Malaria Journal a Quantitative Risk Assessment Approach for Mosquito-borne Diseases: Malaria Re-emergence in Southern France

Background: The Camargue region is a former malaria endemic area, where potential Anopheles vectors are still abundant. Considering the importation of Plasmodium due to the high number of imported malaria cases in France, the aim of this article was to make some predictions regarding the risk of malaria re-emergence in the Camargue.


Background
In the past, malaria was endemic and constituted a major health issue in France in marshy areas, particularly the Camargue, which was an active focus until the beginning of the 20 th century. Malaria decreased drastically due to the draining of marshes, rearing of livestock, improvement of housing and living conditions and the use of quinine [1]. Malaria disappeared from the Camargue after World War II: the last Plasmodium vivax malaria epidemic occurred in 1943, with about 400 estimated cases [2]. Recent entomological surveys reported huge Anopheles populations in this area [3][4][5], and considered Anopheles (Anopheles) hyrcanus as being the main potential malarial vector based on its anthropophilic feeding behaviour and abundance [4,6]. Thus, the Camargue is currently facing an "anophelism without malaria" situation. Moreover, autochthonous transmission was recently suspected in the French Mediterranean coast in 2006 [7], supporting the idea that southern France remains suitable for malaria transmission. The number of imported malaria cases have increased dramatically since the 1970s, in parallel with increased international travels, with an average of about 6,400 cases per year for the last ten years in France, leading to a massive Plasmodium introduction from endemic countries into France [8,9]. These observations suggest that the malaria situation needs to be re-examined, and the aim of this paper is to infer current risk of malaria reemergence, to identify hot spots for malaria re-emergence in the Camargue and to develop a generic model for mosquito transmitted diseases.
The risk of malaria re-emergence in an area (i.e., the recurrence of malaria transmission in an area) may be estimated by three factors: receptivity, infectivity and vulnerability [10][11][12][13], usually assessed at the regional scale in a semi-qualitative way (Figure 1, 2) [14]. In this article, a quantitative entomological risk, which is the product of receptivity and infectivity, is calculated and the impact of vulnerability is discussed. The main objective of this work was to estimate the risk of malaria re-emergence at the local scale, considering the temporal and spatial local variations of the three components in order to identify hot spots for malaria resurgence in the Camargue.
The main difficulty that occurs when modeling is the quantification of biological parameters, especially for entomological data, as the field and laboratory studies are very painstaking, time-consuming and only rarely permit conclusions on a precise value. In this article, a probabilistic approach, taking into account the uncertainties and variability of inputs, was applied to a vector-borne disease, which constitutes an innovative method. Even if the malaria situation needs to be re-examined in the Camargue, this disease does not constitute a major health issue. The aim of this article is not to provide a public health tool that can be used to control malaria in the Risk of malaria re-emergence Figure 1 Risk of malaria re-emergence.
Camargue, but to present an innovative approach to spatialized quantitative risk assessment applied to a vectorborne disease.
Receptivity and infectivity were estimated for the potential vector An. hyrcanus as i) it is now considered as the main potential malaria vector and ii) other Anopheles species are rare in the Camargue area. However, the approach developed here is applicable to other mosquito species.

Study area
The Camargue is the main wetland area in Southern France and covers the Rhone river delta. This area has a Mediterranean climate characterized by warm, dry summers and mild, wet winters. Total annual rainfall usually ranges between 500 and 700 mm and occurs mainly in autumn, and the annual mean temperature is 14°C.
Water pools and marshes cover a large part of the Camargue. Water is provided either by rains or a very tight canal network diverted from the river Rhone used to irrigate paddies or to fill marshes. Management of water is at the level of individual field owners depending on use: grazing for horses, cows or sheep, exploitation of reeds or rice, hunting reserves for waterfowl and nature preservation. Landscapes in the Camargue are strongly affected by the duration of submersion and the salinity of the soils.
They are organized roughly in a south-north gradient of salinity, with agricultural land and reed marshes in the north and natural salty ponds and salt marshes in the south [15].
Moreover, there are various forms of agriculture (including vineyard, paddies, market gardening, fruit growing and exploitation of reeds) and rice, which covers more than 18,000 hectares in the Camargue, is the main cultivation [16]. Livestock includes horses, cows and sheep.
The Camargue hosts nearly 100,000 permanent inhabitants distributed between towns, hamlets and isolated houses. Moreover, the number of people increases in summer due to tourism.

