Figure 1 presents a synthetic view of the phenomena which are involved in the spread of WNV, as adapted for the Quebec context 8. Indeed, there are mainly two populations involved in the transmission of the WNV: the population of mosquitoes (Culex sp.) and the population of birds. In this paper, we mainly consider the Corvidae family and more specifically crows which have been chosen by public health authorities as indicator birds for the WNV. Mosquitoes spawn eggs in sumps and other shelters. The larvae hatch from eggs and evolve into nymphs that emerge to become adult mosquitoes. This cycle mainly depends on temperature and humidity 9. Besides, human intervention can reduce the population of mosquitoes through larvicide treatments (e.g. Methoprene) in order to kill larvae. The transmission of the WNV occurs mainly mosquitoes biting birds. An infected mosquito can infect a bird, which can in turn infect healthy mosquitoes that will subsequently bite the infected bird before its death 10.

Regarding the populations of Corvidae, their spatial and temporal characteristics depend on geographic areas and on the periodicity of displacements and grouping. During early spring bird couples spread over the whole territory and remain for few months around their nesting areas. By the end of July, which happens to be the very beginning of human infections in Quebec 3, Corvidae change their social behaviour and regroup in roosts at night. During the day, the birds fly to surrounding areas in search of food, but they go back to the roosts at night 11. At the end of fall, many of them migrate to warmer areas south of the province 12. Furthermore, the transmission of WNV to the populations of Corvidae can occur either by mechanical infection (an infection after a direct contact between birds) or through the biting of a healthy Corvidae by an infected mosquito (Figure 1).

Since we wanted to simulate the progression of the WNV infection involving a large number of individuals of two main species interacting in a particular geographic region, we selected a geosimulation approach which allows for the study of the spatial and temporal characteristics of the populations' interactions in a virtual geographical environment 6. However, given the enormous complexity involved in representing such phenomena and the lack of detailed data, we had to raise a number of reasonable simplifying hypotheses with regard to the species of mosquitoes and Corvidae of interest, to the factors influencing the evolution of these populations, the geographical region selected for the analysis, the period of simulation and the space-time scale. These hypotheses led us to identify a set of key parameters to carry out the simulations, based on the epidemiologic and surveillance experience with WNV in North America and more precisely in the province of Quebec 4. For example, considering the availability of surveillance data, we selected the American crow as the main indicator bird species; and the Culex pipiens and Culex restuans as the main mosquito's species susceptible to bite crows (and possibly humans). Another example is the period of simulation for the WNV propagation: July 1st to October 1st was selected as the critical time window during which human cases have appeared in Quebec so far (Table 1).

The objective of the conceptual model is to introduce a synthetic view of the phenomena of interest while taking into account the above mentioned simplifying hypotheses (Figure 2). Let us briefly comment upon this model which represents the evolution and interactions of Culex sp. (pipiens/restuans) and crows. Moreover, we simplified the biological cycle of Culex to only consider the change from a larval state to an adult one. From a public health management's point of view, these two states are the most important ones since the virus is spread by adult females and treatments against the progression of the WNV are carried out using larvicides. This simplification has been validated by domain experts (see below). In addition, considering the spatial dynamics of crow populations, we selected the period of the year when Corvidae regroup in roosts. In our model, a roost is considered as the spatial extension of an aggregate of crows (a sub-population of crows which gathers in this roost for the period of the year of interest). During the day, crows fly a variable distance from the roost in search of food, and return at night. Hence, the spatial phenomenon of gathering and dispersion of this sub-population of crows can be represented in a synthetic way in the form of an expansion and a contraction of the area occupied by this sub-population. The surface over which the birds spread during the day ("roost expansion") depends on the roost size. Consequently, we can take into account the variable density of crows in this dynamically changing area. Another fact to consider is that the Culex mosquito has a mostly nocturnal activity 13. Therefore, the crows located in roosts at night will be good targets for them. Moreover, preset variables have been used in order to compute parameters such as the infection probabilities and the mortality proportions. This conceptual model has been validated by domain experts (from the GDG Company, Université de Sherbrooke and Université du Québec à Trois Rivières – UQTR) and was used to orient the development of the geosimulation tool.

