Modeling the Effect of Information Feedback on the SARS
Epidemic in Beijing
Geng Li
University of Bergen
Postbox 366, Fantoft Studentboliger 5075 Bergen, Norway
gli005@ student.uib.no
Abstract
Compared with many preventable epidemics, how did a relatively insignificant disease like SARS
develop into an international scare? This article describes the application of system dynamics to
understand the SARS epidemic in Beijing. The powersim model simulates the structure of transmission
dynamics and factors that impact the epidemic. Here, the probable impacts of changes in the system
delays, including delays to quarantine, delays of disease diagnose, and the authorities’ epidemic
information transmitting delays, are discussed. The model aims to present detailed understanding of
delayed feedback mechanisms inherent to eliminate the misperceptions of basic dynamics, and then to
design high leverage policies for preventing SARS. The article concludes that an open and transparent
public information system is the most powerful weapon to curb SARS panics. The government's
prompt epidemic information feedback system and relatively instant strong quarantine policies have
substantial impacts on containing SARS epidemic.
Keywords: Information Feedback, SARS, Delays, Quarantine, System Dynamics
1 Introduction
1.1 Background Information
SARS (Severe Acute Respiratory Syndrome), an atypical pneumonia of unknown etiology,
broke out in China at the end of February 2003. With symptoms similar to that of
pneumonia, it is easy to get infected through secretion from respiratory organs and
intimate contact. SARS infected 8,439 people in 30 countries on five continents with a
death rate of 10 percent (812 people). China was the country worst affected by the
epidemic, infecting 5,327 people nationally and killing 349. Especially Beijing city
experienced the largest outbreak of SARS, with >2,500 cases reported between March and
June 2003. Moreover, the extreme instances of SARS so-called superspreading events
(SSEs), where single individuals have apparently infected as many as 300 others, appeared
in Beijing.
1.2 Problem Description
Every time there is a scare like SARS, scientists worry that it might be the next big
outbreak. Diseases can be both unpredictable and difficult to contain. Moreover, certain
environments, such as Southeast Asia, with its high interaction between humans and
animals, are optimal breeding grounds for the next super bug. And the increasing
regularity of international travel makes it easy for a regional outbreak to quickly become a
global one. In this regard, SARS is very much a sign of things to come.
The transmission routes of SARS
The virus is predominantly spread by droplets or by direct and indirect contact. The
airborne spread of SARS does not seem to be a major route of transmission. However, the
apparent ease of transmission in some instances is of concem.
Incubation period
SARS patients with chronic illnesses occurring concurrently with fever and/or pneumonia
and who have a plausible diagnosis are the most challenging to the public health and
healthcare systems. Early symptoms of SARS are non-specific and are associated with
other more common illnesses. Unrecognized cases of SARS have been implicated in
recent outbreaks in Beijing. WHO (World Health Organization) stated that the maximum
observed incubation period was 10 days.
Strategies for preventing SARS epidemic
For the unclear virus source, so far, no exclusive medicine, vaccine or treatment for the
SARS disease has been found, but most patients can recover by taking supportive and
appropriate medical treatments in time. The strategies Beijing authority, medical institutes,
and the masses take during the SARS time are three major policies.
1. “Quarantine policies”:
Force to isolate healthy persons who may contact the virus, isolate the infected persons
who still no symptoms during incubation period, and isolate and cure the symptomatic
patients.
> Who should be in Quarantine?
Individuals who have come into close contact with a person with SARS and did not weara
protective mask. They should remain in quarantine for a 10-day period, even if they are
not experiencing symptoms.
2. “Government investment on protection policies”:
A large-scale public SARS protection requires a wide range of services and medical
treatment equipment such as masks, sanitizer, ambulance, anti bacteria medicine to be
provided to individuals and hospitals. In Beijing, these huge investments were invested by
government and some other private social service agencies.
3. “Public protection policies”:
When the public get the information about the density of suspected and in hospital SARS
population, comparing with the safety reference density, they gradually reduce the
opportunity to contact others to avoid being infected, and purchase and use protection
equipment like face masks, sanitizer, and anti bacteria medicine.
