Modeling the C hikungunya Virus: A System Dynamics Approach
James R. Enos, Russell Schott, and Elizabeth Schott
Department of Systems Engineering
US Military Academy
West Point, NY 10996
Abstract
The Chikungunya virus (CHIKV) is a mosquito-bome viral infection of humans that,
although rarely fatal, can cause fever, severe joint pain, muscle pain, headache, nausea, fatigue,
and occasionally a rash. System dynamics modeling is a highly applicable approach that
develops a perspective and a set of conceptual tools to understand the structure and dynamics of
complex systems such as the spread of CHIKV. Using a rigorous, iterative modeling method,
both structure and dynamics are translated into a formal computer simulation that models the
complex behavior of the system. This simulation captures the system's key variables and their
interactions and allows for the design and evaluation of policies associated with combatting the
spread of CHIKV. In order to most accurately model the spread of CHIKV, a variety of
applicable real world data is initially analyzed and calibrated to determine key model parameters
and variable relationships. These parameters and relationships are then formally incorporated
into the system dynamics model and can be continually refined as new data or additional
information is leamed about the spread of CHIKV.
Key Words: Infectious Disease, System Dynamics, Chikungunya Virus
Introduction
Chikungunya (CHIKV) recently emerged in the Caribbean when the first cases were
reported from St. Martin in early December, 2013. The virus quickly spread throughout the
Eastem Caribbean islands from April to May of 2014 and reached Horida in July of 2014
(European Centre for Disease Prevention and Control, 2014). As of January 30, 2015, the Pan
American Health Organization reported 24,521 confirmed and 1,155,354 suspected CHIKV
cases in the Americas (Pan American Health Organization, 2015). The CHIKV virus causes
fever, severe joint and muscle pain, headache, nausea, fatigue, and occasionally a rash during the
acute infection period and severe joint pain may persist for well after the infection (Center for
Disease Control, 2011). The virus is rarely fatal; however, it may prove fatal in patients with
additional health concems. While there is some treatment for the individual symptoms, there is
no specific treatment for the disease.
The interactions between humans and the mosquito population drive the dynamics of the
spread of CHIKV. Nasci summarized the key variables to capture in modeling the spread of
CHIKV as the following: type of mosquito (aedes aegypti and aedes albopictus), westem
hemisphere human movement pattems, CHIKV genotypes and mutations or in other words the
virus lineage (East-Central-South African (ECSA), West African, and Asian); personal
protection measures, vector control efforts and preparedness and response plans (Nasci, 2014).
More specifically, these variables must capture the dynamics of the mosquito population, the
dynamics of the host or human population, the transmission dynamics between the human and
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mosquito populations, the vector control efforts that influence the mosquito population
dynamics, and the personal protective measures that influence the host population dynamics.
System Dynamics provides an approach to model and understand the dynamic
complexity that exists within systems, allows the ability to simulate the behavior of systems over
time, can help adjust individuals’ mental models of the system, and can lead to implementation
of policies to improve system behavior. System Dynamics attempts to understand the dynamic
complexity that is inherent in any natural or human system. Dynamics are the behavior of a
system over time, which are generally complex and non-linear in nature (Forrester, 1961). Even
the simplest of systems, with apparently low levels of structural complexity, can exhibit high
levels of dynamic complexity. This complexity comes from feedback within the system, time
delays between decisions and effects, and the leaming process of the system (Sterman, 2000).
Applications of System Dynamics have provided insights into the dynamics of several different
areas including corporate policy, the dynamics of infectious disease and diabetes, drug addiction
in a community, and the dynamics of commodity markets (Forrester, 1971). This paper relies
heavily on System Dynamics to better understand the spread of the CHIKV virus and develop
potential policies for mitigating the spread of the epidemic.