According to our conceptual model, the progression of the WNV infection involves a large number of individuals of two main species and their interactions depend on the probabilities of finding sub-populations of these species within the same geographic areas at specific times. We already mentioned the interest of using a multi-agent geosimulation approach in such a context. However, we had to adapt it to take into account the large geographic area of interest and the very large size of the involved populations, especially for Culex.

To create the virtual geographic environment representing the studied region (Figure 3), we first collected geo-referenced data and generated the various spatial data layers needed by the MAGS platform. Then, we modelled the two populations involved in the transmission of the virus as well as their locations in this virtual environment. Indeed, the population of Culex represents an extremely large number of individuals and cannot be represented using individual agents. Instead, we decided to model the mosquito population as an 'intelligent density map' which is characterized by population data being attached to reference areas (municipalities) in the virtual space. The idea is to associate to each reference area a list of variables corresponding to the numbers of the different categories of mosquitoes (larvae, healthy and infected adults) located in this place. These numbers evolve during the simulation as a consequence of various parameter changes (temperature, degree of humidity resulting from rainfall, etc.) as well as encounters with crows. For the population of crows, we used agents to model groups of crows associated with specific areas where roosts have been observed in the field. The interactions of the two populations have also been modeled thanks to the geosimulation which enables the system to automatically determine the places and times where groups of crows (pertaining to roosts) will cross areas in which the Culex sub-populations are located.

The qualitative results of the model which represent the distribution of the populations were satisfactory. Indeed, the resulting curves reflect the biological behaviours of the studied species according to the opinion of the consulted domain experts (from GDG and UQTR). However, the quantitative data needed to be calibrated in order to be used in real-life situations. In fact, we calibrated the model by comparing simulation results and field observations (ISPHM-WNV data 4). We evaluated the ratio between the real populations of mosquitoes and the samples of mosquitoes captured in traps (absolute densities) as well between crows and the collected dead crows.

Regarding the populations of Culex, we used Reisen's work 2122 to estimate the mosquito density ratio. A captured mosquito was considered to represent a population of 300 Culex over one km². Since we did not have data for all regions, we only calibrated simulation results for some key municipalities where human infections had occurred. It appeared thereafter that there was a significant difference between the data generated by the model and those obtained from the field. Hence, we tuned up the initial settings of the simulation (e.g. the initial percentage of infected Culex or infected crows, distance between sumps, emerged Culex per sump, percentage of sumps containing larvae, etc) as well as some parameters of the mathematical model (e.g. mosquitoes biting rate of crows per capita, WNV transmission probabilities from Culex to crows of from crows to Culex, etc). These changes have helped us to quantitatively calibrate the model for the processed municipalities.

Figure 8a presents the evolution of the total number of mosquitoes for the municipality of Laval between July 1^st and October 1^st. The smooth blue curve represents the data generated by the simulation while the rugged red curve represents averages of real data over four years (2003 to 2006). We had to consider these averages because we do not have sufficient data from the field (trap measurements are sparse and not carried out regularly in Quebec municipalities). Moreover, these data averages enabled us to adjust our initial data in the simulation (mainly the initial number of mosquitoes) as it can be observed in Figure 8a. The simulation curve and the real data curve fit nicely between July 1^st and August 15^th. The two big drops that are observed in the real data curve are difficult to explain at this point since we consider the average measures over four years. This may be the result of systematic larvicide applications in July and August (3 applications in some municipalities during a WNV season), but we have no sufficient data to confirm this conjecture. In figure 8b, we also observe a similarity between the curves representing the infected mosquitoes. Again, the rugged red curve represents averages of real data over 2003–2006. All drops in the curve result from lack of sufficient field data.

Regarding the populations of crows, we used the results presented by David and colleagues 23 in order to determine whether the numbers of dead birds sighted and tested for WNV are representative of the true bird mortality. We also used the index trend obtained from the ÉPOQ database 24 and from the North American Breeding Bird Survey 25 to adjust the population of crows as well as the population of generic birds. Moreover, changes in the population of crows have been calibrated using field data collection of dead birds and their analyses in the laboratory, as it was done for the population of Culex.

