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2017
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Agent-based simulation study of the intra-urban discontinuity effects in Delhi on dispersal of Aedes aegypti mosquitoes, vector of dengue, chikungunya and Zika viruses

Étude par simulation à base d’agents des effets des discontinuités intra-urbaines à Delhi sur la dispersion des moustiques Aedes aegypti, vecteurs de la dengue, de la fièvre jaune, du chikungunya et du virus Zika
Somsakun Maneerat and Eric Daudé
Translated by Alvin Harberts
This article is a translation of:
Étude par simulation à base d’agents des effets des discontinuités intra-urbaines à Delhi sur la dispersion des moustiques Aedes aegypti, vecteurs de la dengue, de la fièvre jaune, du chikungunya et du virus Zika

Abstracts

In order to fight against the transmission of dengue, yellow fever, chikungunya and Zika viruses, significant resources were allocated to the process of restricting the propagation of their main vector, the Aedes aegypti mosquito. Research on this mosquito’s living areas is thus necessary to characterize more precisely the areas that need to be monitored and treated. An alternative to field surveys consists of evaluating the characteristics of these living areas through spatialized models. It is in this context that we developed the simulation model MOMA (Model Of Mosquito Aedes aegypti), an agent-based model which integrates a vast set of biological and behavioral knowledge about the mosquito in a simulation environment based on the needs and constraints specific to Aedes aegypti. In this paper, we present MOMA and a study of the effects of local configurations on the dispersion capacity of mosquito cohorts. The simulations in this study were carried out using data from an urban neighborhood in the city of Delhi (India). This virtual laboratory, constructed in collaboration with entomologists, thus makes it possible to represent the mosquito’s living areas, which are either restricted or facilitated by spatial amenities conditioning its needs and its capacity of movement during its lifetime.

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This research was conducted as part of the European project DENFREE: Dengue Research Framework for Resisting Epidemics in Europe (grant agreement: 282,378), European Commission's Seventh Framework Research Program. The authors thank Anna-Bella Failloux, Louis Lambrechts and Rick Paul (Institut Pasteur, Paris) for their expertise on the entomological aspects of the model. The authors are also grateful to the other partners of the project, Taillandier Patrick, Vaguet Alain, Cebeillac Alexandre, Lefebvre Bertrand, Eliot Emmanuel and Vaguet Yvette (University of Rouen). The authors finally thank the reviewers for all their suggestions.

Introduction

1Vector-borne diseases account for more than 17% of the world's infectious diseases and cause more than one million deaths each year (WHO, 20161). Aedes aegypti mosquitoes are one of the recognized vectors of these diseases, caused in particular by the transmission of the zika virus, chikungunya, yellow fever or dengue fever. The latter alone affects almost 400 million people annually (Bhatt et al., 2013). The identification of the factors related to the progression of these diseases from a global point of view has limited effects in operational terms because the risk of epidemic explosion results from a complex articulation of local environmental and social factors (Daudé et al., 2015). Until vaccines are available to fight these different viruses, the means of control of these diseases transmitted by Aedes aegypti are therefore based on surveillance and protective measures against this vector (Gubler, 2011; WHO, 2012). Removal of mosquitoes’ breeding sites (reduction at source) or by fumigation and spreading insecticides are the most commonly used measures. These operations, however, require coordination of actions between public health operators, local administrations and citizens, which is a challenge in many countries where intersectoral coordination and risk culture are weak (Daudé and Vaguet, 2015). They also require significant human and financial resources, which is another challenge for developing countries (Gubler, 2011).

2In its overall strategy for dengue control and prevention, the WHO (2012) reiterated the need to increase the capacity to monitor and respond to dengue epidemics on urban and intra-urban scales. Spatial and dynamic models to identify areas at risk on finer levels are part of this arsenal of resources (Guzman et al., 2010).

3It was in this context that we developed MOMA (Model of Mosquito Aedes aegypti), an agent-based model whose objective is to simulate the life of the female mosquito (Maneerat, 2016). MOMA is part of a project to model the dengue’s complex pathogen system (Daudé et al., 2015, Daudé, 2017), in which four subsystems - the vector, the host, the virus and the environment – are made to interact with each other in order to explore the conditions for the emergence and spread of dengue epidemics in urban areas. MOMA represents the vector subsystem where the elementary entity is a mosquito, modeled on the scale of an individual of the species. This mosquito “lives” in an artificial environment characterized by resources, constraints and physical objects that a mosquito can perceive. The simulations presented in this article are both a validation support for the model and an illustration of the possibility that this type of model can offer to help guide vector control campaigns. The dispersion, measured by the maximum distance traveled from the place of emergence by the mosquitoes of the same cohort, is one of the first indicators to have been chosen. The latter can provide information on the local spread potential of the virus by a contaminated mosquito and on the other hand a reference to delimit the spreading radius of insecticides around dengue cases. Moreover, the literature provides numerous entomological studies for this indicator, which constitutes an important material for the validation of the model for the modeler.

