lag of malaria incidence. In the medium level of rainfall at the first-month lag, rainfall 14 starts to be significantly correlated with the malaria incidence at the fifth-month lag and 15 throughout. However, in the low and high levels of rainfall at the first-month lag, the rainfall 16 significantly correlates with the malaria incidence from the second-month lag onwards.

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Rainfall in the medium level of rainfall at first-month lag is associated with delayed malaria 18 incidence as compared with the high level of rainfall. The reason may be that rainfall could 19 provide suitable habitats for mosquitos to breed, which then shortens their life cycle and 20 increases the spread of malaria (10).

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To describe the main effect of the rainfall levels at the first-month lag, the term 1 and 2 are by the random intercept model (19).

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The study has some limitations. First, the meteorological data are from the designated stations 13 and may not represent the specific district. Second, the study is based only on four districts of 14 Meghalaya. However, this should not induce any significant bias result. Third, the study did      The estimates represent the non-linear patterns between rainfall and malaria incidences along the exposure dimension. The logarithm of the relative risk ratio in relation to the reference rainfall 0.0 mm is along the Y-axis. The solid line is the estimated non-linear t with dashed lines representing its 95% con dence interval. The solid lines in the top 3 rows show the scenarios for the 2nd month lag (panel A-C), the 3rd month lag (panel D-F) and the 4th month lag (panel G-I), while the fourth row shows the difference among the results at the 2nd, 3rd and 4th month lags (J-L). The rst three panels in each column represent the speci c rainfall level at the rst-month lag. Speci cally, the columns of (A, D, G, J), (B, E, H, K) and (C, F, I, L) are for the low, medium and high rainfall levels at the rst-month lag, respectively. The range of the X-axis depends on the corresponding observed range of rainfall.

Figure 4
This is the Fig 4 title The estimates are for the non-linear patterns between rainfall and malaria incidence in the lag dimension. The Y-axis represents the logarithm of the relative risk ratio in relation to the reference rainfall 0.0 mm. The solid line is the estimated non-linear t, with dashed lines representing its 95% con dence interval. The three panels of a-c show the scenarios for the rainfall levels of 12.5, 206.5, and 400.5 mm, respectively.

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