2 Conceptual Model
2.1 Problem Hypothesis
The death and infection rate of SARS is similar to the influenza. However, in 2003,
Beijing was hard hit. As of early May, the largest source of the epidemic is in China.
Beijing has quarantined over 18,000 people, with 2,177 confirmed cases and over 114
fatalities. The size of the international response is overwhelming. So the level of fear and
concem of SARS has triggered. When SARS appeared early, people in Beijing started
panic buying food and medicine. Some were holed up at home, others fled to the
countryside. At the beginning of SARS epidemic, the authorities’ inefficient epidemic
information transmitting systems and downplaying the seriousness of the outbreak play a
significant role in the uncontrolled spread of the SARS disease.
Every year, the world has influenza outbreaks that cause over a hundred thousand deaths
with little comment. These 500+ SARS casualties, however, have triggered a worldwide
epidemic of fear and suspicion.
> How did a relatively insignificant disease like SARS develop into an international
scare, causing alarm even in countries that have had no cases, or very few?
Based on the case of Beijing, the 10-day incubation period of SARS induced our
misperception of feedback. At the early stage of SARS crisis, the public did not realize
that the SARS virus already spread like wildfire. After the delay of 10-day incubation
period, the public just found that the amount of infected persons dramatically rose up. So
they immediately took actions to prevent SARS, however, the speed of prevention could
not catch that of virus transmission. Thus, authorities took strong actions to enforce
quarantine. The major spread was under control. But the public did not know the
dynamical trend that the amount of infected persons would fall after about one week; they
only saw that the amount was continuously going up. Subsequently, the SARS global
panic was sparked.
2.2. Causal Loop Diagrams
2.2.1 Public SARS Infection Sector
Susceptible Population
Contact Virus
Rate
i)
Contact Not
Infected
Recovered LUD) Quarantine a
Population Healthy People Contact Virus
Death Quarantine Population
Population —
Re
Quarantine AD
+ Rate Incubation:
Infection Pep Infect
Rate
SARS Population in /
Be S
Incubation
eGCV——
Sick N untion-t——
Figure 1: Causal Loop Diagram depicting the feedback structure of public SARS infection
Explanation of the major feedback structure:
R1: Incubation Population Infect Others
The incubation population, who are in the latent period, not in quarantine, can infect any
other healthy people in the ordinary contact. So the larger the number of incubated not
quarantine population, the higher the contact virus rate will be, the stronger contagion it
has, vice versa.
B1: Healthy People Quarantine
According to the SARS epidemic situation when the govemment force a part of
susceptible healthy population to go to quarantine to halt the contagion with the SARS
disease, the number of susceptible healthy population will decrease, and then after 10-day
quarantine period the susceptible individuals will be released from quarantine.
B2: Contact Not Infected Quarantine
The government force the contact virus not infected susceptible population to go to
quarantine to prevent the potential infection and contagion with the SARS disease.
2.2.2 The SARS Prevention Policy
Without the vaccine and effective treatment to tackle SARS, therefore, nowadays the
common method of quell SARS is to prevent the spread of SARS epidemic. The decline
of SARS cases in the city to two kinds of factors, social one and natural one. Social factors,
especially measures taken by the government, are decisive in reducing SARS cases. The
measures taken by the city government, an important part of the social factors, proved
correct, effective and timely. Those measures include the establishment of SARS-only
hospitals and fever clinics, protection of medical workers, mobilization of the public and
strengthening of surveillance work.
Contact Virus ——__
ae Rate
BD
Effect of Contact Virus
Quarantine ‘Gn Contact Rats Susceptible Population:
Population
And *
Effect of Public +
Protection On Quarantine
Contact Rate Rate a
Infection Virus
+ = e
Authorities
Quarantine Policy Ava)
+ Infectivity cbffestet
Pa nivestment On
- Infectivity
Government
Awareness eS Incubation Pop
+
AR) Government
Investment
cttector +
SARS Population Investment On Sick Po,
in Hospital +. Time to Hospital + P
Sick to Ze
—— Hospital Rate
Figure 2: Causal Loop Diagram depicting the feedback structure of the prevention policy
R1: Effect of SARS Patients on Quarantine Policy
When the authorities get the information about the density of SARS population, they will
change the quarantine rate. When the density is high, the government will dramatically
increase the quarantine rate, vice versa. Thus, more sick people will be in quarantine and
then go to hospital to halt the SARS epidemic.
