Dengue Seasonality and Non-Monotonic Response to Moisture: A Model-Data Analysis of Sri Lanka Incidence from 2011 to 2016
Milad Hooshyar, Caroline E. Wagner, Rachel E. Baker, Wenchang Yang, Gabriel A. Vecchi, C. Jessica E. Metcalf, Bryan T. Grenfell, Amilcare Porporato
DD ENGUE S EASONALITY AND N ON -M ONOTONIC R ESPONSE TO M OISTURE : A M
ODEL -D ATA A NALYSIS OF S RI L ANKA I NCIDENCE FROM TO Milad Hooshyar ∗ Princeton University [email protected]
Caroline E. Wagner
McGill University
Rachel E. Baker
Princeton University
Wenchang Yang
Princeton University
Gabriel A. Vecchi
Princeton University
C. Jessica E. Metcalf
Princeton University
Bryan T. Grenfell
Princeton University
Amilcare Porporato
Princeton University A BSTRACT
Dengue fever impacts populations across the tropics. Dengue is caused by a mosquito transmittedflavivirus and its burden is projected to increase under future climate and development scenarios.The transmission process of dengue virus is strongly moderated by hydro-climatic conditions thatimpact the vector’s life cycle and behavior. Here, we study the impact of rainfall seasonality andmoisture availability on the monthly distribution of reported dengue cases in Sri Lanka. Throughcluster analysis, we find an association between seasonal peaks of rainfall and dengue incidence witha two-month lag. We show that a hydrologically driven epidemiological model (HYSIR), whichtakes into account hydrologic memory in addition to the nonlinear dynamics of the transmissionprocess, captures the two-month lag between rainfall and dengue cases seasonal peaks. Our analysisreveals a non-monotonic dependence of dengue cases on moisture, whereby an increase of cases withincreasing moisture is followed by a reduction for very high levels of water availability. Improvementin prediction of the seasonal peaks in dengue incidence results from a seasonally varying dependenceof transmission rate on water availability. ∗ Corresponding author a r X i v : . [ q - b i o . P E ] S e p Introduction
Dengue fever was first mentioned in a Chinese encyclopedia of disease symptoms and remedies published sometimeduring 265-420 A.D. [1]. The first recorded dengue epidemic occurred during 1779 and 1780 in Asia, Africa, and NorthAmerica [2, 3, 1], and its burden has increased dramatically in recent decades, making it a major problem in the tropics,comparable to that of malaria. According to the World Health Organization (WHO) [4], the number of reported denguecases has surged from about 500k cases in 2000 to over 4.2 million in 2019 while the death toll has increased fromalmost 1000 to more than 4000 in the same period. Because dengue is often asymptomatic or with mild symptoms,it is thought to be under-reported, with the actual cases potentially order of magnitudes larger ( million in 2010,as suggested in [5]). There are four distinct strains of dengue virus (DENV), whereby infection to each strain createslife-long immunity only to that particular strain and makes the secondary infections by a new strain very severe [6, 7].Hydro-climatic conditions can greatly impact several aspects of infection transmission and partly control the temporaland spatial patterns of disease spread [8, 5, 9, 10, 11, 12, 13]. The survival probability and transmission of diseaseagents (e.g., virus, bacterial, and other parasites) are often controlled by hydro-climatic variables such as temperature,rainfall, air humidity [14]. In vector-borne diseases, the abundance of breeding sites, larva development, feeding, andsurvival chance are all affected by climate and water availability [15, 16, 17, 18, 19, 11]. For instance, it is well-knownthat water availability is a key factor in the transmission cycle of dengue as the vector (
Aedes aegypti mosquito) breedsin natural or artificial water containers [20, 21, 22]. This hydro-climatic dependence highlights the possible increasein the future burden of dengue under climate change. It is estimated that almost – of the (projected) globalpopulation in 2085 would be at risk of dengue transmission compared to only in 1990 via the combined effects ofpopulation growth and climate change [20]. These predictions also highlight the potential increase in the spread ofdiseases such as chikungunya, Zika fever, Rift valley fever, and yellow fever for which Aedes aegypti mosquito is acommon vector [23].Dengue fever has been circulating in Sri Lanka for the last 40 years [24, 11]. In a recent epidemic in 2017 kconfirmed cases were reported with a death toll of almost , according to Sri Lanka’s Health Ministry [25, 11]. Thedisease exists in nearly all geographic regions across the country; however, the severity and its seasonal variation arehighly spatially variable. Wagner et al. [11] studied the association of dengue incidence with rainfall and temperatureand found a positive feedback from these climatic variables on the dengue transmission rate with a time lag of severalweeks. This analysis allowed for a quantitative evaluation