Literature Review
Much of the literature in modeling mosquito-bome pathogens references the Ross-
McDonald Theory, which was firmly established in 1970 (Reiner, et al., 2013). Reiner et. al.
reviewed 388 models and found most closely resemble the Ross-McDonald theory. The authors
identified the need to expand the theory “around the concepts of heterogeneous mosquito biting,
poorly mixed-host encounters, spatial heterogeneity, and temporal variation in the transmission
process” (Reiner, et al., 2013). The questionnaire used to evaluate the models provides an initial
guide in identifying key variables among the three common components that are essential to
these models: a host, a mosquito, and encounters between the two. Many aspects of the varying
models referenced by the author could potentially serve to inform parameters or variables within
a system dynamics model.
Several sources were essential to understanding the key variables that were required to
model the spread of an infectious disease. Smith, et Al. summarizes the Ross-McDonald Theory,
Clearly defining the model’s notation and providing an initial starting point in identifying the key
parameters and variables for a system dynamics model. Additionally, the summary discusses
several dynamic relationships that are essential to modeling the CHIKV epidemic (Smith, et al.,
2012). In his work, Nasci identifies potential state variables and some limited associated source
data and identifies the similarity of CHIKV transmission ecology to the dengue virus. Key
variables and dynamics to consider include: 1) type of mosquito (aedes aegypti and aedes
albopictus), 2) westem hemisphere human movement pattems, 3) CHIKV genotypes and
mutations or in other words the virus lineage (East-Central-South African (ECSA), West
African, and Asian), 4) personal protection measures, 5) vector control efforts and 6)
preparedness and response plans. Additionally, he describes the potential to use historical
dengue virus transmission and control efforts that exists for model calibration in the absence of
data on CHIKV (Nasci, 2014).
Another key aspect of modeling the spread of CHIKV is understanding the human travel
pattems that spread the virus. With the short lifespan and travel distance of mosquitoes, it is
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highly unlikely that they are responsible for the virus moving through the Caribbean. Khan, et
al. analyzes air travel in comparison to mosquito distribution (aedes aegypti and aedes
albopictus) in the westem hemisphere to identify potential spread of CHIKV (2014). Temporal
and spatial dynamics of travel and global warming leads to increased potential mosquito habitats
are addressed. As a potential policy consideration, the authors also address some temporal
prevention when host viremia is the greatest (Khan, et al., 2014). Cauchemez et al. attempt to
characterize CHIKV transmission in terms of population movements with the goal to inform
resource allocation for monitoring and controlling through their data analysis of CHIKV spread.
on three islands in the Caribbean. The resulting analysis suggests the growth is exponential.
Additionally, Cauchemez et al., attempt to inform spread through regional movement dynamics,
identifying “most probable” source of transmission for areas (2014).
As a comparison, in the article investigating the spread of influenza Shaman, et al.
developed a forecast of the intensity and timing of influenza to improve focus on mitigation and
response resources. Their analysis, based on a simple SIRS (susceptible-infected-recovered-
susceptible) model, highlights aspects of the SIRS model that are applicable to the CHIKV
system dynamics development and highlights potential mitigation approaches (Shaman,
Karspeck, Yang, Tamerius, & Lipsitch, 2013).
The distribution of potentially infectious mosquitoes is important to consider in mosquito
population and transmission dynamics. Foley, et al. developed a web application that provides a
spatial database of mosquito species with vector bome diseases. The database could potentially
provide spatial distribution throughout the Westem Hemisphere of the aedes aegypti and aedes
albopictus mosquito types that spread CHIKV (Foley, et al., 2010). Volk et al. also consider the
genomic differences in varying strains of CHIKV to inform different epidemic transmission
pattems. The authors suggest that due to similarities between dengue and CHIKV, CHIKV is
likely grossly underreported. Their analysis identified the three geographically associated
genotypes (West African, East-Central-South African (ECSA) and Asian) and they investigated
numerous strains derived from these genotypes (Volk, et al., 2010). Staples, et al. identified
several factors that contribute to CHIKV spread such as “high attack rates associated with
recurting epidemics, high levels of viremia associated with infection in humans, and the
worldwide distribution of vectors responsible for transmitting CHIKV” (2009). They
recommended priorities for additional studies to include evaluating vector competence and
potential transmission factors to provide insight into the effectiveness of strains; and
development of models incorporating ecologic, entomologic, and virologic factors that contribute
to the spread of CHIKV (Staples, Breiman, & Powers, 2009).