R2: Effect of Government Investment on Time to Hospital
When the government gathers the real information about the number of in hospital SARS
population, they will invest plenty of money in prevention materials, services and facilities
to help the sick people go to hospital as soon as possible.
B1: Effect of Quarantine Policy on Contact Rate
According to the density of suspected and in hospital SARS population, when the
govemment implement a strong quarantine policy, the contact rate with SARS infectious
people will dramatically diminish.
B2: Effect of Public Protection on Contact Rate
When the public get the information about the density of suspected and in hospital SARS
population, comparing with the safety reference density, they can spontaneously change
their contact rate with others.
B3: Effect of Government Investment on Infectivity
A large-scale public SARS protection requires a wide range of services and medical
treatment equipment to be provided for individuals and hospitals. When the government
gathers the real information about the number of SARS situation, they will invest plenty of
money in order to reduce the probability of infectivity.
2.3 Sectors
This SARS epidemic model is mainly divided into five sectors as follows:
> The basic module of public SARS infection
> The contact rate
Probability of infectivity
> Quarantine rate
Actual time to hospital
Vv
Vv
3 Formal Model
3.1 Basic Module of Public SARS Infection
Facing the new SARS disease, until now we have not found the vaccine and effective
treatment, therefore nowadays every healthy population, except the SARS recovered
people, has not immunity from SARS virus. Thus, all healthy people excluding SARS
recovered people are the susceptible people.
When the susceptible people contact with the not isolated sick or incubation individuals,
some of them will be very lucky not infected, however, the others will be infected with
virus, and then become the incubation people. The lucky ones will be forced to go to
10-day quarantine period to halt the contagion and will be released from quarantine after
10 days.
According to the power of government quarantine policy, parts of the incubation people
will be soon quarantined and then go to hospital. But the uncontrolled incubation people
are still in the city to contact others. After the delayed incubation period, the incubation
people will have the symptoms and become sick. The sick persons not isolated will be sent
to the hospital at different response time.
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3.2. The Contact Rate
os
Norrral_ Contact Rate
Reference _Density
Eff_of_Suspected_and_Hospitied_Pop_on_Nurrber_of Contact In_Hospital SARS_Pop
7
| |
4
Quarantine_Not_Sick Pop
Adjustrrent_Tire_of_PED
Suspected_pop
won ro
— —
Quarantiné_Incubated_Pop Quarantine Sick Pop
Figure 4: Stock and flow diagram - the contact rate sector
In this sector, we can clearly see the influential factors in the contact rate, the Effect of
Suspected and Hospitizied Population on Number of Contact. When the public receive the
information from media such as newspaper, television, radio, internet about the density of
suspected and in hospital SARS population, they will change the contact rate with others
according to the reported degree of SARS epidemic. When the density is high, the public
gradually decrease the rate of contacting in the region to protect them from infecting, vice
versa. That also names the effect of public protection on contact rate.
eee ea
aed a
4 —
sed |
She ze
| trust <3:
[Pete were asa =
3 py |
Figure 5: Effect of Suspected and Hospitizied Pop on Number of Contact (dimensionless)
So as the Figure 5 above, when the perceived density increases over the safety reference
density, it is the signal that SARS density is high (Perceived Density/Reference
Density>1), so the Effect of Suspected and Hospitizied Pop on Number of Contact will
gradually decrease, and people reduce the contact with others.
However, there are always some delays and over exaggerated reporting from the media.
That is the information delay to get the real information about the density of suspected and
in hospital SARS population. The relative adjustment time of perceived density is how
many days we can get the reliable information.