Micro-mosquito or Macro-mosquito?

4Many models replicate animal population dynamics in a given geographic or ecological context without taking into account the details of the biological and behavioral systems of the individuals composing them (Hill and Coquillard, 1997). Differential equation modeling of the relationships between temperature, precipitation and stock dynamics of vector populations is based on the hypothesis of the existence of general laws - no water, no mosquitoes for example - considered to be insensitive, on a given scale, to the statistical noise and diversity that exist on smaller scales. However, as is often the case, the models are not very resistant to changes in scales, and the weight of factors considered to be secondary on a given scale may appear more important, in addition to local heterogeneities when looking at micro-scale dynamics. This is the case, for example, with factors such as the relative density of vector breeding sites, mosquito displacement capacity, urban microclimates or the presence of green space in the production and local distribution of mosquitoes. When the causalities are numerous and interdependent, often nonlinear, that the actors are heterogeneous, that this diversity influences the dynamics and the data available at the population level is parsimonious, then an alternative to the aggregated models may be interesting. It is then necessary to construct models descriptive of the attributes and behaviors of the individual entities of the reference system in order to produce, via the simulation, observable data at different scales. This approach is only possible if there is a robust knowledge based on both the biological and behavioral characteristics of the modeled entities. MOMA follows this perspective: modeling the elementary behaviors and the life cycle of the female Aedes aegypti mosquito according to its determinants (states and energy) and biological needs (search for foods, breeding sites and resting places) in a heterogeneous and dynamic environment, in order to observe the geography of its places of life, in an urban environment.

  • 2 Notably Louis Lambrechts, Anna-Bella Failloux and Richard Paul (Institut Pasteur, Paris).

5The idea of mosquito-scale modeling to simulate population dynamics is not new. CIMSiM (Focks et al., 1993a, 1993b) is a model that estimates the mosquito production capacity of a vector site under different temperature and precipitation conditions. Based on a daily survival table, this model produces the mean values of many entomological parameters (age, abundance, fertility, etc.) as well as the size of each stock in the different states of the immature mosquito (nymph and larva). This microsimulation approach will be repeated in Skeeter Buster (Magori et al., 2009) to model the intra-container development processes according to the same criteria. More recently, the SimPopMosq model (Almeida et al., 2010) adds the spatial dimension to the CIMSiM model. The model is based on the coupling of an agent-based model composed of four classes (mosquito, human, dog and cat) with environmental data (vector, bedroom and garden). SimPopMosq is used to study the dispersal of mosquitoes inside a house and in its immediate vicinity (garden), as well as the relative effectiveness of mosquito trap placement strategies. If the design of MOMA is inspired by these different works, we extend the spatial influence of the modeling to the level of several urban districts and introduce environmental dynamics in the simulation. The biological parameters of Ae. Aegypti used in MOMA come from Christophers, (1960); Focks et al., (1993); Magori et al., (2009) and collaboration with entomologist partners of the project2. The simulation environment was constructed from field surveys carried out in 2013 in several districts of Delhi, India during the pre- and post-monsoon periods. The data collected was integrated into an open source Geographic Information System (QGIS 2.6.1) and coupled with socio-economic data. The MOMA model was developed with the GAMA 1.6.1 platform and the simulation data analyzed with R (x64 3.2.0). MOMA and the databases used for the simulations presented in this article can be downloaded (DOI: 10.5281 / zenodo.48252).

6The following section is a summary of the main features of MOMA, the complete description of the model and the parameters used for its calibration is given in (Maneerat and Daudé, 2016). Scenarios on the role of environmental contexts in mosquito displacement and dispersal capacity are then explored.

Main features of MOMA

Classes of agents, states and behaviors

  • 3 We call Aedes an agent representing the Aedes aegypti mosquito.
  • 4 Survival is not strictly speaking an activity, it is a biological function that determines the prob (...)