of the future risk of dengue across the island.Here, we refine the analysis of Wagner et al. [11] analysis to allow mechanistically for the impact of hydro-climaticforcing. Specifically, we use a minimalist coupled hydrologic-epidemiological model (HYSIR) to explore the associationbetween rainfall seasonality patterns (RSPs) and dengue seasonality patterns (DSPs) and the phase difference betweenthe peaks of rainfall and dengue cases. In this model, water availability is modeled by a minimalist bucket model [26],which is fed by rainfall and maintains a memory of rainfall forcing. The hydrologic and epidemiological models arecoupled by assuming a functional dependence between water availability and transmission rate. We show that the2ntroduction of hydrologic memory, in addition to the nonlinear dynamics of the disease model, can explain the observedseasonality of dengue incidence without the addition of a lag parameter as was done in [11]. Accurate prediction ofseasonal peaks of dengue cases can be achieved by assuming a seasonally varying response of transmission rate onwater availability. Our results further suggest a non-monotonic relationship between water availability and denguetransmission rate. Such dependence predicts an initial increase in transmission rate followed by a drop under very wetconditions.
There are four distinct monsoon seasons that contribute to precipitation in Sri Lanka [27, 28]. The First Inter-Monsoon(FIM) spans from March through April with rainfall attributed to the disturbances within the Inter-Tropical ConvergenceZone (ITCZ). This is followed by the Southwest Monsoon (SWM) which typically begins late in May and lasts untilSeptember. The second Inter-Monsoon (SIM) includes rainfall contributions from the tropical depressions or cyclonesin the Bay of Bengal and is active during October and November. Lastly, there is the Northeast Monsoon (NEM) fromDecember to February [29, 28].Fig 1a shows the spatial average of annual precipitation across Sri Lanka from 1980-2016. The partitioning of rainfallbetween the four monsoon seasons (i.e., FIM, SWM, SIM, and NEM) is depicted in Fig. 1b. A slight increasing trend( + 27 mm / y) in rainfall exists from 1985-2010 followed by a sharp decrease in rainfall after 2010 ( − mm / y).Regression analysis reveals that although all monsoon seasons had an increasing rainfall trend in this period, themajority of the overall increase ( ) is attributed to the higher rainfall from FIM and NEM (December to April).This trend is followed by a sharp drop after 2010. Despite this overall decreasing trend, the SWM season had increasesin rainfall ( + 55 mm / y), which were surpassed by a significant drop in the rain during FIM and NEM. This analysisreveals that the inter-annual rainfall trend from 1985-2016 is dominated by the change in rainfall from FIM and NEM(increase in 1985-2010 and decrease in 2010-2016).The spatial distribution of mean annual rainfall from 1980 to 2016 across the island is shown in Fig.1c. The annualrainfall ranges from more than m in the southwest to less than m in northern regions. The spatial distribution ofrainfall intermittency in terms of inter-arrival time λ − (the expected time in days between rainfall events) and thedepth φ (the expected amount of rain from each event) is shown in 1d and e. The southwestern region has the highestannual rainfall with more frequent and intense rain events. Total rainfall decreases moving toward the north and rainfallevents become less frequent (on average every days in the northern regions). It is interesting to note that despiterelatively comparable average rain depth in northern and eastern regions, the mean annual rainfall in the north is muchlower mainly due to less frequent rainfall events.The seasonality of rainfall from 1980-2009 can be studied quantitatively by clustering the seasonality patterns. To do so, p m at each location is defined as the ratio of total rain in month m to the total rain during the study period. This gives a3igure 1: Annual rainfall in Sri Lanka from 1980-2016. (a) and (b) show the spatial average of annual rainfall acrossthe country and the partitioning of rainfall into the monsoons FIM (March and April), SWM (May to September), SIM(October and November), and NEM (December to February).