Keith Buenaventura
Arlene De Leon
Abel Marck Manaysay
“The SIMS”
Given that here in the Philippines dengue outbreaks caused by mosquitoes is a
persistent problem, the group “The SIMS”, considered simulating the population of
mosquitoes given a time period. This simulation was started, in the belief that this
simulation model would provide a general idea of the distribution of mosquito
population in a span of a year on a daily basis. This paper would explain the simulation
model and simulating software used.
The project began with a brainstorming of different factors that affect mosquito
population both positive and negative. This was an important step for this brought the
following variables that would run inside the simulation process. The input variables
defined in the brainstorming were the volume of pollution, availability of aquatic
breeding grounds and the life span of a mosquito. According to the discussion in the
brainstorming these input variables would enable a development of a more flexible
system that could encompass several different areas, because these variables changes for
different areas. The external variable considered in the discussion was the role of
climate, this would be randomized, since in the play of nature such things as climates
are out of the control or cannot be given a hundred percent prediction. For the function
of the user, the group had anti-mosquito advertising campaign, defogging and spraying
activities and natural mosquito repelling agents as the policy variables. This means that
the user could manipulate the following in the simulation so as to provide the user some
idea on the resulting impact of each component on the pollution of the mosquitoes.
Then inside the system the current mosquito population would be used in the next time
step, which makes the system a closed system, with the mosquito population as the
feedback variable. Lastly, the end goal of the system is to produce the mosquito
population for each time step.
After finalizing the variables that will be running inside the simulation system the
group created a Causal Loop Diagram which would provide an illustration of the effect
of each variable to other variables inside the system. The group decided on whether a
variable will have a possible or negative effect to another variable based on experience
and logical reasoning. Figure 1 is the actual Causal Loop Diagram which explains the
system.
Figure 1: Causal Loop Diagram
From this Causal Loop Diagram, an initial test was used using random numbers
to represent the weight of each variable on the other variables. This step was the
creation of a pulse process which is used by the group to have a more detailed validation
and grasp of how the value of the variables would run inside the system for each time
step. Figure 2 is the actual pulse process used by the group and Table 1 provides the
corresponding variable for each vector in the pulse process.
Figure 2: Pulse Process Model
Vector
A
B
C
D
E
Variable Representation
Mosquito Population
Volume of Pollution
Anti-mosquito ad campaign
Defogging and spraying activities
Availability of aquatic breeding
grounds
F
Mosquito life span
G
Amount of rainfall
H
Mosquito-repelling plants
Table 1: Pulse Process Vertex representation
Finally, after validating the pulse process the group proceeded in making the simulation
model using the software poweSim. Again the model used in powerSim resembles the
variable dependencies in the Causal Loop Diagram. Figure 3 is the actual model used by
the group for the powerSim simulation.
Figure 3: PowerSim model
The following formulas were used for the derivation of each variable.
Amount_of_Rainfall = Poisson (2,0)
Available_Aquatic_Breeding_Grounds =
IF(Amount_of_Rainfall>5,INT(ABS(ABS(2*Amount_of_Rainfall)
ABS(0.5*Anti_Mosquito_Campaign))),INT(ABS(0.5*ABS(2*Amount_of_Rainfall)ABS(0.5*Anti_Mosquito_Campaign))))
Pollution_Rate =
((SINWAVE(DELAYPPL(Available_Aquatic_Breeding_Grounds,3,0),4)))
Anti_Mosquito_Campaign = IF(Pollution_Rate>1,0.01*RAMP(Pollution_Rate,0),0)
Mosquito_Repelling_Plants =
IF(Anti_Mosquito_Campaign>2,PULSE(5,0,10),PULSE(1,0,30))
Life_Span = 20
Defogging_Activities = PULSE(0.6,0,20)
Birth_Rate = (((SINWAVE(1, 0.25*Life_Span))(SINWAVE(Defogging_Activities+Mosquito_Repelling_Plants,0.25*Life_Span))))
Death_Rate = (((SINWAVE(1,
0.5*Life_Span))+(SINWAVE(Defogging_Activities+Mosquito_Repelling_Plants,0.5*Li
fe_Span))))
Mosquito_Population : Initial value = 10000
Flow:
+dt*(Pollution_Rate)
+dt*(Birth_Rate)
-dt*(Death_Rate)
The time step used is in days. So, for a year, there are 365 time steps. Within a year,
there could be no trend in the graph of the mosquito population. But, when it is
generated for two or more years, the mosquito population’s graph is seen to be
increasing and decreasing according to the seasonality of rainfall. The increase and
decrease is not so significant since the value is still close enough to the initial population
value. Thus, the goal of maintaining the mosquito population is achieved.
Meanwhile, the graphs of other variables for the model are also shown by PowerSim
program. The mosquito’s death rate and birth rate fluctuate according to the sine
function and is between -1 to 1. The Anti-Mosquito campaign variable is generated by
ramp and pulse function where there are only campaigns when there is a significant
value for pollution rate, a variable that must be visible in the community (i.e. garbage,
stagnant water, etc.)
In the long run, for example, when the simulation is generated for 10,000 time steps,
the pollution rate variable tends to be zero. This, in fact, can be achieved when for the
next 10,000 days the community really does implement the policy variables (i.e. antimosquito campaign and defogging activities).
In conclusion the group graphed the estimated population of mosquitoes
for each time step as shown in Figure 4.
Figure 5: PowerSim output
Table 2: Powersim Variable values for each timestep