7MOMA models the adult female Aedes aegypti responsible for the transmission of viruses during her blood meals. The activities of Aedes3 are: feeding, breeding, resting, moving and surviving4. These activities are linked to needs that can be satisfied depending on the presence of blood (C1) and nectar (C2) resources for feed, breeding sites (C3) for breeding, shaded areas (C4) for rest and circulation zone (C5) for flight. Survival depends on temperature and humidity conditions (C6). Aedes has a capacity of perception of his environment limited to about ten meters (Christophers, 1960, Iams, 2014, Kennedy, 1940). It acts according to its biological state, defined by its internal variables, and according to the resources present in its immediate environment. Figure 1 presents the general design of the transitions between Aedes states as well as the activities and resources associated with them.

Figure 1 - General concept of the Aedes life cycle.

Figure 1 - General concept of the Aedes life cycle.

The states and transition conditions between states (on solid arrows) are represented in the circle shaded with V (virgin), O (oviposition), Gn (gonotrophic) and D (death). Deaths are represented by the dotted arrows and their causes are listed in the red box. The main actions associated with each state of the Aedes agent are shown in the blue boxes, in bold. Next are the resources whose weight on the behavior of Aedes varies according to its state, low (-) to priority (++). The exact values are derived from mathematical functions presented in (Maneerat and Daudé, 2016).

8The genericity of MOMA is an important objective of the research program, the principle of which is based on the assumption of portability of the mosquito's behavior from one geographical context to another. Aedes thus has a set of skills that it can use according to its needs and its environment, which is heterogeneous. When Aedes traveled a certain distance, his environment changed, with new resources available for example. We will later study the effects of these local changes on mosquito dispersal. But the variation of the environment and the transferability of skills must also be taken as an opportunity to apply this model of simulation in other cities, where Aedes aegypti are or could be present.

  • 5 In MOMA, the host is not modeled as an individual entity but as a stock variable, see Supplementary (...)
  • 6 The shaded portion of a spatial object represents the percentage of the total surface that is not e (...)

9A new agent class has therefore been created, allowing to build the simulation environments. This class, called SpatObj, describes spatial objects such as buildings, streets, parks and open spaces (eg vacant land or parking). These spatial objects have a topology constructed from a GIS and attributes that correspond to the needs and factors that influence the mosquito. In this sense, spatial objects constructed in MOMA respect the spatial and temporal dimensions of the functional habitat of the species (Hartemink et al., 2014), here Aedes aegypti. This environment is made up of both constraints and opportunities for the mosquito, and these may evolve over time: stocks of blood available at different times of the day5, egg-laying spots or shade6 for resting for example. The first four resources (from C1 to C4) of a SpatObj act as targets that can be perceived by an Aedes. Blood resources (C1) vary each hour depending on the function of the place: for example, a commercial building will be busier during the day, while a residential building will be busier in the evening. The number of water deposits (C3) varies every day according to the weather conditions and according to the land use class. The presence of nectar (C2), just like the presence of shade (C4), depends on the land use class and the surface of the object. The presence of walls influences the mobility of mosquitoes, limiting the passage from one house to another. A porosity coefficient for each spatial object (C5) has therefore been introduced to simulate this effect on the Aedes displacement, it acts on the probability of success of passing between objects. The porosity of a spatial object varies between 0 (impossibility of crossing the object) and 1 (possibility of crossing the object). The probability of passing from one object to another is obtained by the product of the porosities of each object, then it is confronted with a random value resulting from the uniform law between 0 and 1. The porosity values used in this article were estimated on the field using a comparative approach, by prioritizing the types of objects according to their permeability to the passage of mosquitoes. Indeed, if individual houses, large buildings or large bodies of water constitute an obstacle to the movement of Ae. Aegypti, open spaces or parks may facilitate the dispersal of this population (Hemme et al., 2010, Mahabir et al., 2012). Each object of each land use class has a defined porosity value in the following ranges: building [0.3 to 0.5], green and open space [0.9 to 1] and roads [0.6 to 0.9]. These interval ranges make it possible to introduce a certain heterogeneity between the objects of the same category, replacing information that is not represented in the attribute tables such as the number of windows or doors of a building. The differences between the ranges of values of the different classes of objects make it possible to respect the differences between the categories of objects since it is generally observed that a garden is more easily crossable by a mosquito than a very large avenue. The porosity value is thus defined in the interval by the drawing of a random value according to a uniform law and recorded at initialization as parameter of each instance of SpatObj.