(c), (d), and (e) show the spatial distribution of meanannual rainfall, the inter-arrival time, and depth of rainfall events. The monthly variation of mean daily rainfall, theinter-arrival time, and depth of rainfall events for southern (below the latitude ) and northern (above the latitude )regions are shown in (f), (g). and (h).vector p with 12 elements summing up to unity which describes normalized seasonal rainfall patterns. These vectors arethen fed into a K-means clustering algorithm to detect the most distinct rainfall seasonality patterns (RSPs) in the island.K-means is a clustering method that categorizes n-dimensional data points (here n = 12 ) into k clusters (here k = 3 )by minimizing the sum of the variance within clusters. Fig 2a-c show three distinct RSPs across Sri Lanka from 1980to 2009. Each seasonality pattern is characterized by a mean (centroid of the cluster defined as the average of allcluster members) shown as solid black lines. The RSP at each location is then assigned to the cluster with a minimumEuclidean distance from its centroid. The spatial extent of these RSPs is shown in Fig. 2d.4he rainfall in the northern region ( Fig. 2c) exhibits an (almost) ’unimodal’ seasonality; this is largely driven by thedominance of SIM spanning from October through December. The Eastern part of the island exhibits a fairly differentseasonality pattern with an expanded winter rainfall from SIM (from October to December) and NEM (from Decemberto February), as shown in Fig. 2b. This region also has relatively little rainfall from the summer monsoon. The rainfallin the southwest peaks during October and December mainly due to the SIM, with a second peak expanding throughMarch to June from the FIM and SWM (Fig. 2a).We further examine the change in seasonality patterns after 2010. This is achieved by comparing seasonality in2010-2016 at each point with the centroid of the clusters (black lines in Fig. 2a-c) and assigning them to the one withthe smallest Euclidean distance. As shown in Fig. 2e, the patterns exhibit changes after 2010, with the encroachment ofthe eastern and western patterns toward the north. This is in line with the analysis of inter-annual rainfall trend whichrevealed lower rainfall from FIM and NEM after 2010 which implies a greater relative contribution from the summermonsoon and thus a more pronounced bi-modal pattern.Figure 2: The seasonality of rainfall in Sri Lanka. (a-c) show three seasonality patterns extracted by clustering thevector p where p m is the ratio of total rain in month m to the total rain during 1980-2009. The centroid of seasonalitypatterns are shown as black solid lines. (d) and (e) are the spatial extent of each seasonality patterns during 1980-2009and 2010-2016, respectively. The color codes corresponds to the pattern in (a-c).Rainfall seasons also exhibit diverse intermittency patterns. Fig 3 shows the probability distribution of the depth ofrain events during two main seasons (April-May and October-November) in the areas associated with each RSP in Fig.2a-c. The total rainfall in the April-May season is generally less than that of October-November, as shown in Fig. 2a-c;however, in the eastern and southern regions, the rain events in April-May are relatively more intense, as highlighted bythe extended tail in Fig. 3a and b. 5igure 3: The probability distribution of the depth of rainfall events during two main seasons (April-May and October-November) in the areas associated with each RSP in Fig. 2a-c. The PDFs for events in April-May have an extendedtails in the southern and eastern regions which implies more intense rain events. As shown in the last section, rainfall in Sri Lanka exhibits spatially variables patterns associated with the four activemonsoon seasons. Here we discuss the implication of these rainfall seasonality patterns in terms of the burden of denguefever in Sri Lanka.The co-circulation of all four serotypes of dengue fever is well-documented in the last 40 years [24]. Fig. 4 shows thenumber of monthly reported cases from 2010-2016 from Sri Lanka’s Ministry of Health. In 2017 there was a severeoutbreak that has been associated with the emergence of a new strain [11, 30], short-term migration, and changes in thebreeding sites of the mosquitoes [30]. Thus, our analysis here is focused on the period 2010 to 2016 to avoid a bias dueto the high number of cases in 2017.Fig. 4a and b show two dengue seasonality patterns (DSP) that are extracted in a similar way as the rainfall patterns inFig. 2. In this case, the clustering is performed on I m defined as the ratio of the number of cases in month m to thetotal cases during 2010-2016. The corresponding locations of the patterns are marked at the coordinates of the districtscapitals in Fig. 4c. 6he DSPs exhibit uni- and bi-modal behaviors. The bi-modal pattern peaks in July and December and is prevalentmainly in south and southwest regions. The uni-modal pattern peaks in January and is spatially scattered throughout theisland except for the southwestern part. The spatial extent of the rainfall seasonality pattern is shown in the backgroundof Fig. 4c. It is evident that the bi-modal DSP is mostly associated with the RSP in the southwest where two dominantrain season exists, although the dengue cases reach their maximum with an almost two-months delay relative to therainfall peaks. The uni-modal DSP exists within regions with a relatively low contribution of spring rainfall in theeastern and northern regions.It is interesting to note that even without significant rainfall in April-May, dengue cases may peak during the summerin July. For instance, the two black dots in the northern regions in Fig. 4b