Several sources emphasize the potential policies to consider in combatting the spread of
CHIKV. Gibney, et al., described the epidemiology of confirmed CHIKV cases in the U.S. and
compared them with retuming viremic CHIKV cases, thereby identifying potential risk measures
of transmission (2011). The article highlights the importance of recognition, diagnosis, and
reporting of CHIKV. This article provides some useful data analysis based on available
infection data in the U.S. and highlights “ArboNET” as the database utilized to track CHIKV
epidemiology. (Gibney, et al., 2011). “ArboNET is a national arboviral surveillance system
managed by CDC and state health departments. In addition to human disease, ArboNET
maintains data on arboviral infections among presumptive viremic blood donors, veterinary
disease cases, mosquitoes, dead birds, and sentinel animals” (Centers for Disease Control and
Prevention, 2014). The Center for Disease Control and Prevention also provides a robust
website specific to CHIKV prevention with many useful links to additional sources (2014). The
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European Centre for Disease Prevention and Control also provides a useful summary focused on
mitigation policies. They provide a “Rapid Risk Assessment: Chikungunya Outbreak in
Camibean Region (25 June 2014).” Consistent with the other literature, their risk assessment
summarizes several key points to prevent the spread of CHIKV. Potential policies include
reducing exposure to aedes aegypti and aedes albopictus mosquitos, preventing exposure through
personal protection against mosquito bites, conducting and vector control, and seeking medical
care if presenting with CHIKV after retuming from an exposed area. Additional preparedness
efforts should also be considered, such as strengthened surveillance systems, rapid notification of
cases, review of contingency plans for mosquito-bome outbreaks, education and collaboration of
the general public in the control of mosquito breeding sites, strengthened vector surveillance
systems and rapid implementation of vector control measures around each case (European Centre
for Disease Prevention and Control, 2014).
System Structure
Epidemics of infections typically follow an S-shaped growth pattem. The cumulative
number of cases will grow initially slowly until hitting a critical mass of infections that begin to
spread exponentially. The epidemic then begins to taper as the epidemic ends and/or health
organizations take action to mitigate the epidemic. This Susceptible, Infected, Recovered (SIR)
model captures this model very well as demonstrated by the basic model of the SARS epidemic
in Taiwan (Repenning, 2013). Figure 1 presents the basic stock and flow diagram for a SIR
Model. One of the interesting aspects of the structure for the CHIKV epidemic is that there are
two populations that must interact for the virus to spread.
Infected Recovered
Infection Rate Recovery Rate
Figure 1: Basic SIR Model Structure
Interactions of several subsystems drive the dynamics and spread of CHIKV in the
Westem Hemisphere. First, the mosquito population system determines the number of
susceptible mosquitoes in an area. Second, a human population system that accounts for the
human dynamics in the area. However, neither group can spread the CHIKV on their own as
transmission of the disease only happens between a viremic human and a susceptible mosquito or
between an infected mosquito and a susceptible human. This cycle reinforces itself with more
and more mosquitoes infecting more and more humans and vice versa. CHIKV spread quickly
becomes exponential unless health officials bring to bear extemal policies to the problem. Our
system structure first looks at the mosquito population and the human population and then
incorporates the two.
Mosquito Population: The mosquito population is initialized with an initial stock of
“Mosquito Eggs’ and an “Initial Mosquito Population.” Figure 2 presents the causal loop
diagram for the mosquito population to visualize the dynamics of the mosquito population
without the virus. If left to its own accord in ideal conditions, the mosquito population would
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continue to lay eggs, eggs would continue to hatch, and the mosquito population would continue
to grow with no infected mosquitoes. Eggs and mosquitoes would die off based on their typical
lifecycle attributes. As aconsideration, climate clearly has an impact on mosquito viability, and
only two types of mosquito species are considered, as aedes aegypti and aedes albopictus are the
two species that can transmit CHIKV.
