Overview
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].
Figure 1. Overview of phenomena of interest for the WNV-MAGS Project.
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).
Table 1. Specifications of the simulation parameters.
Conceptual model
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.
Figure 2. Conceptual model representing the dynamics of Culex and Crows.
Geosimulation of the populations
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.
Figure 3. The geographic area of interest which contains all the municipalities belonging to the ecumene (Southern Quebec, Canada).
Intelligent density map
The populations of Culex do not move much and they are present practically everywhere in the selected territory [3,14].
Because of the extremely large number of individual mosquitoes, we
represent sub-populations of mosquitoes as characteristics of the
virtual geographic environment and we use what we call an "intelligent
density map" that represents the distribution of Culex sub-populations
over the different reference areas depending on the geographic
characteristics and the locations of favourable habitats for
mosquitoes. This intelligent density map is a kind of cellular
automaton associated with rules that enable the system to simulate the
evolution of the different categories of mosquitoes (larvae, adults,
healthy, infected, etc.) in each reference area under the conditions
that influence the mosquitoes' life cycle (temperature and
precipitations). The system gets these conditions either from actual
meteorological data (from specific databases: see Section 4.3) or from
the parameters set in scenarios that the user wants to explore. This
map contains the polygons representing all the municipalities of the
Quebec province (the reference areas). On the user's screen, the color
of each municipality changes according to the relative densities of the
Culex populations (ratios of healthy, and infected adults) computed by the simulator (Figure 4).
Figure 4. Using an intelligent density map to represent the population of Culex.
Agents' roosts
A
roost synthesizes the behaviour of a group of crows. It is modeled by
an agent having some initial characteristics such as the number of
individuals, the position of the roost on the map, and the maximum
radius of its expansion area. These characteristics are computed using
various field data as presented in Section 4.3. Moreover, this agent
inherits from all the functionalities of MAGS agents. For example, it
uses some behaviour rules in order to model how crows scatter around
the roost. In addition, an operating range parameter is
computed for each roost in order to estimate the maximum distances
covered by the crows when they search for food during the day.
Each roost agent is implemented as a particle system [15]
which simulates the way crows spread around a roost during the day.
Hence, such particle systems behave as agents, as described above. Each
particle represents one or several crows, depending on the number of
individuals attached to the roost. In Figure 5
we can see a snapshot of a simulation in which roosts are displayed as
"clouds of blue particles". Each particle has different characteristics
(velocity, direction of movement) that enable it to travel at a
distance from the roost location during a number of simulation steps
representing a day. Hence, the set of particles associated with a given
roost covers a circular area with a maximal radius set by the operating range parameter.
We calibrated the parameters of the particle system by computing the
density of crows in the area covered by the expansion of the roost and
comparing it to observed field data and other estimated data.
Figure 5. Using roosts to represent the populations of crows.
Interaction between the two main populations
The
interaction between the two main populations is a very important
functionality of our system, since it is the way of representing the
evolution of the infection. Indeed, while traveling in the geographic
space, one or several crows represented by a particle can cross areas
in which Culex mosquitoes are located. Consequently, there is
a probability that some of these crows will be bitten. Technically, in
order to determine the probabilities of encounters between mosquitoes
and crows, the corresponding particle takes into account the
characteristics of the Culex population associated with each
reference area of the 'intelligent density map' over which it travels.
Therefore, the system can estimate the number of infected individuals,
based on the likelihood that a number of individual crows be bitten by
mosquitoes and be infected with WNV (using the equations of the
mathematical model described in Section 4.2). Moreover, the user can
visualize the extent of the spread of WNV on the map in different ways.
The system can either change the color of the particles representing
the infected crows or the color of the polygon representing a
municipality containing a high density of infected Culex.
The influence of other bird species
Our initial simulations involved the two main species of American crows and Culex pipiens/restuans that we selected and that enabled us to apply Wonham's mathematical model [16] (see Figure 12a
in section 4.2). We quickly found out some limits with this model,
since it does not take into account the influence of temperature on the
evolution of mosquito's populations. When we applied this model, it
led, after a number of iterations, to the complete "extinction of
crows". This, obviously, does not conform to reality, although a
dramatic decrease of Corvidae populations have been observed in recent years due to the spread of WNV [17].