have a significant number of cases in July;however, their RSP is almost uni-modal with a relatively small rainfall during April-May. This suggests that there maybe other hydro-climatic (humidity, temperature) or social (increase in human activities which can lead to more exposureto mosquito bites) factors that drive the dengue spread in that period. This is also reinforced by the fact that the smallerrainfall peaks in April-May (see Fig. 2a) leads to the larger dengue cases peaks in July, as shown in Fig. 2a.Figure 4: (a) Reported cases of dengue fever in Sri Lanka from 2010-2016. Data is from the Ministry of Health. (b) and(c) show two seasonality patterns extracted by clustering the vector I where I m is the ratio of the number of cases inmonth m to the total cases during 2010-2016. The centroid of seasonality patterns is shown as solid black lines. (d)shows the spatial extent of each seasonality pattern where the color codes correspond to the pattern in (b) and (c). Theextent of rainfall seasonality pattern in the same period of time is shown in the background (same as Fig. 2e).7 Modeling dengue dynamics with the HYSIR model
We modeled the dengue transmission using a hydrologically driven SIR model [31]. In this formulation, the wateravailability w is given by a simple bucket model given as dwdt = − ρw + R ( t ) , (1)where w quantifies the water availability, R [ d − ] is normalized (by a parameter w ) rainfall rate. The parameter ρ isproportional to L max w o where L m ax is the maximum rate of water loss and ρ − captures the hydrologic ’memory’ [32].This type of bucket model has also been used to describe the temporal dynamics of soil moisture in the top soil layer[26, 33]. In this study, we used w = 150 mm although the choice of w simply changes the scale of w and does notalters the results presented here. We used ρ = 0 . d − which introduces a -day memory in the w dynamics.Dengue transmission with a hydrologic component is modeled using the well-known SIR formulation [34, 35, 36, 37], dSdt = −B ( w ) IS − ηS + ηdIdt = B ( w ) IS − ηI − γI (2)where the ratio of susceptible, infected, and recovered individuals to the total population are denoted by S , I , and R ,respectively. γ is the recovery rate and η is birth/death rate thus γ − and η − are the expected time of infection andindividual life span, respectively. The function B is the moisture-dependent transmission rate. The reported dengue cases in Sri Lanka are limited to incidence, whereas the number of susceptible individualsremains unobserved. We used the TSIR method [38, 39] to reconstruct the ’true’ times-series of cases and susceptibleindividuals. The TSIR uses the reported time-series of incidence, birth, and population to compute the reporting rate forthe reconstruction of the ’true’ incidence. The susceptible S and transmission rate B time-series are then computedusing a Generalized Linear Model (GLM) to find the best fit to the dynamics of I given in Eq. 2. The TSIR requires thefrequency of recorded data to be equal to the recovery rate of disease which we take to be / days as in [11]. Thus,we used simple linear interpolation to reconstruct bi-weekly time-series from monthly incidence, birth, and populationdata. Fig. 5 shows the reconstructed incidence and transmission rate time-series in the districts Colombo and Vavuniya.8igure 5: The reconstructed time-series of the incidence I and transmission rate B in the districts Colombo andVavuniya. These results are achieved from the TSIR method [38, 39] using the district-level reported cases, birth, andpopulation time-series which were interpolated to bi-weekly temporal scale. To study the impact of water availability on the transmission of dengue in Sri Lanka, we assume a relationship between w and B of the form ln B = ψw + ζ d (3)where the intercept ζ d is defined for each district d . Eq. 3 describes a linear relationship between the (log of) transmissionrate and water availability given by water availability w . This simple linear dependence aims to capture the positivefeedback of water availability on the mosquito life cycle, in terms of availability of breeding sites and improved survival.We should note that this formulation is a minimalist representation of a hydrologically driven mosquito-borne infectionand neglects the explicit modeling of the mosquito life cycle [40]. The constants ζ d quantify a non-seasonal control ontransmission and capture the spatial variation of observed dengue cases across the island. Given the time-series of B (see Fig. 5b and d for examples), we used OLS [41] to compute ψ and ζ from Eq. (3). Fig. 6a shows the observedversus predicted transmission rate as compared to a one-to-one trend expected for the perfect model.The hydrologic impact on the transmission rate from Eq. 3 can be better visualized by subtracting the spatial components ζ from the observed transmission rates ( ˆ B = ln B − ζ d ). The relationship between ˆ B and w is compared to the predictedlinear