6 Chapter 6: Modeling Case Studies

In this section of the Learning Guide, you will have a chance to exercise your modeling skills with realistic and more open-ended problems involving decision-makers and stakeholders. In each case study, you will be given some guidance to help you apply the four-stage process outlined in Figure 34.

Some of these case studies are more challenging than others. Their level of difficulty is indicated with a CHALLENGE LEVEL rating.

• ENTRY level case studies are those in which either the models depend largely on building blocks you already know or extensive modeling guidance is provided.
• MODERATE level cases provide less prescriptive guidance for building your model, but whose model complexity has many similarities to what you’ve already seen in this text.
• ADVANCE level cases are the most open-ended of all. These cases will require you to construct a model with minimal prescriptive guidance.

6.1  Outbreak!  Planning for a Deadly Flu Outbreak (Challenge Level: Entry/Moderate)

Today, worldwide, there is an apparent increase in many infectious diseases, including some newly-circulating ones (HIV/AIDS, hantavirus, hepatitis C, SARS, etc.). This reflects the combined impacts of rapid demographic, environmental, social, technological and other changes in our ways-of-living. Climate change will also affect infectious disease occurrence.”

Source: World Health Organization, 2014

6.1.1. Background: The local challenge from an emerging flu virus

Most years, seasonal influenza causes severe illness in three to five million people worldwide, and it kills hundreds of thousands of people. Occasionally, the spread and lethality of the influenza virus are more severe ― by many orders of magnitude. For example, an estimated 50 million deaths ― and perhaps as many as 100 million ― resulted from the 1918 global flu pandemic (see Figure 34).

Since that time, other serious pandemics have occurred with significantly higher than normal morbidity and mortality^[1]. The potential for such pandemics in the face of an evolving climate is considered to be one of the significant threats created by climate change.

Since 2003, 650 human infections with highly-pathogenic H5N1 viruses have been reported to the World Health Organization. These infections have come from 15 different countries. About 60% of people infected with this virus died from their illness. Fortunately, unlike other types of flu, H5N1 does not usually spread between people.  In late 2019, COVID-19 was identified and kicked off a global pandemic that as of April 2024 had killed over 7 million people worldwide according to the World Health Organization^[2].   and into 2020, the world faced such a pandemic with the spread of COVID-19.

What would happen if a virus like H5N1 acquired the capability of sustained human-to-human transmission? Researchers have used computer models to explore possible scenarios and to try to understand some of the factors that affect how influenza progresses in individuals and through a population. Along with genetic and social factors, the spread and severity of flu pandemics depend on environmental factors such as weather, humidity, temperature, and airflow. What impacts could global climate change have on the transmission, morbidity and lethality of possible emergent influenza strains?  Answers to these questions are unknown. A good place to start is to build a baseline model for how such a disease might spread in a human population.

Your goal is to create, analyze and present a computer model of the spread of a serious influenza epidemic such as a highly-infectious H5N1 strain that has acquired the capability of human to human transmission. You will build your model to help public health officials in a local community evaluate different public health strategies for impacting the progression of the disease in their city.

Behavior Over Time (Hopes and Fears)

Figure 39 shows the a typical BOTG for the flu season in the U.S. This particular graph shows the number of cases reported to U.S. doctors during the 2023-2024 flu season (running roughly from late September through the following June).  This BOTG shows an early period of exponential growth, followed by a slowing in the disease spread until it nearly dies out after about 30 weeks. The duration of the outbreak is a function of how contagious the disease is, how wide of a geographic region is affected, and the level of contact between people across that region. Because this graph represents the entire U.S., one would expect that an outbreak in a town like Smallville would be over in a shorter time period (possibly much shorter), but that the shape of the BOTG would look roughly like this figure. While this graph represents the behavior of all influenza-like illnesses in 2023-2024, it is expected that an H1N5 outbreak would exhibit a similar overall pattern.

When tracking the progress of a disease over time, public health officials and other stakeholders typically track (among other things) the following:

1. #Cases (by day and overall):  The number of new cases of people exhibiting disease symptoms each day (similar to Figure 39), and the total number of cases so far.
2. #Deaths: The total number of deaths from the disease so far
3. #Hospitalized: The daily number of people requiring hospital care
4. Cost: Cumulative cost of providing health care for disease victims
5. #Inoculated: Number of people who are resistant to the disease because of vaccination (if a vaccine is available)
6. #Quarantined: Number of sick people placed in quarantine

Stage 2: Create a Model, Test, and Develop an Interface

The basic stock and flow structure for a flu-like disease outbreak

One of the most common frameworks that epidemiologists use for describing how infectious diseases like the flu, HIV, Tuberculosis, COVID19 and others spread through a population is the SEIR model. The letters, SEIR correspond to the names of four stages through which people in a population might pass during a disease outbreak.  You can think of these four stages as stocks containing people. There are flows running from one stock to the next.  The four stages are listed below. The first letter of each stage is highlighted, indicating the four letters S-E-I-R.

Susceptibles. This stands for everyone in the population that could potentially get the disease. In the case of a disease like the flu or an infectious version of H5N1, the Susceptibles would be everyone in the population. That’s because each strain of the flu is unique from the previous year’s strain. If someone had the flu last year, they might be resistant to that particular strain, but not necessarily this year’s strain. Hence, everyone is susceptible.  Of course, if some people have been inoculated with an effective vaccine for this year’s strain, they would be resistant and less likely to get the disease.  For now, we will assume that there is no vaccine for H5N1. Hence, at the beginning, everyone is susceptible. If someone catches the disease from someone else, they move into the next stage.