Quantitative risk assessment using a probabilistic approach
The objective of this method was to organize and analyse scientific information in order to infer the risk of malaria re-emergence taking into account the variability and uncertainty of the input components and the final risk estimate. Such analysis, using reiterated simulations, have been performed for a decade for risk assessment in food microbiology, for example [17,18]. Information and data for the development of the entomological risk model were obtained from field surveys, literature, unpublished data and expert opinion. Biological parameters were estimated Entomological factors Figure 2 Entomological factors. m is the vector-host ratio, i.e., the anopheline density in relation to man. a is the vector biting rate and is calculated as follows: a = h/u. It refers to the average number of people bitten by one mosquito in one day. ma is the human biting rate, i.e., the number of bites per human per day.
h is the proportion of blood meals taken from people (as opposed to other animals that are not infected with human malaria). It is also named anthropophily.
u is the length in days of the trophogonic cycle, considering the approximation that An. hyrcanus takes only one blood meal per cycle. The trophogonic cycle is the period delimited by two consecutive blood meals, and comprised of the time necessary for blood digestion, to find a pool to lay eggs in, and to find a host for the next blood meal.
p is the daily survival rate, i.e., the probability of a mosquito surviving through one whole day.
n is the length in days of the sporogonic development, i.e. the time necessary for parasites to fulfil a complete development from ingested gametocytes during the blood meal to sporozoites in the salivary glands (the stage at which the parasite is transmissible to humans).
b is the susceptibility of mosquitoes to Plasmodium species, i.e. their intrinsic ability to replicate and transmit Plasmodium. It expresses the proportion of female mosquitoes developing parasites after an infective blood meal.
by probability distributions in a plausible way that is coherent and conceivable and they were fitted with Pert or beta distribution [18,19] (Figure 3). An amount of 10,000 reiterated simulations generated by the Latin Hypercube method associated with the probability distributions was used to describe both variability and uncertainty within the input parameters and the model [20,21]. The outcome is a statistical distribution of risk, as well as a mean value of the risk estimate. Sensitivity analysis was performed to point out factors responsible for the main impact on the risk estimate. The @risk ® (Palisade Corporation) software version 4,5,3 was used.

Meteorological data
Daily temperatures (2005) and mean monthly temperatures (from 2002 to 2006) recorded by MeteoFrance at Aigues-Mortes (western Camargue) and at Tour du Vallat (south-eastern Camargue) were used. Daily temperatures were smoothed with a moving average (running mean) of three days to filter daily variations. For both types of data (daily and monthly), we calculated the average temperature for the Camargue based on the two stations. Humidity was recorded in 2005 at Marais du Vigueirat. These meteorological data were used to estimate some of the biological parameters of An. hyrcanus.

Entomological data: receptivity
In order to assess receptivity, it was necessary to evaluate the human biting rate (ma), the vector biting rate (a), the survival rate (p) and the sporogonic cycle (n) and their spatial and temporal variations ( Figure 2).

Space and time-dependency
Although we sampled a huge amount of An. hyrcanus (125,848 specimens captured, 504 females dissected), it has not been possible to estimate precisely potential spatial variations of some biological parameters. Thus and due to the small size of the Camargue, the biology of An. hyrcanus was considered to be homogeneous in the whole area, which means that the vector biting rate (a), survival rate (p) and sporogonic cycle (n) ( Figure 2) did not vary spatially. On the contrary, as An. hyrcanus presence and density depend on the biotopes and the season [4,5], the vector-host ratio m (and hence the human biting rate (ma)) ( Figure 2) presents a strong spatial heterogeneity (Table 1). Spatial variations were assessed based on a Geo-  Beta distribution describes the true probability of an event occurring, given x trials and s successes. It is expressed as follows: probability (event) = Beta (Į 1 ,Į 2 ), where Į 1 = s + 1 and Į 2 = x -s + 1. We used this when the process of biological data collection or biological experiment could be assimilated as a number of s successes among x trials, which was the case for the parity rate estimate (s parous females among x dissected females) and susceptibility estimate (s positive mosquitoes among x tested).
Pert distribution is generated from the Beta distribution, and requires three parameters: the minimum value (v), the most likely value (w) and the maximum value (z). Pert (v, w, z) means that v is the minimum value of the distribution, z the maximum, and w the most likely. It is used to model expert knowledge in the absence of an extended dataset allowing one to determine the distribution of biological parameters. In this case, experts are asked to provide v, w and z.
graphic Information System (GIS) computing data for each 30 meter-wide pixel in the Camargue [22].
All parameters were considered time-dependent, except the Anopheles anthropophily (h) and, as a practical approximation, the survival rate (p) ( Table 1). Time-variations, which are detailed below, were described at a monthly time step.