3.3. Probability of Infectivity
tivity
Ref_Probability_of_Infectivity
Reference Investrets
Rot_on_infectivity
Actual_Investermet
Tirme_To_Aquire_Investrents
Figure 6: Stock and flow diagram - the probability of infectivity sector
As soon as the government receive the already delayed information about the density of
suspected and hospitizied population, they will increase the investment for a large-scale
public SARS protection to supply a wide range of health services and medical treatment
equipment such as masks, sanitizer, ambulance, anti bacteria medicine, respirators to the
individuals and hospitals. On the other hand, when the SARS epidemic is controlled and
no more new infection cases appear, the government will gradually decrease the ratio of
investment.
3% [etn | ee | |
Figure 7: Effect of Suspected and Hospitizied Population on Investment (dimensionless)
It is easy to find that the Effect of Suspected and Hospitizied Population on Investment
also shows the S-shape. When the perceived density is less than or equal to the safety
reference, the investment will be the same as amount of reference investment. If the
perceived density is more than the safety reference density, the investment will soon
exponentially increase at first, but then gradually slows toward the equilibrium level,
twice as large as the reference investment.
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— | [Bi hvesemnrrerrorescinvoamars
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Figure 8: Effect of Investment on Infectivity (dimensionless)
The infectivity of the disease is the probability that a person will become infected after
exposure to someone with the disease. When the goverment pays more attention and
investment on public health and medical service, there will be more advanced medical
treatment equipment and facilities available to the public in order to reduce the probability
of infectivity. Thus, as the Figure 8 shows, when the Actual_Investemnt/Reference_Investmets>1,
the increased investment to crack the SARS will help to lessen the probability of
infectivity.
3.4 Quarantine Rate
ate
Perceived_Density
Reference_Density
&g_quarantine_Rate
Reference_Sick_in_hospital
Act_quararly
Ref_quarantine_Rate
Percelved_in_hospital_pop
Perc_of_Treatrent_Proc_Tire
Figure 9: Stock and flow diagram - the Quarantine Rate sector
10
Figure 9 represents the structure of the quarantine rate, which is determined by the
reference quarantine rate and two effects--- Effect of Perceived Density on Quarantine
Rate, and Effect of Hospital Population on Quarantine.
The Effect of Perceived Density on Quarantine Rate shows the strength of government
policy. When the government gathers the delayed information about the density of
suspected people and in hospital SARS population, comparing with the safety reference
density, the government will change the quarantine rate. When the density is high, the
public quarantine rate quickly goes up, vice versa.
2 [ts | ee | =]
Figure 10: Effect of Perceived Density on Quarantine Rate (dimensionless)
The Effect of Hospital Population on Quarantine rate is another influential factor to
quarantine rate. It describes that when the information about the number of in hospital
SARS population has been received by government, comparing with the reference number
(how many sick persons are in hospital is considered to be safe or acceptable), the
government can change the quarantine rate. If the perceived number is less or equal to the
safety reference value, the government will gradually diminish the quarantine rate. The
isolated healthy people can leave their quarantine period to the normal working and daily
life.
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Figure 11: Effect of Hospital Population on Quarantine rate (dimensionless)
As follows, there is also an information delay about the number of perceived patients in
hospital. This is an actual portraiture of the government information transmitting system.
ll
3.5 Actual Time to Hospital
Reference_Tire_To_Hospital <> <>
Perciglied_Density
wa
ee
AeWET BATE Reference_Investrrets
Figure 12: Stock and flow diagram - the Actual Time to Hospital sector
The actual time to hospital reflects how many days sick persons will go to hospital. There
are also two effects, effect of sick population on time to hospital and effect of investment
on time to hospital, to impact the time to hospital.
Figure 13: Effect of Sick Population on Time to Hospital (dimensionless)
When the perceived density of suspected and in hospital SARS population increases over
the reference density, the sick people will be more attention and go to hospital more
quickly, vice versa. Moreover, there is also an information delay to get the real time
reports of the epidemic density.
The effect of investment on time to hospital has the same tendency as the effect of sick
population on time to hospital. When the government pay more attention and investment
on medical service, such as the more advanced medical treatment equipment, special
SARS ambulance and other facilities available, to the public, the time of sick people to
12
hospital doing the treatment will be shorter. There is also a material delay for the public to
get the investment.
