Distribution of Anopheles gambiae s.l

Occurence of Anopheles gambiae s.l. in Africa (TC50)

Figure 2 is showing the presence data collected as part of this work. Data collection on An. gambiae was focused on areas where little information about the occurrence of An. arabiensis and An. gambiae s.s. was available. Figure 3 shows the modelled mean density of An. arabiensis and An. gambiae s.s.. The white contours are indicating the presence of each species. The pattern is consistent with the general perception of the species range [3]. This is the first time a model [1–4] has been able to reproduce the absence of An. gambiae s.s. in Ethiopia. Still there are some unresolved issues. To date there are no records of An. arabiensis in Côte d’Ivoire; no models, this included, have been able to model the absence of this species in Côte d’Ivoire. A look at the figure also reveals some probable inconsistencies with respect to the species distribution in southern Chad where An. arabiensis should be dominating [37]. In South-Africa the distribution is consistent with observations from 1958 [38], although the species observed might have been An. quadriannulatus. There are however no recent available surveys of An. gambiae s.l. in the states of Gauteng, North West or South Western Limpopo. In Namibia, where An. gambiae s.l. has been observed as far south as -23.7°N[39], the model limits the range to approximately -21°N. Since there are no available data on the recent distribution of this complex in Namibia, it is difficult to know whether the model is correct or wrong. The model also suggests An. gambiae is absent in large parts of Gabon. Previous studies have found An. gambiae in Lambarene [40] and Moyen-Ogooue [41], while Mouchet only found this species in Libreville of twelve sites sampled [42]. It should be noted that Mourou et al later found An. gambiae in Port-Gentil [43], as predicted by the model, while Mouchet [42] did not record this species 26 years earlier. Elissa et al[44] also found low concentrations of An. gambiae s.s. in Haut-Ogooué, which was also predicted by the model. In the north-eastern part of Gabon it has not been possible to find any recent mosquito surveys, and it is therefore hard to conclude if the predicted absence of An. gambiae in this region is correct.

Figure 2 Presence points for An. arabiensis , An. gambiae s.s. and An. gambiae . Full size image

Figure 3 Mean density of An. arabiensis and An. gambiae s.s. , 1990-2008. White contours show where the species were present during the simulation. Full size image

To evaluate the quality of the model with respect to classifying the presence and absence of the species the methodology described previously was used. Table 1 shows the mean absolute error for the four papers [1–3, 5], expert opinion and this model. For reference, a MAE of 1 would be equivalent to completely wrong predictions, and 0 would be perfect. While the genetic algorithm of Levine [2] and the predictions based on satellite imagery by Rogers [1] show poor skill, the recent papers by Moffet et al[5] Sinka et al[3] are great improvements compared to those. Still, they have less skill than the expert opinion if comparing to the unweighed MAE. This model (OMaWa) has lower MEA than all the models included in this analysis, and including weights in the MEA makes it superior even to the expert opinion. The occurrence data suggest the expert opinion for An. arabiensis is wrong over West Africa and Southern Cameroon. A mosquito survey in Namibia, and north-eastern Gabon, would also clarify the present-day species composition in these countries.

Table 1 Mean absolute error species presence/absence (Weighted mean absolute error) Full size table

Relative fraction of each species, Madagascar (TC50)

Since Madagascar has a sharp separation between An. arabiensis and An. gambiae s.s., the island is well suited to address whether the model is able to reproduce the relative fraction of each species.Three measures to evaluate the model was defined. For method a) the mean absolute error was 0.22. The box plot in Figure 4 show the fraction of An. arabiensis from the model, grouped by the fraction in the observations. It is clear, while capturing the main tendencies well, the model has problems with the exact separation between the two species. In the mixed group, the model tends to let one species dominate over the other, possibly letting An. arabiensis dominate too easily.