Human biting rate (ma)
The presence and density of An. hyrcanus were inferredusing remote sensing, entomological adults and larvae collections [22]. Analysis of larval data led to the definition of a larval index that was calculated for each pixel in the Camargue based on environmental key factors. An adult abundance index was generated from the larval index and was also calculated for each pixel in the study area. Comparison of the adult abundance index and the maximum number of An. hyrcanus captured in the same pixel with CDC-light traps+CO 2 showed a highly significant linear regression, allowing us to infer, using key environmental factors, the maximum number of An. hyrcanus captured during the year with CDC-light traps+CO 2 for each pixel in the Camargue [22].
The mean annual dynamics of An. hyrcanus in the Camargue was inferred from the results of several capture campaigns conducted during several years, in several places, using several capture methods (   was associated with the estimation of ma in order to obtain ma for the entire night ( Table 3).
The result is the spatio-temporal distribution of ma in the Camargue, i.e., an estimation of the human biting rate for each 30 m × 30 m pixel and each month. The human biting rate was figured for the month of August in order to illustrate this paragraph ( Figure 4). Variability and uncertainty were taken into account for each step leading to the assessment of variability and uncertainty of ma for each pixel.
Anopheles hyrcanus anthropophily (h) (Figure 2) was estimated from the comparison between human landing, light traps and horse bait trap results for An. hyrcanus and other Anopheles species [4], and was fitted as follows: Pert distribution (0.4; 0.5; 0.8)( Figure 5). It was assumed that h did not vary throughout the year.
The length of the trophogonic cycle (u) (Figure 2) was calculated using the following formula, which estimates the length of time of blood digestion: u = f 1 /(T-g 1 ) where f 1 and g 1 are factors depending on humidity and T is the temperature. f 1 and g 1 were experimentally determined and evaluated at 36.5°C-days and 9.9°C, respectively, when the humidity reached 70-80% (from June to September 2005, mean monthly humidity varied from 63 to 90% in the Camargue) [23]. Moreover, Detinova assumed that it was reliable to add 24 hours to take into account the time necessary to find a host and the time Adult abundance index relative to the pixel where the capture was conducted is indicated. Human landing results are relative to the hour following sunset which represent the An. hyrcanus aggressiveness peak [4] and approximately 80% of the total number of An. hyrcanus captured during the entire night. Each line corresponds to a human landing catch session carried out by one volunteer belonging to the research team (two people were present at Hu6 and Hu7).
necessary to find a pool to lay eggs in, in order to fulfil a complete gonotrophic cycle [23]. Considering expert knowledge and bibliographical data [24], a two day range of values was fixed for each month in the Camargue, and the length of the trophogonic cycle was fitted as indicated in Table 5.
In order to illustrate this, the distribution of the length of the trophogonic cycle was determined for August ( Figure  6).
The daily survival rate (p) (Figure 2) was estimated from parity rates (P) using the following formula: p = P 1/u [25] which is relevant in the case of stable populations. Considering that the An. hyrcanus population increases and decreases progressively according to the Anopheles biology, the approximation that populations were stable during the summer was used [5]. Parity rates observed in June, July and September 2005 in Carbonnière and Marais du Vigueirat were used (due to the low number of dissected mosquitoes, the parity rate calculated in June in Carbonnière was not included) [4]. They were fitted as indicated in Table 6, and the mean value was calculated from the five probability distributions in order to obtain the mean An. hyrcanus parity rate in the Camargue from June to September 2005.
During the same period (June to September 2005), the daily temperature varied from 18.5°C to 26.4°C, with a mean value of 23.2°C. The length of the trophogonic cycle, calculated using the same method as before, ranged from 3.2 days to 5.2 days, with a mean value of 3.7, and was fitted as follows: Pert distribution (3; 3.5; 5.5). Using the formula p = P 1/u , a mean p value of 0.79 was obtained ( Figure 7). Due to difficulty in obtaining a precise value for parity rates for the entire year, it was considered that p did not vary from March to October in this model.
The length of the sporogonic period (n) (Figure 2) was calculated as follows: n = f 2 /(T-g 2 ), where T is temperature and f 2 and g 2 are Plasmodium speciesdependent factors [26]. f 2 and g 2 were experimentally evaluated at 111°C-days and 16°C, 105°C-days and 14.5°C for Plasmodium falciparum and P. vivax, respectively. However, Grassi and MacDonald estimated threshold temperatures under which the sporogonic development is not completed: 18-19°C for P. falciparum, 15-17°C for P. vivax [24,27].