4 Model Validation
4.1 Extreme Conditions Test
Through developing the extreme input or policies on the model, we will examine the
robustness of the model. Here are two extreme conditions tests in this section. One is the
condition where the infection rate suddenly drops to zero, to see how the behavior of the
system changes correspondingly.
4.1.1 Extreme Condition Test I: A Sudden Drop of the Infection Rate
In this scenario, the total simulation time horizon is 730 days (2 years). Suppose that after
20 days, the infection rate suddenly and unexpectedly drops to zero. What would happen
to the behavior of the system?
When we run the model under this extreme condition, if there is no infection rate, there
will be no more people infected after all the incubation patients go to hospital,
consequently there is no need to be afraid of the SARS, and, certainly, there is no need to
have health people quarantined in the home. Thus, after somewhat delay, the healthy
people will leave from the quarantine period and the SARS infection would disappear.
Does the model generate the same behavior fashion as what we hope? Let us check it out
in the following graphs below.
Total_Infectious_Contacts*Fraction_of Contacts_with_Susceptibles+STEP
(-Total_Infectious_Contacts*Fraction_of_Contacts_with_Susceptibles, 20)
4
\
i
a 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 G80 720
Time
13
e
10,000,001
Ine NE Sick Pe
5,000,001
0 200 “400 600
Time
Figure 14: The System Behavior in Extreme Conditions Test I
Represented in the above equation, the infection rate suddenly drops to zero after 20 days.
Figure 14 shows that the quarantine SARS population starts to drop after a certain time of
delay. The number of recovered population and the cumulative population will reach the
equilibrium state at last. The behaviors resulting from the model match our expectation.
So the model passes the extreme condition test I.
4.1.2 Extreme Condition Test II: A Sudden Drop of the Quarantine Rate
In this scenario, the total simulation time horizon is 730 days (2 years). After 50 days, we
assume that, for some reasons, the authorities and public suddenly stop the quarantine
policy (the quarantine rate decreases to zero). Under this extreme situation, there are no
more people no matter the healthy or infected to be in the quarantine period. Then, what
would happen to the society? No doubt, a serious SARS epidemic will break out in the city.
The SARS will attack lots of people soon. A huge number of populations will be infected
through contagion. The panic and rumor of SARS will spread around the city.
Time
14
619,841
a
553,28
513,76
474,241 53
434,72
395,20
355,68 ri
316,161 Maer __In_Hospital SARS_Pop
276,641 S. _y— incubation_population
237,121
197,60
158,08
lisse
79,04
39/52
2
\ TF uaranine Sih Pop
#
‘e
0° 40 80 120 160 200 240 280 320 360 400 440 380 520 560 600 640 680 720
Time
Figure 15: The System Behavior in Extreme Conditions Test II
As Figure 15 depicts that when the quarantine rate decreases to zero after 50 days, the
total number of infected population will dramatically increase. Lots of healthy people are
infected. A severe SARS epidemic happened. The behaviors resulting from the model
successfully meet our expectation under this extreme test, and demonstrate the robustness
of the structure.
4.2 Sensitivity Analysis
In this research, what counts here is behavior mode sensitivity and policy sensitivity.
Given the limited time and resources, to do a comprehensive sensitivity analysis is
impossible since it requires testing all combinations of assumptions over their plausible
range of uncertainty. We execute two sensitivity analysis tests to the effect of suspected
and hospitizied population on number of contact rate and the time delays in the model.
4.2.1 Sensitivity Analysis Test I: the Effect of Suspected and Hospitizied Population
on Number of C ontact Rate
When there are no policies of investment and quarantine in the base run, we change the
effect of suspected and hospitizied population on the number of contact rate to test the
model sensitivity.
Run 1-strong effect Run 2-normal effect Run 3-weak effect
Figure 16: The change of the effect of suspected and hospitizied population on number
of contact rate
15
In the structure of this model, the contact rate is determined by the reference density and
the effect of suspected and hospitizied population on number of contact rate. We form the
table functions that describe this effect mainly based on our knowledge. We need a
numerical description to formulate the equations. However, neither the current literatures
nor available data offer the detailed information of the effect. Therefore, in this test, we are
going to check whether the model behavior is still robust when we change the effects
during the plausible range of uncertainty.