Figure 9 represents a comparison of the simulated data (smooth blue curve) and real data (red rugged curve) for the collected dead crows. The general shapes of the curves are similar. This is encouraging since data available for dead birds are even sparser than for mosquitoes.

Then, we looked at real data for Laval Municipality for 2003, the year for which we have the most complete data set. We created the temperature scenario for 2003 and launched the simulation. Figure 10a presents the difference between the simulated data (blue smooth curve) and the real data. In order to explain this difference, we checked with the SOPFIM Company if larvicides had been sprayed in Laval Municipality in 2003. It was indeed the case, with interventions on June 18, July 17, and August 13. We created a new scenario using these three dates for larvicide spraying and we got the curve displayed in Figure 10b. The curve of simulated data now approximates the real data fairly well (the rugged curve of real data being again explained by missing data). This is an encouraging result showing that the parameters adjusted for calibration provide reasonable results.

In order to improve precision and validate our models and the simulation parameters, we will carry out the simulation on a different data set. We are currently collecting data (for mosquitoes and crows) for the city of Ottawa. We expect to get a more complete data set, since measurements have been more frequent and regular in the Ottawa region (Canada) over the past 6 years. This work is in progress.

Based on the requirement specifications and using the conceptual model of the phenomena (see Figure 2 in section 2.2), we designed a conceptual architecture of the WNV-MAGS system which includes all the needed system components and their relationships 32. While constructing this architecture, we identified all the processes to be developed (represented as rectangles numbered as Pi in Figure 11) and all the data stores (represented as ovals numbered as Ai in Figure 11) that gather data and feed the system processes. Indeed, most of the necessary data are obtained from external databases (EPOQ 24, Weather data, etc.) and GIS. They are represented as 'cylinders' at the bottom of Figure 11.

The architecture is divided into four parts. The first part (processes P1 to P4) deals with data preparation, including the extraction of data from all the required databases. The second part (processes P5 and P6) computes the evolution of populations using the mathematical model presented in Section 4.2. The third part (processes P7 and P8) deals with the interactions between the sub-populations of crows and the sub-populations of Culex. It reflects the interactions between the agents' roosts and the intelligent density map. The last part (processes P9 to P12) is responsible for the management of scenarios, as well as for the display, analyses and calibration of the results. We used different databases (as presented in Section 4.3) in order to initialize the populations of Culex and crows at time t₀ (beginning of the simulation). We used these populations to compute the dynamics of crows, the dynamics of Culex and the interactions between the two populations while increasing the time by one step, at time t. Then, we get the new populations at time t+1 (taking into account the state changes of the sub-populations of mosquitoes and crows reflecting the infection spread and deaths) and the system triggers again the same processes to simulate the joint evolution of the two populations. The simulation results can then be displayed on the map. Domain specialists can also calibrate the simulation using the WNV surveillance data (that we have pre-processed). The user can manipulate the results and create various scenarios. Then, the simulation results can be assessed and compared.

We need to compute the evolution of the populations of Culex and the populations of crows in order to simulate their interactions using the geosimulation system. To this end, we selected the model proposed by Wonham and colleagues 16 to compute the dynamics of the two populations. This model is based on 8 differential equations (Figure 12a) which can compute over time the evolution of the different categories of individuals (called 'compartments'): susceptible,infected, recovered and dead birds, the larvae of mosquitoes and the susceptible, exposed and infected adult mosquitoes. We proposed some modifications in order to correct some discrepancies that we found in the model. We also included climate effects in the model using the work of Madder and colleagues 33 as a starting point. This was a difficult task because the model was no longer in equilibrium and this required several modifications to the differential equations 18. Figure 12b presents an overview of the new equations of the proposed model. We notice that the birds equations (dS_BJ/dt, dI_BJ/dt, dR_BJ/dt, dX_BJ/dt) have an index j which represents a different bird species that we want to include in the simulation. Climate effects are computed using another set of equations that is not presented in this paper. These equations modify certain parameters in the differential equations of Figure 12b. For example v_xL in the dL_M/dt equation represents the rate of progress of larvae toward the state of nymphae, this rate depends on temperature conditions defined in a different set of equations. The adjusted model gives satisfactory results in terms of quality (e.g. distribution of the mosquitoes' generations). Indeed, the pace of the established curves reflects the biological behaviours of the studied species if we refer to the specialized literature. However, the quantitative results (e.g. the number of larvae, eggs, emerged Culex, dead crows, etc.) had not been conclusive with the first results of the simulation. We corrected this problem with the calibration of the system as presented in Section 2.4.