trend (i.e., ˆ B = ψw ) in Fig. 6b. For small w , the transmission rate linearly increases with w in agreement withthe functional form assumed in Eq. 3. However, we observed a deviation from this linear trend at high w . The reductionof transmission rate at high w may be related to the adverse effects of flooding on mosquito life-cycle [42, 43], althoughother epidemiological feedbacks such as changes in human and mosquito activity patterns may play a role here.We also used Eq. 3 with the fitted parameters to simulate the incidence from 2011 to 2016 and compared the seasonalitypatterns with the observation as shown in Fig. 6c and d for the districts Colombo and Vavuniya. For these simulations,the initial conditions were set to the observed condition at / / . We used a simulated time-series of w (using Eq.9) to compute B at each time step. Here, we performed a single deterministic simulation for each case and ignoredthe uncertainty in the fitted parameters by only considering the best-fitted values. Although the model captures thetiming of incidence peaks accurately (see Fig. 6c for instance), the relative magnitude of the peaks is poorly modeled.It should be noted that without any additional parameters, the 2-month phase difference between rainfall and denguecases peaks is captured in this minimalist approach. This is due to the nonlinearity introduced by the multiplicativetransmission term in Eq. (2) as well as the hydrologic memory modeled by ρ − .Figure 6: The performance of the linear model of transmission rate (see Eq. 3). (a) shows the observed versus predictedtransmission rates as compared to the one-to-one trend expected for a perfect model. (b) shows the hydrologic controlson the transmission rate that is visualized by the relationship between ˆ B = ln B − ζ d and w . The observations arebinned and the mean, th , and th envelops are shown. The fitted linear trend ˆ B = ψw is shown in red. (c) and (d)are seasonality of the incidence from observation and simulation in the districts Colombo and Vavuniya. The simulationare performed by forcing the HYSIR model with the observed rainfall and the transmission rate given in Eq. 3. Inspired by the drop in transmission rate at high w (Fig. 6b), we explored a more flexible functional form forhydrologically driven transmission rate, ln B = ψw + θw + ζ d . (4)The quadratic term with coefficient θ allows for a non-monotonic dependence of the transmission rate on wateravailability. Fig. 7 shows the performance of the transmission model in Eq. 4. Although the hydrologic impact on the10ransmission rate is now captured more accurately, as compared to the linear model (Fig. 7b), the magnitude of theseasonal peaks of incidence are still not fully resolved.Figure 7: Same as Fig. 6 for the transmission model given in Eq. 4. To further improve the model performance, we modified the hydrologic portion of the transmission rate expression byallowing seasonal variation in the coefficient ψ , ln B = ψ m w + θw + ζ d , (5)where m is the index for the month. In this model, the coefficients ψ are month-specific, the intercepts ζ are location-specific, and θ is a constant. Allowing for seasonal variation in ψ enables a more flexible dependence of transmissionrate on water availability at the monthly time scale. Fig. 8a shows the relationship between the observed and predictedtransmission rate by Eq. 5 after fitting to the observed time-series of B . The fitted function is then used to simulate theincidence using the HYSIR model. The seasonality of observed versus simulated incidence in the districts Colomboand Vavuniya are shown in Fig. 8b and c. It is evident that the addition of the seasonal coefficients ψ allows for amore accurate prediction of the seasonal peaks of dengue incidence. A similar comparison for all 21 studied districts isshown in Appendix I (Fig. 9). 11he monthly variation of the parameter ψ is shown in Fig. 8d which exhibits an almost symmetric bimodal patternwith peaks during April-July and October-December. This indicates a relatively more pronounced response of thetransmission rate on water availability in those periods as also depicted by the red lines in Fig. 8e . On the other hand,the values of ψ in February, July, and August are not statistically significant ( p Value > . ) which indicates that thetransmission rate is unresponsive to water availability in those periods. At the transition between these two regimes, thetransmission rate moderately increases with water availability before dropping at high values of w (the blue lines in Fig.8e).Figure 8: The performance of the model with the transmission rate given in Eq. 5: (a) shows observed versus predictedtransmission rates as compared to the one-to-one trend expected for the perfect model;(b) and (c) are seasonality ofthe incidence from observation and simulation in the districts Colombo and Vavuniya (refer to Appendix I for theresults of other districts. The simulation are performed by forcing the HYSIR model