Figure 4 Box-plot of fraction An. arabiensis , Madagascar. Blue is the fraction from the model, while red is observations. The arabiensis group is where observations showed more than 85% An. arabiensis, gambiae is where observations showed less than 15% An. arabiensis, and mixed is the remaining data. Dot/triangle indicate the median. Full size image

Figure 5, created using method b), shows the fraction of An. arabiensis as modelled, and observed. An eyeball comparison shows the separation is shifted westward in the model, and a bias in the South-Eastern tip of Madagascar. Whether this is a result of (climate) model resolution, failing to accurately separating the west/east gradient in topography, or the biological parametrization being inaccurate is hard to quantify. It is hoped this can be tested in a future analysis with higher model resolution.

Figure 5 Fraction of An. arabiensis . Model 1990-2008, and observations smoothed with a squared inverse distance weighted kernel with cut-off at 100 km. Full size image

Table 2 shows the distance to the closest model point, distance to the closest model point with correct prediction, and distance to the closest point with wrong prediction as described in c). At all quantiles the distance to the closest correct prediction is 1.5 to 7 smaller than the closest wrong prediction. A Mann-Whitney test with confidence level of 0.99 shows the difference in location between wrong and correct predictions is 9.84 (5.07 25.68) km (p < .0001). Thus, although with biases, it is concluded that distance to closest correct prediction and closest wrong prediction are non-identical populations.

Table 2 Distance to closest correct and wrong prediction Full size table

Temporal variability

It is important that mosquito models reproduce the seasonal cycle correctly, since this will be an indication of the sensitivity to climate. Here results from the model are compared to a number of observational studies. The comparison with each individual study might not have much information, but it is recommended that readers look at the results as a whole, having in mind the continental analysis showing the model is able to separate the distribution of An. arabiensis and An. gambiae s.s.. These results are meant to complement the continental analysis. Eth30 and Eth18 refers to the weather data used to drive OMaWa.

KEN11: 2007-2008 larva density in central Ethiopia (Eth30)

In this study [26] Kenea et al reported the An. arabiensis larva density in six locations in central Ethiopia, December 2007 to June 2008. Five of the sites followed the same seasonality, while one had the highest density before the rainy season started. The model is not designed to capture such local variations, but is rather aiming to describe the median, or sometimes mean, state within a certain area. In their study all anopheline positive habitats present within a 500 m radius of each irrigated village/town and 700m along the major drainages (lake or river) were sampled. This means that the data should be comparable to what is modelled. The seasonality of larva density, l sum = ∑ ı = 1 4 l ı , per puddle area, A p , is then calculated as C l l sum A p [ m 2 ] , where C l is a dimensionless constant. Correlations with the median relative seasonality, model vs. Kenea et al., is 0.97(0.81,0.99), and mean relative seasonality 0.92(0.55,0.98). The observations and modelled results can be seen in Figure 6.

Figure 6 Scaled variations over time of six locations (dashed grey line), and the median seasonality (solid grey line) in Central Ethiopia [26] (data from KEN11). Blue solid line shows modelled relative seasonality in the same area. Full size image

TAY2006: 2001 mosquito catch Sille, Ethiopia (Eth30)

In 2001-2002 Aseged Taye et al[27] recorded number of man biting An. arabiensis in Sille, Ethiopia. For simplicity it is assumed the human biting rate is independent of temperature and availability of breeding sites. This means the relative monthly mean sum of mosquitoes from the model should be directly comparable with the records from the paper. The model seems to under-predict the relative abundance of An. arabiensis in October 2001, and over-predict the rise in mosquito numbers in February. Otherwise the modelled number of mosquitoes seems comparable to what was observed by Taye et al. The correlation between observations and model (2001-2002) is 0.91(0.36,0.99). The observations and model results are shown in Figure 7.