We already mentioned that our approach takes advantage of GIS data in order to properly locate the agents' roost in space. Indeed, we used the Geomedia GIS software in order to handle the geo-referenced data of the DMTI Spatial (CanMap Streetfiles) and the digital maps of INSPQ. Using this data, we created the bitmap from which the MAGS platform generates the simulation environment. This bitmap contains polygons representing a list of 945 municipalities (out of a total of 1476 for the whole province of Quebec) being part of the ecumene (inhabited part of the studied region) of the geographical area of interest. Moreover, this bitmap is also used by the intelligent density map presented earlier (see Figure 3 in section 2.3).

In addition, we had to pre-process all the data needed to feed the system (see processes P1 to P4 of the conceptual architecture in Figure 11, section 4.1). We estimated the initial populations of Culex and crows at the beginning of the simulation. For the population of crows, we used the SAS statistical software and the MapInfo GIS to compute a specific density of birds per region (number of individuals by square kilometer). This done by estimating an average of the sighting mentions provided by professional or amateur ornithologists (from 1997 to 2005 and located inside the ecumene) using the ÉPOQ database 24 (Table 2). We also processed the data relative to crows' roosts (obtained through an email survey involving expert birders or extracted from the ÉPOQ database 24). This data included the co-ordinates (latitude/longitude) as well as an approximate number of individuals for each mentioned roost. We computed an average of the number of individuals in the case of several records of the same roost (same latitude and same longitude). This data is used to characterise the roost agents (Table 3). Moreover, we studied the literature and discussed with domain experts in order to collect relevant information about crows' behaviours. We used this information in order to specify some behavioural rules for the roost agent such as the way that particles spread around the roost to simulate the birds' daily search for food.

Considering the Culex population, we computed the number of individuals of the initial population, estimating the number of adults that emerge from the larvae laid down in sumps (which we supposed to be the main reservoirs of mosquitoes in urban and sub-urban areas). To this end, we developed a Visual Basic application in order to query the geo-referenced databases in Geomedia and to compute the total length of roads for each municipality of interest. We then computed the number of sumps in each municipality by using the total length of roads (Table 4). We assumed that there is an average of one sump for each 30 linear meters of road. This average distance conforms to the standards used by the Ministère des transports du Québec (MTQ) when they install sumps. However, the user of the WNV-MAGS system can modify this value, since it can vary in relation to the considered regions such as urban and rural areas. We also assumed that there are only 20% of sumps containing larvae. This default value can also be modified by the user as well as the average number of Culex adults which emerge from a sump at the beginning of a simulation. These numbers were obtained by consulting data provided by the SOPFIM Company 34 in relation to the monitoring of larval and adult Culex in certain Quebec regions during the summer of 2005.

Furthermore, we used a DLL which enables us to integrate the climate data into the system. This DLL represents one of the functionalities of the BIOSIM software 35. We used it to interpolate values for temperature and precipitations at certain precise locations on the territory, taking into account the data of the four neighbouring weather stations and the elevation data. This computation can be done using either real data or the Canadian Climate Normals 20 which are produced over several years.

After the data preparation, we implemented the system using the MAGS platform which is developed in C++. This simulator includes several modules performing various tasks. It contains a controller to manage the threads of application (Processes Module), a user Interface and a module managing the simulation environment (Environment Module). In addition to these modules, MAGS contains a module in charge of data display, modules to specify agents' populations and agents' behaviours, and a module simulating particle systems. In order to simulate the propagation of the WNV, we added a module which simulates an epizooty (Epizootic Manager) which has been developed in a generic way in order to be easily extended to simulate epizooties different from WNV (Figure 13).