10A third agent is finally modeled, called World, it represents the overall environment of the simulation. This unique agent contains the meteorological data over the simulation period and manages the scheduling of the other two classes and their respective agents. The simulation time is related to the physical time of the real world. The World agent is also responsible for managing the instantiation, destruction and observation of the other two classes of agents in the system.

Local and global arrangement

11The spatial unit is the meter (m) and a time step (iteration) is set to one minute. The time of a simulation is divided into 3 scales according to the processes: day, hour and minute (Figure 2).

Figure 2- Sequence diagram of the global arrangement of the model.

Figure 2- Sequence diagram of the global arrangement of the model.

The upper part is relative to the instantiation of the agents of the model, first the environment then the Aedes. Next are the daily and hourly conditions and activity loops per minute.

12Each day SpatObj agents access the information stored by the World agent to update the local air and water temperature and possibly increase the water volume of the breeding sites. The air temperature of a SpatObj controls the mortality rate of the Aedes agents in this object. The temperature of the water conditions the development speed of mosquitoes in the aquatic stages (eggs, larvae and nymphs). The presence of water deposits is a resource for an Aedes who is looking for a nesting site.

13Each hour, the SpatObj agents update the brightness. This variable affects the period of activity of the Aedes who are located there. The quantity of available blood resources is also updated by time slot, which is derived from spatial distribution laws of hosts according to spatial object types (see supplementary document S3 in Maneerat and Daudé, 2016).

14Every minute, active Aedes agents can observe their environment, select a target that meets their needs and move. If no target is selected, as none can meet one of the expressed needs, the mosquito moves at random. If a target is selected, Aedes moves (+/- 30 °) and moves at a speed between 0.5 and 1 m / s towards its target (inspired by Cummins et al., 2012 and Iams, 2014). Aedes agents, during a single iteration, cannot move beyond the spatial objects of the neighborhood closest to the spatial object on which it is located. In the displacement mechanism, the porosity coefficient plays a key role because it will limit, for example, the passage between a road-type spatial object and a house (barrier effect), whereas it will facilitate the passage of a road to an open space (corridor effect).

Calibration and validation of MOMA

15More than 50 parameters and variables are used in the model to characterize mosquito agents and the environment. This level of detail of MOMA makes its calibration and validation particularly complex. Indeed, the possible combinations of parameters make it virtually impossible to systematically explore their domains of variation. The validation was therefore carried out according to two criteria:

  • Validation by expert opinion: it consisted of recording the biography of each Aedes, from place and time of birth to place and time of death. For each iteration, internal states, actions and locations were recorded in order to produce an individual log of daily activities. This journal was submitted to entomologists who checked the consistency of the sequence of activities over time and their duration (see an example of a journal in Supplementary document S8 (Maneerat and Daudé, 2016)). Comparison between simulations, expert opinions / literature and calibrations have gradually improved the realism of MOMA;

  • Validation from survey data: the age pyramid of mosquito populations and the dispersal of mosquitoes around a nesting site are two important criteria in the study of dengue dissemination factors. We therefore recorded these two information in order to compare them with data from field surveys and available in the literature. It is this criterion of dispersion that we present here.

Effects of local geographic configurations on mosquito dispersal

16The displacement of an infected mosquito, which takes two to three blood meals every two or three days, promotes dispersal of the virus and thus local epidemics. The risk of this displacement is variable depending on wether the mosquito moves a few meters throughout its life or several hundred meters. There are some studies that attempt to define this maximum dispersal distance of mosquito cohorts, but they are both small and very contextual. Computer simulation offers the advantage of overcoming the difficulties of this type of survey, and makes it possible to carry out numerous virtual surveys, and on various “grounds”. The scenarios that we are exploring here are therefore aimed at exploring the effects of the local heterogeneity of physical objects and their attributes on the dispersion of Aedes cohorts. The dispersion in a scenario corresponds to the average of the maximum distances reached by all the mosquitos born from the same deposit, out of 50 simulations. Another indicator, known as the distance limit, is calculated by taking into account at each simulation the mosquito that has traveled the longest distance from its birth place. The average distance limit corresponds to the mean of the distance distances traveled by the 50 “best performing” mosquitoes on 50 simulations.