Maturation iy
OS Rate
Mosquito Mosquito Mosquito
Eggs J Death Rate
Mosquito Egg RMS
Rate
Figure 2: Mosquito Population Causal Loop Diagram
Human Population: In the human population model, a country’s population represents
the initial “Susceptible Human Population.” The “Infected Human Population’ becomes
initialized in time (minimum infected is 1) based on when the Pan American Health Organization
(PAHO) first reported a case of CHIKV in the country. This reported infection (or infections)
initializes the transmission dynamics between the mosquito and the human populations. On
average the CHIKV virus will incubate in the “Infected Human Population” for 5 days before the
human enters the stock of “Viremic Human Population.” A human is viremic on average 7-days
before entering the stock of “Recovered Human Population” where the human is now considered
immune. Transmission dynamics from human to mosquito occur only when the human is
viremic.
Human / Mosquito Infection Tr ission Dy ics: The transmission dynamics
between populations begin when a mosquito from the stock of “Susceptible Mosquito
Population” bites a viremic human. The mosquito enters the “Infected Mosquito Population”
where the virus incubates on average 7 days. The mosquito then flows into the “Infective
Mosquito Population” and is now a threat to infect humans with the virus. Now viremic
mosquitoes begin interacting with the “Susceptible Human Population” creating an increase in
the “Infected Human Population’. The cycle now can repeat itself as viremic mosquitoes infect
humans and viremic humans continue to infect mosquitoes. This reinforcing loop if left
unabated will continue to increase and grow exponentially. Figure 3 presents the overall causal
loop diagram that depicts the interaction between the human and mosquito population that results
in the transmission of the virus.
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— a
+ Infected = ———
Mosquito Mosquito ~
> Susceptible Human to. Pepubition s \
“+ — Infected Mosquito vs Infection Rate
f- Contacts F
/ ; \
\ Susceptil
\ \ ptible
Susceptible B2 \ (= ] 83 Mosquito
' Pe Ni
Human Population | "1 lation
Y +
\ Pag es )
Contacts
He Ps ~~ /
tnitection Fe Infected Human Susceptible Mosquito
Infection Fete: # Population a to Infected Human ze
Human
Recover Rate +
Figure 3: Interaction Causal Loop Diagram
System Dynamics Model
System Dynamics models build upon the causal loop diagrams used to understand the
structure of the system and introduce stocks and flows. A stock is a measurable accumulation of
material in a system. A flow is an instantaneous rate of change of material between stocks in a
model (Forrester, 1961). Mathematically, the value of the stock is equal to the integral of the
combined inflows and outflows into and out of the stock. Stocks and flows enable the model to
account for delays inherent to the system, such as the incubation period or the time period a
mosquito or human is contagious. The model uses this basic structure to capture the interactions
of the mosquito and human population to model and simulate the dynamic behavior of the
CHIKV epidemic.
In developing an understanding of the system and its interactions and feedback structure,
we expand on the basic premise that the spread of CHIKV requires a mosquito, a host, and an
interaction between the two. We initially model two different subsystems—creating a mosquito
population model and a human population model—and then link the two models together
through the interactions that occur between the two populations. Since conditions in each
country differ, the model adapts to each individual country using different initial conditions to
model the spread of CHIKV.
Figure 4 presents the mosquito sub-system model, which is a series of stocks and flows
that takes the mosquito population from the egg to the susceptible population. From the
susceptible population, interactions with the human population cause a portion of the adult
mosquito population to become infected. Although there are several stages in the mosquito’s
maturation from egg to larva to adult, the model does not account for these stages, as they are not
critical to understanding the transmission of CHIKV (Singapore National Environment Agency,
2013). The model does account for the Average Incubation Period of the virus, which is 7 days,
during which the mosquito is infected, but cannot spread the disease to humans (Center for
Disease Control, 2011). The model also accounts for various vector control policies by
incorporating them into the mosquito death rates along with the normal mosquito death rate due
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to their 14-day life span (Singapore National Environment Agency, 2013). The initial model was
set to equilibrium by adjusting the effects of vector control on the death rate to ensure that the
mosquito population did not experience exponential growth.