Hence, we proposed an extension of this model which enables us to
model several species of birds and to take into account the impact of
the temperature in terms of cumulated degree-days which influence some
parameters of the model (see Figure 12b in section 4.2). We cannot discuss here the details of such a model and its implementation (for more details, see [18]).
In the current experiments, we modeled the interactions between crows
and mosquitoes as described in the previous section. Since surveillance
systems provide data about crows as indicator birds, we used this
species to set the simulation parameters and to calibrate the system.
However, we added other bird species in the simulation to increase "the
biting opportunities" for mosquitoes, so that the "crow population"
does not become extinct by the end of the simulation period. Indeed,
this is a plausible hypothesis: mosquitoes bite other birds as well as
crows.
We thus introduced in the WNV-MAGS system another 'global'
population of birds, that we called "generic birds" (Common Raven, Blue
Jay, American Robin, House Sparrow, European starling and Mourning
Dove) which are resident in the municipalities and known to carry WNV [17].
This population of generic birds appears in the mathematical model with
similar equations as those used for the crows (each bird population is
represented by a different index j in the equations: see Figure 12b
in section 4.2). However, the parameters for each bird family may be
different. Due to lack of data, we currently set some average
parameters to the equations of the "generic birds". Getting more
accurate parameters will require further research from bird
specialists. In the simulation, one distinction that we established
between crows and "generic birds" is that we assumed that birds do not
move outside the municipality (as crows may do while flying away from
the roosts). Hence, generic birds stay in contact with the same
mosquito population during the simulation. Indeed, this is a
simplification. Since our system is parameterised, we will be able to
introduce parameters for other bird species as soon more precise data
will be available with respect to the ecology and epidemiology of other
birds affected by WNV.
Using various short-term climate scenarios
In our system,
multi-agent geosimulation is at the heart of a decision support tool.
Hence, our approach is somewhat different from more traditional
simulations used for prediction purposes [19].
The WNV-MAGS System simulates the WNV epidemics and enables a user to
specify scenarios in order to explore various situations including
climate change and different intervention strategies. The user may
choose one among four different scenarios which influence the dynamics
of the Culex population (Figure 6).
The first scenario is the default scenario which can be set in order to
use average conditions of temperature and precipitations (using in this
case the Canadian Climate Normals [20]).
In order to estimate the number of mosquitoes located in each
municipality, we computed the number of sumps that are along the
municipality's roads (see section 4.3). Sumps offer ideal locations for
the maturation of larvae and the emergence of adult mosquitoes. They
are also the main targets of larvicide spraying. But abundant rains may
flush sumps, killing a large proportion of larvae. In a second type of
scenario, the user can choose a date during which abundant rains may
flush sumps in some municipalities (Figure 7).
In the same way, the third scenario is used to simulate the use of
larvicides in a certain area (municipality). The last scenario is a
combination of the second and third scenarios. Hence, it is possible to
choose a date for the flushing of sumps and another date for the
application of larvicides. Most larvae are supposed to die after the
flushing of a sump, although the dynamics of the larval populations
starts all over again since there are always Culex adults in
the vicinity of the sump that will spawn new eggs. Moreover, the
WNV-MAGS System offers a variety of functionalities to the user in
order to modify the parameters of the mathematical model, to visualize
the progress of the infection in and around the crows' roosts, to
extract data from the simulation and to generate graphs showing the
evolution of the involved populations.
Figure 6. Using management scenarios.
Figure 7. The dynamics of the larval populations before (a) and after (b) the flushing of sumps in Laval Municipality on August 15th (hypothetical scenario defined by user).
Calibration of the system
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 [21,22] 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 1st and October 1st.
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 1st and August 15th.
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.
Figure 8. Model
calibration using the average total mosquitoes captured in traps (a)
and those among them which are infected with the WNV (b) during the
considered simulation period (1 July – 1 October) for Laval
Municipality (2003 to 2006).
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.
Figure 9. Model
calibration using the average collected dead birds during the
considered period of the simulation (1 July – 1 October) for Laval
Municipality (2003 to 2006).
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.
Figure 10. Model
calibration using the total mosquitoes captured in traps during the
simulation period (1 July – 1 October) for Laval Municipality in 2003:
(a) without larvicide application, (b) with three larvicide
applications (18 June, 17 July, and 13 August).
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.
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