Figure 16 shows the three different formulations of the table function of effects. Run1 is a
strong effect on contact rate. When the public receive the information about the high
density of suspected and hospitizied population in the city, they will soon decrease the
contact rate with others to a very low number. Run2 is a normal effect and Run3 is a week
effect on contact rate respectively, by expanding different tendency in the graph.
Ee
=; Fecovered_population
we
8,000,001
6,000.00
4,000,001 _y-tecovered_population_1
z 3 Fecovered_population 2
2,000.00
/ es
oF
0” 30 Go. 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 G00 630 G60 690 720
Time
ener 1 Hospital SARS_Pop
i TF Hosp SARS_Pop_t
0 200 400 600
Time
100,00
=, Quarantine Sick Pop
50,004
2 Quarantine Sick Pop_1
3 Quarantine Sick Pop_2
Time
2,000,000.
1,500,000-
1 incubation_population
3,000,000. incubation_population,
—z- incubation_population_1
500,000. 3 incubation_population_2
fl 200 400 00
Time
Figure 17: The comparison of the model behavior in sensitivity analysis test I
A set of behaviors resulting from the three runs is exhibited in the Figure 17. The pattem
of behavior in each run is similar, but the amplitude for the level of the recovery
population and the sick population is different. In the case of strong effect on the contact
rate, the average level of the recovery population and the sick population climes up to a
16
higher level than the other cases. In addition, the shape in the behavior shows a shorter
period of delay.
From the results of the test, we do not identify a significant change in the pattern of
behavior when we change the assumption of the effects on the contact rate over the
different range of uncertainty. Therefore, we conclude that the model is not qualitatively
sensitive to the table functions of the effects chosen in the model.
4.2.2 Sensitivity Analysis Test II: Time Delays in the Model.
In the structure of the model, the major time delays include the adjustment time of
perceived density, percentage of treatment process time, and the time to acquire the
investment. The time delays have no data available to estimate their values accurately.
Therefore, in the sensitivity analysis test, we run the model with the time delays changing
over different range of uncertainty to check whether the behavior has been changed.
When there are government policies of investment and quarantine in the run, we change
the adjustment time of perceived density, which is how many days we can get the
information about the density of suspected and in hospital SARS population, to test the
model sensitivity; percentage of treatment process time, which is how many days we can
get the information about the number of in hospital SARS population.; and the time to
acquire investment, which is how many days we can get the investment.
al /
wl /
Figure 18: The comparison of the model behavior in sensitivity analysis test II
Normal Run1: Adjustment_Time_of_PED=7, Perc_of_Treatment_Proc_Time=5
Time_To_Acquire_Investments=7
17
Strong Run 2: Adjustment_Time_of_PED=21, Perc_of_Treatment_Proc_Time=15,
Time_To_Acquire_Investments=21
Weak Run 3: Adjustment_Time_of PED=1, Perc_of_Treatment_Proc_Time=1,
Time_To_Acquire_Investments=1
As we can see from the Figure 18, the pattern of behavior in three runs keeps the same.
The only difference is that with a longer delay involved, the tendency of the quarantine
rate shows a correspondingly longer period. With longer delays it takes more time for the
system to respond the perceived requirements.
From the above results of the test, we do not find a significant change in the pattern of
behavior when we change the assumption of the time delays over the different range of
uncertainty. Therefore, we certainly conclude that the model is not qualitatively sensitive
to the values of time delays chosen in the model.
5 Simulation and Behavior Analysis
This section represents the result of model simulation under three scenarios: a base run
and problem statement, policy design and an ideal situation.