A virtual space documented from a real terrain

17An area south of Delhi (India) was selected, comprising four contiguous districts with significant heterogeneities in terms of spatial organization and socio-economic context. This area covers the districts of Malviya Nagar, Hauz Rani, Khirki and Saket (Map 1), which is referred to as MHKS. This 1.8 km² study area was digitized from Google Map, Google Earth and Bing Map aerial images and saved in Shapfile (.shp) format. This Shapefile represents the simulation zone, each polygon is associated with a class of land use of a spatial object: building, open space, park and street. The attributes of each of the classes were taken from a field survey carried out in June 2013 in Hauz Rani. The attributes of the spatial objects of the other three districts take the mean values of the attributes of the spatial objects of this neighborhood. This choice has the consequence of homogenizing the attributes between the districts but it allows to focus the analysis on the effects of the variation of the forms and the spatial arrangements of the objects: with equivalent resource levels by classes of land use, Does the configuration of the places and the size of the objects influence the dispersal of the Aedes mosquitoes?

Map 1- The different land use classes in Malviya Nagar, Hauz Rani, Khirki and Saket (Delhi, India)

Map 1- The different land use classes in Malviya Nagar, Hauz Rani, Khirki and Saket (Delhi, India)

18The meteorological data used for these simulations was recorded between the 1st and 30rd of June 2008 in Delhi7). The month of June corresponds to the pre-monsoon period. Precipitation begins towards the end of the month. In June 2008, weather conditions were favorable to the survival of mosquitoes, which is why we selected this period to limit the number of deaths by desiccation (temperature affects the daily survival rate of the mosquito). The temperature fluctuated between 28 and 37 °C with an average of 30 °C, humidity varied from 30% to 80% during cloudy days. The average daily rainfall was about 4 mm with a few days of heavy rain, especially during the second fortnight.

Simulation Scenarios

19The strategy used to carry out these simulations is the following: we select 7 spatial objects, called the 7 scenarios, characterized by different land uses and having spatial objects of differentiated densities and organizations in their neighborhood (Table 1). We calculate for each of them the cumulative layout and the profile of the types of land use. The layout of building walls gives an indication of the number of obstacles to be crossed in the scenario, while the layout of open spaces, such as parks, indicates the presence of corridors that facilitate travel within a scenario. Note that these details are not known to mosquitoes, they are used as variables to describe the area to seek correlations with the distances traveled by the cohorts of mosquitos. However, an Aedes agent knows its position and the porosity value of the spatial object on which it is located and the target one.

  • 8 “Random Seed” is a number chosen for the initialization of variables by a pseudo-random number gene (...)

20For each scenario, a cohort of 100 Aedes is instantiated, ie 700 Aedes for each simulation. As a simulation takes place over a period of a month, we do not make emerge any new Aedes. The main reason for this choice is that this study focuses on the mosquito's ability to move during its life in different environmental contexts and not on the “conquest” of a territory by a cohort of mosquitoes and their offspring. The simulations are enacted fifty times for these seven scenarios. The same random seed8 is used for all simulations, this ensures the “biological” identity of the Aedes generated at each simulation and the identity of the attributes of the spatial objects for the seven scenarios.

Table 1- Description of the local landscapes of the 7 scenarios

Scenario Description

Representation of the landscape around (50m) the hatching area (yellow point)

Description of the hatching area of a cohort of Aedes.

S1

Hatching point located in an area with a high-density of buildings and close to a large green space.

S2

Hatching point located in an open space (parking), surrounded by a vast green space and a few buildings.

S3

Hatching point located in a building inserted in a developed area and characterized by a low density of buildings, and a few small open spaces and green areas. Presence of roads.

S4

Hatching point located in a building between a developed area characterized by a low density of buildings and a zone with a high density of buildings. Presence of small green spaces, open space and roads.

S5

Hatching point located in a building that is part of an area with a very high density of buildings, with the presence of many alleys.

S6

Hatching point in a building of a developed area with an average density of buildings and the presence of roads and alleys.

S7

Hatching point in a big mall framed with roads.

21Each scenario is characterized by different proportions of land use classes (Figure 3), which allows for significant inter-scenario differentiation. For example, green spaces are very present in scenario S2 (70% of total area) compared to scenario S7 (less than 2%), while roads are under-represented in scenario S1 (35%) in comparison to scenario S6 (73%).

Figure 3 - Ratio of occupied area by land use class and length of observed barriers (in km) within a radius of 50 meters for each of the seven scenarios.

Figure 3 - Ratio of occupied area by land use class and length of observed barriers (in km) within a radius of 50 meters for each of the seven scenarios.

22For each simulation and for each scenario, when the Aedes dies, the maximum distance traveled from the origin and its age are recorded. There will later be a distinction between the maximum distance traveled by a mosquito from a cohort and the average distance traveled by all mosquitoes in the same cohort. In the first case the averages are calculated on 50 mosquitos, in the second on 5000, for 50 simulations per scenario.