Entomological data: infectivity
Anopheles hyrcanus susceptibility was estimated based on data derived from experimental membrane-feeding experiments conducted with cultured P. falciparum in the laboratories of Radboud University Nijmegen Medical Centre (The Netherlands) following a routine protocol [28,29].
Among 350 An. hyrcanus tested, none were found able to transmit tropical P. falciparum strains. Hence, An. hyrcanus susceptibility to P. falciparum was fitted with a beta distribution: Beta (1; 351) ( Figure 8).
Anopheles hyrcanus susceptibility to P. vivax has not yet been tested, but this species has been considered a vector Distribution of An. hyrcanus anthropophily of P. vivax in Afghanistan for more than 30 years [30,31]. Genetic comparison based on ITS2 sequences between French, Afghan, Turkish and Iranian specimens concluded that they were identical. Hence, it was considered that An. hyrcanus was susceptible to tropical P. vivax strains, and estimation of its susceptibility, based on expert knowledge, was fitted as follows: Pert distribution (0.05; 0.20; 0.70) (Figure 9).
An. hyrcanus susceptibility to either P. falciparum or P. vivax was considered to be homogeneous through time and space (Table 1).
Anopheles hyrcanus susceptibility to Plasmodium ovale and Plasmodium malariae was not inferred, as very little is known about European Anopheles susceptibility to these two species.

Parasitological data: vulnerability
Vulnerability is related to gametocyte carriers as the gametocyte is the stage transmissible to mosquitoes. Nevertheless, very little is known about gametocyte carriers, and any information must be considered in the context of imported malaria cases, i.e. taking account of the fact that the illness is diagnosed and treated. Since anti malarialtreatment in France is generally conducted with drugs that do not prevent gametocyte emergence [8], an assumption that every patient may develop some gametocytes was made. Hence, we used imported malaria cases to approach the gametocyte presence in the Camargue.
Data relative to imported malaria cases were obtained from five public hospitals localized in important towns in/around the Camargue (Montpellier, Nîmes, Avignon, Arles and Marseille). These data were analysed with regard to the date, Plasmodium species, patients' residence for the 2004-2005 period and contamination place.
It was estimated that imported malaria case data obtained from public hospitals represented about 50-55% of all imported malaria cases, with other cases being diagnosed by private laboratories [32,33]. Thus, the total number of imported malaria cases was estimated using a 52.5% correcting factor assuming that epidemiological data provided by public hospitals were representative of the total number of imported malaria cases.

Vulnerability
In 2004 and 2005, 657 imported cases were diagnosed in the region (corresponding to a total of 1251 estimated imported cases), among which P. falciparum, P. vivax, P.  Distribution of the length, in days, of the trophogonic cycle in August

Entomological risk (receptivity*infectivity)
The mean value of the entomological risk was assessed for P. falciparum species from June to September, and for P. vivax for the month of August for each pixel of the Camargue map ( Figure 10, 11, 12, 13, 14) (the entomological risk was not assessed for P. ovale and P. malariae due to the low number of imported cases and the lack of information concerning both species). It was calculated with 10,000 different randomly selected sets of values extracted from input distributions.
Strong differences were observed in the entomological risk for the two Plasmodium species: P. falciparum transmission risk estimate ranges from 0 to more than 1 although P. vivax transmission risk estimate ranges from 0 to more than 100.
Distribution of An. hyrcanus susceptibility to P. falciparum Distribution of An. hyrcanus susceptibility to P. vivax Figure 9 Distribution of An. hyrcanus susceptibility to P. vivax.

Uncertainties of the risk estimate and sensitivity analysis
For each pixel the outcome of the model is a statistical distribution of the risk estimate, generated by variability and uncertainty within inputs. For example, the entomological risk estimate ranges from about 9.10 -6 to 20, with 95% of the values being between 0.016 and 4.7 for pixel having a mean value of about 1.
The sensitivity analysis was conducted for pixels of which the mean entomological risk estimate is about 1. Results of the sensitivity analysis show the correlation coefficients Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in September in the Camargue Figure 13 Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in September in the Camargue. Classes were arbitrary chosen with a logarithmic scale.
Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in July in the Camargue Figure 11 Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in July in the Camargue. Classes were arbitrary chosen with a logarithmic scale.
Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in June in the Camargue Figure 10 Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in June in the Camargue. Classes were arbitrary chosen with a logarithmic scale.
Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in August in the Camargue Figure 12 Spatial variations of P. falciparum transmission risk estimate (ranging from 0 to more than 1) in August in the Camargue. Classes were arbitrary chosen with a logarithmic scale.
between different varying inputs and the consecutive varying risk estimate ( Figure 15).
Sensitivity analysis carried out for pixels presenting a lower risk estimate showed a predominance of susceptibility. However, correlation coefficients of the survival rate and the human biting rate were approximately equal. Sensitivity analysis carried out for the P. vivax entomological risk estimate showed the equal importance of the susceptibility, the survival rate and the human biting rate.