5.1 Scenariol: Base Run & Problem Statement
We first run the base run, which has not the government policy and public policy in
quarantine and investment. So the government policies are all the constant 1:
Effect_of_Investment_on_Infectivity=1 Eff_of_investment_on_time_to_hospital=1
Eff_Of PED_on_quarantine_Rate=1
In this scenario we do not consider the government investment and quarantine methods. In
addition, the public policies are also the constant 1:
Eff_of_Suspected_and_Hospitizied_Pop_on_Number_of_Contact=1
Eff_of_hospital_pop_on_quarantine=1
Base Run:
—
18
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Less.29 RRB 068
ae aeeiereemenen
si
735,68 §
551,76 :
367,84 g. 3
183,921 es —_
0°40 ‘80 120 160 200 240 280 320 360 400 440 480 520 560 6U0 640 680 720
Time
& 0.10-
0.05.
g
0.004
° 200 400 600
Time
Figure 19: The Behavior of Scenariol: Base Run & Problem Statement
With a disease like SARS, the mortality rate (eventually 20 percent of those infected) was
high enough, if quarantine procedures were not initiated quickly, what will be the result of
uncontrolled? We can clearly get the answer through the Figure 19; the simulation
outcomes show a severe SARS epidemic. More than half of the people in the Beijing city
will be infected by SARS virus. No doubt, we have to take a serious look at epidemics
when considering disaster scenarios. There are many ways by which the impact of an
epidemic can play out. The real worry is if a contagious disease will not be controlled as
quickly as possible, and we may face the realistic horror as the scenario 1.
5.2 Scenario2: Policy Design
In this model, we consider three strategies for preventing SARS epidemic in Beijing. They
are respectively quarantine policies, government investment on protection policies, and
the public protection policies. Through the simulation, we can clearly see the behavior in
the following Figure 20 to synchronously analyze the affectivity of the policies in the
model.
Initial Value:
sick_pop =300, incubation_population =100, Reference Density =0.00001
19
0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720
Time
In_Hospltal SARS_Pop
0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720
Time
fo) 200 400 600
Time
Figure 20: The Behavior of Scenario2: Policy Design
Assume that the initial number of SARS sick population is 300 and the amount of the
incubation population is 100. Set the reference safety density, how many sick persons per
100 is considered to be safe or acceptable, as 0.00001. According to the Figure 23, it is
easy to find that the number of recovered population and sick people effectively diminish,
however, in the second year, about 500 days later, the SARS comes back. The time delays
in the system beget the small range oscillation.
5.3 Scenario3: An Ideal Scenario
Through the policy test, we totally agree that the public quarantine policies and protection
policies really effectively and dramatically reduce the bad large SARS contagion, and halt
the degree of epidemic. In 2003, human beings stopped the serious spread of SARS
disease; however without vaccine and immunity, what will happen later?
No doubt, the next issue we have to face is how to prevent the back of SARS epidemic.
How can we halt the tendency of the comeback of SARS and other global pandemic?
Through the section of policy design, after analyzing the simulation behaviors, we can
find that the value of reference density is a key point.
20
Initial Value: sick_pop =300, incubation_population =100, Reference_Density =0.000001
{e) 200 400 600
Time
Figure 21: The Behavior of Scenario3: An Ideal Scenario
In this scenario, we decrease the reference density to a smaller number, which means there
will be more attention paid to prevent SARS in the society. When the government showed
both courage and effectiveness in correcting the initial statistical confusions and gave
daily reports of the incidence via TV, newspaper and radio, set the reference safety density
as 0.000001. According to the Figure 21, it is easy to find that the number of recovered
population and sick people effectively diminish. The panic subsided quickly. Moreover, in
the second year, there is no oscillation; the SARS epidemics do not come back. This
policy certainly effectively diminishes and even retards the restoration of the SARS
epidemic.
6 Conclusion
Complex system such as SARS epidemics with many variables, long time delays,
nonlinearities and uncertainty about the cause and effect, is harder to explain and estimate
without the use of system dynamics. Using system dynamics method, we have learnt how
to create a map of the complicated causal inter connections within all variables so that we
can chart a clear route of disease infection. Providing a method of eliciting mental models
about problems and visualizing them as models helps the public and goverment to
understand the structure and enhance the accuracy of data provided from surroundings
with dynamic complexity, long time information and material delays.