Results and discussion

23The maximum distances traveled in each of the seven scenarios (Map 2) show that the Aedes are relatively sedentary with respect to their ability to travel, with a distance of no more than 100 meters around the places of emergence. The smallest maximum distance reached is 67 meters in Scenario S5 and the largest is 105 meters in Scenario S2. These two scenarios have very different spatial characteristics (Figure 3), respectively very densely built for one (with many barriers of the wall type) and mostly characterized by green spaces (thus open) for the other.

24The mean dispersion in the seven scenarios is by construction lower, it is equal to 22.36 m with a standard deviation of 5.11 m. This simulated data is consistent with the few field studies carried out in different geographical contexts, which show that Aedes aegypti do not move far from their emergence site, only between 16 and 25 m in Muir and Kay, (1998) and 30.5 m in Ordóñez-Gonzalez et al., (2001).

Map 2 - Simulated maximum dispersion for Aedes born in 7 different “urban landscapes”

Map 2 - Simulated maximum dispersion for Aedes born in 7 different “urban landscapes”

25On average in the different scenarios, between 50 and 80% of the Aedes did not go beyond the 30m area around the site of emergence, and less than 10% went beyond 60 m. This small dispersal distance is probably due to (1) the availability and abundance of resources necessary for the survival of Aedes in a highly-urbanized environment, and (2) the barrier effects induced by urban development. Indeed, the needs and mobility of the mosquito depend on the characteristics of its local environment, with which it interacts. If the mosquito has all the resources necessary for its survival and development, it will have little incentive to move. On the other hand, in the case of a local shortage of any of these resources, space can facilitate its movement, as is the case in scenario 2, or constrain the search for new resources. In this case, the configuration of the space measured by the layout of walls or by the number of obstacles that it must overcome to move play an important role in this potential dispersion.

26A chi-2 test on the average dispersion of mosquitoes in the 100-meter radius around the location of emergence and in the 7 scenarios allows us to reject the hypothesis of the uniformity of the dispersion behavior of these cohorts (α = 5%). Each cohort therefore has a dispersal behavior that is specific and depends on the local context in which they were released. This is the expression of a very high concentration of mosquitoes in a 30 m radius of the place of birth and a significant differentiation between the scenarios in this area (Figure 4). The distribution of populations of Aedes in the 0-15m range strongly separates the scenarios S2 and S3, respectively congregating 16.76% and 48.3% of their population. This can be explained by the existence of a much more open environment in S2 than in S3, with respective cumulative barriers lengths of 0.17 km and 2.38 km. Therefore, Aedes born in scenario S2 fly further than those born in S3, up to a distance greater than 100 m. One can also observe this phenomenon with the S5 scenario where the presence of numerous barriers and lack of green space are associated with a very low dispersion of Aedes.

Figure 4 - Maximum flight distance of a population of 100 Aedes according to different environmental contexts.

Figure 4 - Maximum flight distance of a population of 100 Aedes according to different environmental contexts.

27The coefficient of determination (R²) between the maximum dispersion of Aedes and cumulative barriers in their living spaces is therefore relatively high (R² = 0.68, P <0.05) in the direction of a negative relationship. This is the “obstacle jumping” effect which can either provoke a constriction of the route, or lead the mosquito away from his birthplace. The dispersion of the mosquito also strongly tends (R² = 0.75, P <0.01) to increase with a decrease in the number of available breeding sites in homes and buildings. It is the “shortage” effect of intra-home breeding sites which leads Aedes born inside buildings to come out to search the suburban residential areas for potential hatching sites. Once outside (houses, buildings) an increase in the dispersion is observed with the increase of the available lodgings (R² = 0.74, P <0.01). This is the “abundance” effect, it allows mosquitoes located in an open environment such as a park to have a greater supply of empty sites and therefore promotes its dispersion in space. This phenomenon is modeled with the idea that Aedes will prefer when the situation arises, to lay eggs in several nearby sites, focusing on empty sites (Christophers, 1960). MOMA actually reproduced the main reason for moving in Ae. Aegypti quite accurately, it seems associated with the research of breeding sites and blood resources, which are most of the time ubiquitous in urban areas (Harrington et al., 2005). The barrier effect should thus be put into perspective with the level of available resources on this scale. This means that if blood and breeding sites are available in abundance, there will be a settlement of mosquito populations.