Figure 4: Mosquito Population Sub-System Model
Figure 5 presents the human population sub-system model. Due to the short duration of
the CHIKV epidemic, the model does not need to simulate the entire human lifecycle; thus we
can assume that population size remains relatively fixed over the duration of the epidemic. This
model only accounts for the Susceptible Human Population, the Infected Human Population, the
Viremic Population and the Recovered Human Population. Unlike mosquitoes, humans can
transmit the virus to mosquitoes during the viremic or infected phase of the virus (Center for
Disease Control, 2011). The variables for Average Human Incubation Period (5 days), and
Average Time to Recovery (7 days) are all based on studies by the CDC (Center for Disease
Control, 2011). It is important to make these two populations distinct because only the viremic
population would show signs of the virus and seek medical attention, but there would still be the
possibility to transmit the disease to mosquitoes without the human knowing they had CHIKV.
Average time to ‘Average Human Human Infectivity
Recovery
Incubation Period ¢ Probably
Population
aia Ha
Recovered Human
Population Murnan
Intecion Rate
Te tui aw
Population
Figure 5: Human pauililiod Sub-System Model
Figure 6 presents the portion of the model that captures the dynamics of the transfer of
the virus between the mosquito and human populations. It is similar to the basic SIR model,
however, instead of an interaction between individuals in the same population, the CHIKV virus
requires the interaction of an infected mosquito or human with a susceptible member of the other
population. Two key variables that affect the transmission of the disease between humans and
mosquitoes are the Mosquito Infectivity Probahility (0.75) and the Human Infectivity Probability
(0.80) that determine what contacts result in transmission of the disease (Poletti, et al., 2011).
There is accurate data on the number of feedings per day as well as the mosquito infectivity
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probability; however, data for average mosquito contacts per person is not readily available. So,
this variable becomes essential to calibrate the model to simulate actual data.
ted
ation
~ Population
taf
Figure 6: CHIKV Transmission Model
In addition to the transmission dynamics between the two populations, the model
attempts to replicate historic data by capturing the Cumulative Reported Cases of CHIKV. The
stock of cumulative reported cases utilizes the Human Infection Rate and the Probability of
Reporting to model the number of cases. The variable Probability of Reporting captures several
aspects of the virus as a constant in the model. First, the symptoms of CHIKV may be similar to
other common illnesses, so people may not go to a hospital or clinic for treatment. Volk et al.
note this as a major problem in tracking the CHIKV virus because of its similarities to the
dengue virus (2010). Second, depending on the country’s medical infrastructure, cases may go
unreported. Although historic data exists for nearly every country in which the CHIKV virus
exists, this paper focuses on simulating the behavior in St. Martin and Martinique, two of the
first countries to report the epidemic in the Caribbean.
Model Output and Validation
The model generates the S-shaped growth that one would expect of an epidemic such as
CHIKV and follows the same pattem as the historic data from St. Martin and Martinique.
However, the magnitude of the spread of the disease and the timing of the S-shaped growth did
not match historic data given the model's initial assumptions about the calibration variables. The
calibration variables are the Average Mosquito Contacts per Person and the Probability of
Reporting. Probability of Reporting accounts for the probability of a person reporting the illness
and takes into account several factors, including the fact that only a certain percent will actually
develop symptoms despite being infected. In addition, this variable could vary by country based.
on access to healthcare facilities and cultural differences. The Average Mosquito Contact per
Person is the average number of mosquito to human contacts per day. Again, this variable
enables the calibration of the model as different countries could have differing conditions that
lead to human exposure to mosquitoes.