with observed rainfall and thetransmission rate given in Eq. 5); (d) shows the monthly variation of the parameter ψ . The ψ at February and August arenot statistically significant ( p Value > . ). The hydrologic controls on the transmission rate given by ˆ B = ψ m w + θw for each month is shown in (e). The colors corresponds to those shown in (d). Understanding the role of hydro-climatic conditions on the spread of vector-borne infections is essential for quantifyingthe risk of these health hazards, especially in the face of the future changes in patterns [11]. With this in mind, westudied dengue transmission in Sri Lanka and showed that the hydrology plays a major role in the observed seasonalitypattern of dengue incidence. This analysis highlights the importance of the seasonality of climatic variables (e.g.,rainfall) which are important drivers of infection dynamics. These seasonal patterns have been have been changingrapidly [44] and are expected to continue doing so, especially in tropics where the burden of vector-borne infections isthe highest [5] . 12ur analysis also shows a non-monotonic dependence of dengue transmission rate on water availability w . The initialincrease in the transmission rate with high w may be related to the positive feedback of water availability on themosquito life cycle, which leads to an abundance of breeding sites and a better chance of survival. A similar increasingtrend has been observed in mosquito populations [45, 46]; however, the opposite trend has also be reported in theanalysis of dengue cases with river level in Bangladesh [47]. The effect of intense floods and flash-floods can be morecomplicated and difficult to predict. Flash-floods may disturb the mosquito life-cycle, destroy their habitats, and reducetheir food resources which may lead to a decrease in their population size [42, 43]. This can explain the decrease intransmission rate at high w observed in this study. For instance, Lehman et al. [48] argued that the heavy flooding andstrong winds of Hurricane Katrina might have actually decreased the risk of mosquito-borne diseases by dispersing anddestroying mosquito habitat in Louisiana and Mississippi, USA. However, at longer time-scales, flash-floods may havepositive feedback effects on the abundance of mosquitoes as they can reduce the population of mosquito antagonists[42].Although the rainfall seasonality was shown to drive the seasonality of dengue cases in Sri Lanka, even in the absenceof climatic seasonality, the HYSIR model exhibits noise-induced cyclic behavior that is controlled by the hydrologicmemory introduced by parameter ρ [31]. Here we assumed a constant ρ ; however, accounting for the spatial andtemporal variation of ρ can potentially improve the model predictions. Our analysis focused on water availability andrainfall, although other hydro-climatic variables such as temperature, humidity, wind speed, etc. may be important aswell [18, 19, 11, 12, 13].Our model for transmission rate assumes a dominant linear dependence on water availability with slope ψ at low valuesof w . This parameter varies seasonally in order to capture the seasonal peak of dengue cases. The parameters ψ isa surrogate for a range of controlling factors such as the abundance of ’potential’ breeding sites (e.g., the density ofbuckets regardless of their water content). We should also note that the value of ψ may as well reflect monthly variationsin other aspects of the disease spread, such as changes in human-mosquito activity and contact processes, etc. Forinstance, the observation of two annual peaks in ψ coincides with the sowing and growing periods of Yala and Mahacultivation seasons in Sri Lanka [49]. We acknowledges support from Princeton Environmental Institute and Princeton Institute for International and RegionalStudies at Princeton University though the climate and disease initiative. The numerical simulations in this articlewere performed on computational resources provided by Princeton Research Computing, a consortium of groupsincluding the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of InformationTechnology’s High Performance Computing Center and Visualization Laboratory at Princeton University.13
Data
We used precipitation data from the Climate Hazards group Infrared Precipitation with Stations (CHIRPS) with aspatial resolution of 0.05 ◦ at a daily time scale [50]. The monthly reported case of dengue in Sri Lanka is from theofficial website of the epidemiology unit of the Ministry of Health of Sri Lanka [25]. We birth and population data wereacquired from the Department of Census and Statistics of Sri Lanka [51]. The observed and simulated seasonality patterns of dengue incidence from the quadratic model in Eq. (5) is shown inFig. 9.Figure 9: The comparison of incidence seasonality from observation (black lines) of simulation (red lines) in the studieddistricts. The transmission rate is given by Eq. (5).
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