  • 9 y = -2.9991x + 91 408 with (y) mosquitoes dispersion capacity in adjacent areas based on kilometers (...)
  • 10 Classification method through natural breaks (Jenks).

28These results can be used as part of mosquito eradication strategies. In Delhi (India), while recording dengue cases with the monitoring system, a team is responsible for spreading insecticide in the home and in its vicinity in order to minimize the risk of contamination (Daudé and Mazumdar, 2016). But the estimation of the boundaries of the area to control is not easy and takes place mostly at the discretion of the team on the field. The treated areas may differ between ten and several hundred meters around the home of the index case. With all things equal (hatching sites, blood, shade), the equation of the line of regression9 can estimate the potential dispersion of the Aedes. We applied this equation by 50 m cells in the MHKS area when the stress barriers vary. Map 3 shows on a smaller scale the likelihood that mosquitoes from a cohort would leave their hatching sites to go out to colonize neighboring spaces10. Used in the context of insecticide fumigation, it provides an estimate of the “risk of local spread of the virus”: the reddest areas show the maximum risk because infected mosquitoes in these areas could fly away and contaminate remoted hosts. These red areas, located primarily in the Saket neighborhood, correspond to the presence of a large park near the commercial areas. They are opposed to more closed off areas like the Khirki neighborhood (in yellow) and the Khirki extension (in beige) where the buildings are nested within each other with shops and winding roads littered with solid waste.

Map 3 - Estimated propensity for the dispersal of mosquitoes from their place of emergence and by the heterogeneity at the micro scale (50x50 m) of urban landscapes.

Map 3 - Estimated propensity for the dispersal of mosquitoes from their place of emergence and by the heterogeneity at the micro scale (50x50 m) of urban landscapes.

29These simulations thus provide an indicator to determine the surfaces to be treated in case of the presence of dengue cases. The initial intuition that the “closed” areas would present a low probability of dispersal of mosquitoes is thus confirmed, and simulations provide an objective mapping. Pragmatically this reinforces the strategy to use an aerial image of the site via a mobile app, Google Maps, for example, to quickly assess the extent of the treatment area around an index case built according to density, the presence of corridors, parks and open spaces.

30The second advantage of this set of simulations is to provide a vectors dispersion equation based on an urban characteristic measured here by the layout of objects of the same class, identifiable and calculable via satellite image processing tools for example. This equation can then be used in a vector model not just on the scale of a single mosquito but on the scale of a whole cohort of mosquitoes to simulate the dispersion, first step towards the simplification of the MOMA behavioral model.

Conclusion

31MOMA is a virtual laboratory wherein the life cycle of the mosquito Aedes aegypti is modeled. Built and set from knowledge acquired in the field and in laboratory experiments, the goal was to model Aedes aegypti at a detailed level of its movement, predation and breeding behaviors that produce realistic macroscopic data. MOMA is simulated in an environment created according to the needs and constraints that can influence the behavior of the mosquito. An audit work on outputs of simulations performed with entomologists has verified that the circadian activity of the mosquito was consistent with domain knowledge. This first stage of “internal” validation then lead us to instantiate several hundred mosquitoes to study an important criterion for intervention against the transmission of vector-borne diseases, the spread of mosquito cohorts, for which we had several empirical studies. The results converge with those studies and are another step in the validation of the model.

32The demonstration of local geographical contexts favorable or not the dispersion of mosquitoes is useful information for mosquito eradication campaigns. In areas of dense housing, mosquitoes flying capabilities can be greatly reduced due to the presence of many building walls or closed windows. By contrast, in lower density environments, the existence of parks and public spaces can allow mosquitoes to travel longer distances. These first results, inferred on the scale of a city by the methods of remote sensing for example, would identify the characteristics of urban areas that potentially favor the presence of mosquito hotspots.

33These results also guide further research on the effects of the abundance of resources that mosquitoes need on their dispersion. Indeed, beyond the effects of the physical environment on mosquito behavior, the availability of resources for its survival is also decisive. Thus, the heterogeneity of the presence of hosts for blood meals, the heterogeneity of potential breeding places for laying eggs and the heterogeneity of dark, damp spaces serving as resting places are probably factors that coexist to explain the heterogeneity of spatial and temporal vector densities. The search for threshold effects in the availability of these resources, beyond which the mosquitoes would have to travel further to satisfy their needs or die because of too much competition on the resource, will be the subject of future simulations.