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Total Initial Week 32 Infected Probability of |AV9 Mosauito
4, a Contact Per | R*2
Population | Infected Actual Model Reporting Person
[St. Martin 74852 89 4653 5243 0.075 0.75 0.67
Martinique 386486 8 57435 66152 0.22 0.6 0.61
Table 1: Model Summary Table for Key Variables
Table 1 presents a summary of the key variables for both St. Martin and Martinique for
the CHIKV epidemic. In both cases, the model predicted slightly more cases than were actually
reported. The PAHO tracks the spread of the CHIKV epidemic to include the data for the total
population, initial number of reported infections, and number of reported cases for Week 32
(2015). The coefficient of correlation was relatively high for the simulation; however, more
refinement of the model could be performed to increase these values. However, the model does
generate similar behavior to the historic data and the magnitude and shape of the curves are
consistent.
Figure 7: St. Martin CHIKV Reported Cases "Figure 8: St. Martin CHIKV Reporting
The historic data from St. Martin in Figure 7 is consistent with the S-shaped growth
hypothesized for an epidemic such as CHIKV. Also depicted by Figure 7, the model simulates
behavior very similar to the historic data in St. Martin. Although historic data of the CHIKV
reporting is not available, an important aspect to modeling the spread of CHIKV is the rate at
which people report the virus as depicted in Figure 8.
Week oO 2 4 6 8 zo [ 12 [ 14 [ 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32
[Actual a9_| 204 | 477 | 601 | 711 | 2795 | 3422 | 3630 | 3773 | 3953 | 4033 | 4113 | 4173 | 4223 | 4333 | 4453 | 4553
[Model g9_| 100 | 136 | 173 | 333 | 725 | 1541 | 2758 | 3908 | 4621 | 4967 | 5122 | si90 | 5220 | 5234 | 5240 | 5242
Delta o | -194 | -341 | -428 [| -378 | -2070 | 1981 | -872 [| 135 [ 668 | 934 | 1009 | 1017 [ 997 | 901 | 787 | 689
Table 2: Model Data Comparison for St. Martin through Week 32
Table 2 presents a bi-weekly summary of the actual reported cases of CHIKV and the
output of the model along with a delta between the two. For St. Martin, the actual reported cases
experience rapid growth between weeks 8 and 10 that the model was unable to simulate
effectively. For the first 14 weeks, the output of the model lags behind the actual data.
However, after week 16, the output of the model is slightly higher than the actual reported cases.
The two sets of data are somewhat correlated with each other as the coefficient of correlation is
0.67, which is not great, but does indicate some level of correlation. The model does generate
similar behavior to the actual spread of the CHIKV virus and can provide valuable insights for
potential policy altematives to avert the epidemic earlier in time horizon.
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Figure 9: Martinique CHIKV Reported Cases Figure 10: Martinique CHIKV Reporting
Like St. Martin, the historic data for Martinique, in Figure 9, follows the S-shaped growth.
pattem; however, it does not experience the exponential growth like St. Martin did around week
10. Figure 9 also present the simulated behavior from the model, which generates similar
behavior over time. Figure 10 presents the output of the rate of reporting the CHIKV virus from
the simulation, which has a similar pattem to St. Martin but occurs later in the simulation.
iz | 14 | i6
Table 3 presents a bi-weekly summary of the actual reported cases of CHIKV in
Martinique and the output of the model along with a delta between the two. Unlike St. Martin,
the actual reported cases did not experience the strong growth in the first 10 weeks of the
epidemic. However, the simulation does lag behind the actual data for the first 28 weeks of the
time horizon. The two sets of data are slightly correlated with each other, as the coefficient of
correlation is 0.61 for Martinique. Like St. Martin, the model generates similar behavior to the
actual spread of the CHIKV virus in Martinique. The fact that the model can generate similar
behavior to the spread of the virus in multiple countries adds to the validity of the model for use
in policy analysis.