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The leading-edge computer simulation techniques help us see the outcome of policies and
use system dynamics models to analyze effective policy options. The goal of this system
thinking and system dynamics modeling is to improve our understanding of the ways in
which our performance is related to its internal structure and operating policies, and then
to use that understanding to design high leverage policies for preventing SARS epidemic.
6.1 Major Findings and Results
Expected Outcomes and Insight:
The system dynamics model described in the paper shows how the delayed feedback
mechanisms inherent in the complex SARS transmission structure influence the behavior
patterns overtime. It emphasizes the difference between the actual and perceived
conditions as a basis for changes in the structure. The model aims to present the clear and
detailed understanding of the delayed transmission system to eliminate the misperceptions
of the basic dynamics.
Beijing's SARS outbreak case yields important lessons for global public health and crisis
management. From panics to scientific policies in Beijing's SARS events, we could find
that transparency is the most powerful 'weapon' to curb public panic and the spread of
rumors, which could have stirred more panic. We cannot overcome the threat of SARS
without an open and prompt public information system.
To sum up, the response time and the strength of control measures have significant effects
on the scale of the outbreak and the lasting time of the SARS. Detect the SARS cases early,
then isolate infected persons swiftly, take the treatment quickly. According to these
policies, we can gradually control the disease and actually break the chain of transmission.
6.2. Limitation and Future Work
Future work should certainly focus on other epidemiological parameters in a variety of
circumstances and use SARS-specific parameters to construct more detailed models of
transmission that realistically incorporate the effects of heterogeneities in specific settings.
In addition to the control measures considered here, I expect other aspects of SARS
transmission, such as the duration of acquired immunity, the effect of seasonality on
transmission rates, and the role, if any, of animal reservoirs, will be important
determinants of the future course of the SARS epidemic.
On the other hand, it’s a simple hypothesis. In the real model, the situation will be much
more complicated. Every city is not an isolated point. The movement of people between
cities connects all surrounding cities into a very complex system. We can try to enrich the
creation of a multi-city disease model and the incorporation of travel statistics to give the
public another reference point to reduce the contagion by travel.
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Finally, with the development of antibiotics, advanced medical procedures, global
communications and much improved epidemiology, this syndrome, SARS, will not be a
worldwide health threat. The world works together to find its cause, cure the sick, stop its
spread and finally we will definitely crack the SARS.
References
Sterman, John D., Business Dynamics, McGraw-Hill
Jay W. Forrester, Industrial Dynamics, MIT Press, 1994
Andrew Ford, Modeling the Environment, Island Press, 1999
Charles H. Hennekens, Julie E. Buring, Epidemiology in Medicine
George P. Richardson, Alexander L.Pugh, Introduction to system dynamics modeling with
dynamo, MIT Press, 1983
David Ingram, The Dynamics of SARS: Plotting the Risk of Epidemic Disaster, Risk
Management Magazine, 2004
Marc Lipsitch, Ted Cohen, Transmission Dynamics and Control of Severe Acute
Respiratory Syndrome, 20 June, 2003, Science Magazine
Zhuang Shen, Fang Ning, Weigong Zhou, Superspreading SARS Events, Beijing, 2003,
Emerging Infectious Diseases journal Vol. 10, No. 2 February 2004
Guofa Zhou and Guiyun YanSevere, Acute Respiratory Syndrome Epidemic in Asia,
Emerging Infectious Diseases journal Vol. 9, No. 12 December 2003
Exclusive Authorized SARS Release by the State Council Information Office in China at
http://www.china.org.cn/english/features/SA RS/62902.htm
Beijing Centers for Diseases Control and Prevention (CDC) at http://www.bjcdc.org
World Health Organization (WHO) at http://www.who.int/csr/sars/en/
Mass SARS quarantine in Beijing at
http://www.cnn.com/2003/W ORLD/asiapcf/east/04/25/sars/
The SARS Epidemic in Easter & Southeast Asia at
http://newton.uor.edu/D epartments& Programs/A sianStudiesD ept/sars.html
SARS lesson: How to address crises at
http://www.chinadaily.com.cn/en/doc/2004-01/20/content_300458.htm
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