34The choice of a model on the mosquito scale, quite lightly parsimonious in terms of implemented behavior and in number of settings, was not without a certain number of roadblocks which had to be overcome, from the design process to the communication of results. The main difficulties in the use of behavioral models with a significant level of detail is that change in a parameter, behavior or space descriptor can have a domino effect on remote components from an algorithmic as well as thematic standpoint. We must therefore check, through the recording of witness variables, that any change of a condition does not get these witness elements out of their range of acceptable variation, as defined by specialists. These witness variables can be an age pyramid of mosquito populations, densities per square meter, or biographies such as we discussed them. Once these conditions have been met, the simulations allow us to explore scenarios that would be impossible to observe in situ. Finally, the choices made here in the modeling of structures and environmental dynamics and host population dynamics, very sparse compared to the model of the mosquito, most likely have an impact on the simulation results. These two essential components of the dynamics of dengue are therefore being improved, particularly with the use of remote sensing to systematically describe the environment and the exploitation of data from social networks to calibrate the daily mobility of urban hosts.

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Notes

1 http://www.who.int/mediacentre/factsheets/fs387/en/

2 Notably Louis Lambrechts, Anna-Bella Failloux and Richard Paul (Institut Pasteur, Paris).

3 We call Aedes an agent representing the Aedes aegypti mosquito.

4 Survival is not strictly speaking an activity, it is a biological function that determines the probability of surviving in given temperature and humidity conditions.

5 In MOMA, the host is not modeled as an individual entity but as a stock variable, see Supplementary Document S3 in (Maneerat and Daudé, 2016).

6 The shaded portion of a spatial object represents the percentage of the total surface that is not exposed to solar radiation. It was estimated from field observations and satellite images. This variable essentially represents the shade caused by buildings or by the relative position of spatial objects.

7 http://www.imd.gov.in

8 “Random Seed” is a number chosen for the initialization of variables by a pseudo-random number generator in a computer language.

9 y = -2.9991x + 91 408 with (y) mosquitoes dispersion capacity in adjacent areas based on kilometers of barriers encountered in space (x).

10 Classification method through natural breaks (Jenks).

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List of illustrations

Title Figure 1 - General concept of the Aedes life cycle.
Caption The states and transition conditions between states (on solid arrows) are represented in the circle shaded with V (virgin), O (oviposition), Gn (gonotrophic) and D (death). Deaths are represented by the dotted arrows and their causes are listed in the red box. The main actions associated with each state of the Aedes agent are shown in the blue boxes, in bold. Next are the resources whose weight on the behavior of Aedes varies according to its state, low (-) to priority (++). The exact values are derived from mathematical functions presented in (Maneerat and Daudé, 2016).
URL http://cybergeo.revues.org/docannexe/image/28499/img-1.png
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Title Figure 2- Sequence diagram of the global arrangement of the model.
Caption The upper part is relative to the instantiation of the agents of the model, first the environment then the Aedes. Next are the daily and hourly conditions and activity loops per minute.
URL http://cybergeo.revues.org/docannexe/image/28499/img-2.png
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Title Map 1- The different land use classes in Malviya Nagar, Hauz Rani, Khirki and Saket (Delhi, India)
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Title Figure 3 - Ratio of occupied area by land use class and length of observed barriers (in km) within a radius of 50 meters for each of the seven scenarios.
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Title Map 2 - Simulated maximum dispersion for Aedes born in 7 different “urban landscapes”
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Title Figure 4 - Maximum flight distance of a population of 100 Aedes according to different environmental contexts.
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Title Map 3 - Estimated propensity for the dispersal of mosquitoes from their place of emergence and by the heterogeneity at the micro scale (50x50 m) of urban landscapes.
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References

Electronic reference

Somsakun Maneerat and Eric Daudé, « Agent-based simulation study of the intra-urban discontinuity effects in Delhi on dispersal of Aedes aegypti mosquitoes, vector of dengue, chikungunya and Zika viruses », Cybergeo : European Journal of Geography [Online], Model Papers, document 819, Online since 11 July 2017, connection on 25 November 2017. URL : http://cybergeo.revues.org/28499 ; DOI : 10.4000/cybergeo.28499

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About the authors

Somsakun Maneerat

CNRS - UMR IDEES
Université de Rouen, France
maneerat.somsakun@gmail.com

Eric Daudé

CNRS - UMR IDEES
Université de Rouen, France
eric.daude@cnrs.fr

By this author

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Copyright

© CNRS-UMR Géographie-cités 8504

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