Discussion
The entomological risk index used in this article refers to the risk of transmission (Figure 1): the risk of transmission being high when the entomological risk is high.
Results clearly indicate a maximum risk of P. falciparum transmission in August in the Camargue considering the spatial distribution and value of the entomological risk estimate, which results from length of the trophogonic cycle and sporogonic period and the human biting rate. The length of the trophogonic cycle and sporogonic development period are directly influenced by the mean temperature in our model, and the human biting rate depends directly on the An. hyrcanus dynamics and density [5]. The human biting rate being the only space-dependant factor in our model, one could be tempted to approach roughly the risk of transmission by the human biting rate. Nevertheless, the entomological risk presents also temporal variations, which depend not only on the human biting rate but also on the impact of temperature on the length of the trophogonic and sporogonic cycle. Dynamics of An. hyrcanus and mean temperature do not evolve exactly in the same way in the Camargue, which shows the necessity of estimating all the parameters of the entomological risk.
The risk of P. vivax transmission is more than one hundred times higher than the risk of P. falciparum transmission, which is due to infectivity and the length of sporogonic cycle differences.
Nevertheless, the entomological risk calculated herein is a theoretical index as the human biting rate reaches more than 10,000 bites per human per night reflecting the abundance of An. hyrcanus. This will, of course, never happen as no one can endure such a large number of bites. This suggests that, in the future, it could be necessary to combine the entomological risk with human presence and exposure to mosquito bites in order to evaluate the real human biting rate. Such analyses would require complementary geographical and sociological studies.
Although all of France faces a large number of imported cases [8], particularly in the south-east of the country, vul- nerability in at risk areas is very low because most imported cases are present in large cities.

Sensitivity analysis
The entomological risk, referring to the risk of transmission in this article (Figure 1), has to be interpreted in a relative way due to its definition and the estimation of its parameters. Thus, this study underlined space, time and Plasmodium species-dependant of the risk of potential transmission. Of course, the risk of potential transmission is connected with the risk of malaria re-emergence when gametocytes carriers are introduced within at risk areas.
Considering the entomological risk and the length in days of the infectious period of humans would allow estimation of R0 and the following absolute risk of malaria reemergence. Finally, the current risk of malaria re-emergence seems negligible due to the very low number of imported Plasmodium.
As stated in the introduction, the aim of this study was not to build a public health tool for controlling malaria in the Camargue. The emphasis was on presenting an innovative approach of spatialized quantitative risk assessment applied to a vector-borne disease, which has not been previously conducted. The main advantages of such a probabilistic approach are the possibility of integrating the uncertainty and variability of inputs within a model and to quantify the uncertainty of the final risk estimate. The deterministic approaches used thus far have not taken uncertainty and variability into account [27,[34][35][36] and have produced precise outcomes, which could lead to misinterpretation as the final risk estimate could vary significantly due to input variability. Integration of uncertainty and variability in deterministic models would rapidly lead to complicated models, requiring laborious mathematical developments [18].
Moreover, the approach applied in this study is based on distributions that are combined, resulting in quite sophisticated analyses that are intuitive and easily understood. The uncertainty within the risk estimate is a crucial point for decision makers, which usually apply some rough "safety margin" around a deterministic estimate to express their feeling of uncertainty. The pros of the approach developped in this article are rightly to quantify this uncertainty.
Such a method could be applied to other areas where malaria is still a threat or to emerging vector-borne diseases, such as the dengue or chikungunya virus infections. This method could be used in a controlled way, in order to identify areas and time periods that correspond to the highest risk of transmission, and to focus control measures where and when transmission is elevated.
It has been shown recently the impact of anthropogenic changes on potential malaria vectors in the Camargue over the last 60 years [37]. This method could be used also to predict the probable impact of future decisions concerning land use for example, and could be a useful tool for decision makers.
The sensitivity analysis underlined factors responsible for entomological risk uncertainty and variation, of which susceptibility, the survival rate and the human biting rate of An. hyrcanus have a major impact in this model. Variability in either of these parameters leads to variability and uncertainty in the risk estimate. In contrast to the susceptibility, survival rate and human biting rate, variability in the anthropophily range and the length of the trophogonic cycle range has only a minor impact on the risk estimate. The sensitivity analysis thus appears to be a tool particularly useful for the identification of key factors, which need to be assessed in field surveys.
In the context of emerging vector-borne diseases, emphasis is currently on developing and improving such quantitative risk assessment models integrating variability and uncertainty of biological parameters, which are usually difficult to assess, and especially parameters recorded in the field.
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