Figure 7 Scaled variations over time of An. arabiensis in Sille, Ethiopia (data from TAY2006), observed (grey solid line), model 2001-2002 (solid blue line), model multi-year monthly mean (dashed blue line). Full size image

YE2003: 2001 3 month larva variability in Zwai (Eth30)

If it is assumed larva per dip has units LPD = C larva m 2 , where C is a constant, and that the samples are representative for a larger area, the relative number of larva in that area can be estimated as L P D · W a , where W a is the mean water area in m2. This way it is assumed the number of puddles is constant from July to September, and that the puddles only change their surface area. These values are roughly comparable to the modelled number of larva. Since only the latitude (and not the longitude) is reported in the paper, and Zwai is not located at latitude 9°N, model data between longitudes 38.69 to 39.23°E and latitudes 7.88 to 8.42°N, an area covering Zwai, were selected. Using this method correlation is 0.99(0.321.00). Confidence interval is estimated using 1,000 random samples of the points within the bounding box, and the 2.5% and 97.5% quantiles of the correlations is reported. Since the sample size is small and the data might not be directly comparable, the correlation should be interpreted with care. The data from the observations and the model can be seen in Figure 8.

Figure 8 Scaled variations over time of An. arabiensis larva in Zwai, Ethiopia (YE2003). Observed (grey solid line), and model (solid blue line). Full size image

BAL2001: 1999-2000 mosquito catch Awash, Ethiopia (Eth30)

This study was carried out in 1999-2000 in Metehara at longitudes 39.50 to 40.00°E and latitudes 8.75 to 8.92°N. The data are based indoor space spray collections. Since the malaria model was not run for 1999, and 2000 is considered as a spin-up year, the multi-year monthly mean for the years 2001-2006, and 2008-2009 was used (since the climate model was done as two separate runs, one starting January 2000, and one starting January 2007). The observations are compared to the scaled sum of mosquitoes of all age groups, which should be comparable to what was reported in the thesis. Correlations in Buse + Gelcha (two locations described in the thesis) was 0.75(0.1,0.95), 0.79(0.27,0.95) for Sugar Estate, and 0.76 for Metehara Town. Confidence intervals are not reported for Metehara Town since the number of observations are low. The data can be seen in Figure 9.

Figure 9 Scaled variations over time of adult An. arabiensis in Awash, Ethiopia (BAL2001). Observed (grey solid line), and model (solid blue line). Full size image

FEK2012: 2009-2010 mosquito catch Chano Mille, Ethiopia (Eth18)

As seen in Figure 10, and correlations in Table 3, the model corresponds well with the observations in Chano, 2009-2010. While the weather station in Arba Minch recorded some heavy rainfall events in October/November 2009 the regional climate model did not capture these events, or did not dump the precipitation in the right location [45]. In general the driving model (WRF) was too wet in spring 2009, and too dry in autumn 2009. This might be the reason for the slight mismatch in mosquito numbers in these seasons. To have confidence in malaria/mosquito models at these fine scales, there is a need for a better representation of precipitation in the climate models. The differences between the trapping methods also highlight the uncertainty of related to data collection, especially when the number of mosquitoes is low. From December 2009 to March 2010 the observed number of An. arabiensis was very low (Figure 10). It is interesting that despite of this, malaria started to rise in these months [30].

Figure 10 Modeled and observed variations in An. arabiensis . The left panel shows catches broken down to catch method (grey dotted lines), and modelled An. arabiensis. The right panel shows modelled mosquitoes and total twice monthly catches (data from FEK2012). Full size image

Table 3 Correlations for model and mosquitoes captured in Chano Mille Full size table

Summary of temporal variability analysis

Each of the five case studies consist of short time series, with different observational methodologies. It was attempted to show how the model results can be compared to the different type of observations, and in general the model is in good agreement with the observations. Since none of the studies cover several years, it was only possible to validate whether the model captured the seasonal cycle in mosquito numbers. The good agreement with all of the five case studies, means the model probably responds correctly to the environment, and thus it is likely OMaWa can reproduce year-to-year variability as well.