Potential Policy Alternatives
In developing potential policy altematives, and in validating our current model, we have
identified several shortcomings in explicitly modeling CHIKV spread. For example, for many of
the 58 countries we modeled we had to adjust the Initial Human Infected Population to capture
the drastic, steep initial exponential increase in cumulative CHIKV cases at the beginning of an
outbreak. This is attributable to a lack in the reporting of CHIKV infections initially, as we
summise that only a small percentage of people will report or be diagnosed with CHIKV during
the initial part of an outbreak and true reporting doesn’t start until the outbreak is already well
established. This led to an adjustment in our model. Using St Martins as a comparison, Figure
11 shows the effect of adding a variable to the model, the Probability of Reporting, which better
accounts for the sharp growth upon the onset shortly after reported infections.
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Current model does not account for sharp The addition of a variable to capture
initial growth, likely attributable to a delay in reporting lag, Probability of Reporting (10%)
reporting cases until the outbreak is known. contributes to improved fit here.
Cumulative Reported Cases Cumulative Reported Cases
oso 4300 =}
et
4 e
F 4500 } 3000 f
2 Bes | ! |
o « 2 i 2 305 366
Tee Os)
Figure 11: Adding the Probability of Reporting
This just represents one of the enhancements we can continue to make to the model to
better inform policy decisions. Along these lines, additional enhancement of variable
representation or additional model structure can capture various potential surveillance and
reporting programs considered for implementation.
Other areas of policy analysis to investigate are the effect of vector control efforts and the
effect of personal protective measures. The variables identified as having the greatest effect on
model behavior and the resultant effect in increasing or decreasing the S-shaped behavior include
Average Mosquito Contact Per Person, Fractional Mosquito Egg Death Rate, Average Mosquito
Feedings Per Day, and Infectivity (to a lesser degree). When these variables are increased, the
number of CHIKV cases gets large rather quickly. In particular, there is an inability to
appropriately balance the sharp exponential growth of reported cases before it quickly explodes .
Enhancing our current model with vector control or containment and personal protective
measures that balance these variables should be more explicitly included in the structure of the
model, balancing the exponential growth aspect associated with spread. Vector control structure
can be added explicitly within the mosquito population model, and personal protective measure
structure can be implemented to reduce the exposed human population. Variations of these
structures can serve to model various policies.
Conclusions and Future Work
The strength of system dynamic modeling lies in its ability to investigate multiple policies
or altematives to asystem. The current model is relatively simple, can be run on any computer
and the software being used is readily available online to be downloaded to any typical desktop
or laptop computer. The current model runs instantaneously. Although this CHIKV model is
relatively simple in its current state, it can continue to be enhanced and improved to get better
grounded in available data to achieve better forecasting results. Various policies to mitigate the
spread of CHIKV can be investigated by changing parameters or modifying the existing model
structure, running the new simulation, and analyzing and comparing the resulting output. As an
example, specific vector control efforts, and their resultant effects can be analyzed and compared.
to identify cost effective vector control efforts to best mitigate CHIKV spread. Additionally, this
system dynamic model is easily tailored to other epidemiological problems, such as Dengue
Fever or even Ebola.
Page | 11
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About the Authors
MAJ James Enos is currently serving as the Systems Engineering Branch Chief, Joint
Requirements Assessment Division on The Joint Staff. He has over 15 years of service as an
Amny Infantry Officer and Operations Research Systems Analyst for the United States Army.
He previously served as an Assistant Professor in the Department of Systems Engineering, at the
United States Military Academy. He eamed a Masters in Engineering and Management from.
Massachusetts Institute of Technology in 2010 and is currently pursuing a PhD in Systems
Engineering from Stevens Institute of Technology.
LTC(R) Russell Schott is a working as a consultant and data analyst. He has over 20 years of
service as an Infantry Officer and Operations Research Systems Analyst for the United States
Amny. He previously served as an Assistant Professor in the Department of Systems
Engineering, at the United States Military Academy. He eamed.a Master in Industrial
Engineering from Georgia Institute of Technology in 2001.
LTC Elizabeth Schott is currently serving as an Academy Professor and the Engineering
Management Program Director at the United States Military Academy at West Point. She has
over 20 years of service as an Army Quartermaster Officer and Operations Research Systems
Analyst. She eamed her PhD in Industrial Engineering from New Mexico State University in
2009.
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