Exposed. Every Susceptible person who is exposed to the disease and absorbs the virus into their body moves into the Exposed category.  Exposed individuals have not yet shown symptoms and don’t know that they have the disease. That’s because their body’s immune system has not yet fully recognized the presence of the virus and has not kicked into high gear. An exposed person is hence asymptomatic ― they have no fever, no aches and pains ― no symptoms of the disease. Neither they nor anyone around them suspects that they are now contagious and about to get sick. Unfortunately, Exposed individuals can pass the disease to others.   People who are Exposed will stay in this state for as long as it takes the disease to develop and show symptoms.

Infected. This stands for everyone who now has the disease and is feeling its effects (fever, aches, etc.). Infected individuals can continue to pass the disease along to others, just like Exposed people can. In addition, over the course of the disease, some fraction of Infected people will die. The disease typically lasts for a limited time, after which those individuals who survive and recover will advance to the final stage.

Recovered. This stands for those individuals who have recovered from the disease. These folks no longer show symptoms. While they may remain weak for a while, we will consider these folks to be fully recovered once they reach this stage. These individuals are not infectious: they cannot pass the disease along to anyone. In addition, they are resistant to the disease – i.e. they cannot get it from someone else.

Factors affecting the rates of flow between the S-E-I-R stocks

There are several things that impact how quickly a disease might spread and whether the disease can cause a serious epidemic.  In terms of a stock and flow diagram, these factors affect the rates of flow between the S-E-I-R stocks in your system dynamics model. Each of these factors represents the physical characteristics of the disease and the social characteristics of the human population.  Your model will need to account for the way these factors impact the stock and flow dynamics of the SEIR model.

Here are the flows that impact the stocks.

• Catching the Disease flow: The daily rate at which Susceptible people catch the disease and move to the Exposed stock.
• Developing Symptoms flow: The daily rate at which Exposed people begin to show symptoms of the disease and move to the Infected stock.
• Recovering flow: The daily rate at which Infected people recover and move into the Recovered stock.
• Dying flow: The daily rate at which Infected people die. Have these people flow into an additional stock called Infected Deaths.

Listed below are other variables that affect the flows (and hence behavior of the stocks over time)

• Infectivity: This refers to the likelihood that someone who comes in contact with an Exposed or Infected person will catch the disease. We don’t know what the infectivity of an H5N1 virus might be. Some infectious diseases have infectivities near 100% (say, 0.9), while others are quite low. Suppose that the H5N1 virus could have an infectivity somewhere between 0.05 and 0.9.
• Contact Rate: This refers to the typical number of times an individual has the kind of contact with others that could place them at risk of catching the disease. This is expressed as the number of such contacts per person each day, and it reflects the social nature of the community ― how mobile and physically connected people are. In remote rural regions, the Contact Rate will be smaller than in a large crowded city or on a college campus. In the case of the common flu, contacts involving only near proximity to an infected person is all that is necessary.  In other types of diseases like HIV, more intimate physical contact is required in order to contract the disease.  The higher the Contact rate, the more chances that a Susceptible person will come into contact with Exposed or Infected people, and the greater the chances that they will get sick.  Assume that this contact rate is somewhere between 1 and 10 contacts per person each day.
• Infected Population – The number of people in Smallville that are contagious and could pass the disease to others. This would be the total number of Exposed and Infected people.
• Fraction of Population Infected – The fraction of Smallville residents that are carriers of the disease and that can therefore pass it on to others. For example, suppose that only 1 out of 1000 people (0.1% of the population) were carriers. In that case, a susceptible person would be much less likely to have contact with a carrier than if 20% (1 in 5 people) were carriers.
• Number of Diseased Contacts per Susceptible – This stands for the average number of contacts with disease carriers that a Susceptible person has per day. It is a function of the number of Susceptibles and the Fraction of Population Infected.
• Initial Population: The number of people living in Smallville. This variable is important because it determines the initial number of Susceptible people.
• Current Smallville Population: This is the number of people in Smallville, after subtracting the number of deaths from the disease.  This number is also used to calculate the Fraction of disease carriers at any point in time (calculated as the ratio of total Exposed and Infected to the Current Smallville Population.
• Incubation Time: The amount of time it takes for an Exposed person to start showing the symptoms of the disease. For diseases like HIV, the Incubation Time can be years. For the flu, the Incubation Time is a matter of days. During the Incubation Time, the victim is already contagious.
• Recovery Time: the average amount of time it takes someone to recover from the disease. In the case of some diseases (HIV) no one ever fully recovers. In the case of flu viruses like H5N1, the Recovery Time can be a few days to a few weeks. For this problem, assume that the Recovery Time is somewhere between 10 and 25 days.
• Daily Death Fraction: The fraction of Infected people who die from the disease each day. Because 60% of past H5N1 victims have died (over what typically a 15-day battle with the disease), CDC epidemiologists estimate that the Daily Death Fraction could be somewhere between 0.03 and 0.20.

Extending Your Model to Account for Policies

Now that you’ve built a model that mimics the behavior of a typical infectious disease outbreak, you can add features to the model to account for the policies that your decision maker (Dr. Constantine) wants to consider. Later we’ll discuss how to add features to the model to also  account for the concerns and interests of the other stakeholders. Together these additions will provide a means for evaluating the impact of different policies in light of the concerns and interests of all the stakeholders.

Dr. Constantine wishes to evaluate which of the following policies (or combinations of policies) offer the most hope for an effective response to a possible outbreak of H5N1.  We briefly outline them here and then provide you with some guidance on how to add structure to the model to account for these.

• Policy option #1 – Inoculation: Develop a vaccine for H5N1 (estimated cost: $200 million) and use it to inoculate the population. Inoculation effectively removes people from the Susceptible stock and places them into a new Inoculated stock from which they cannot contract the disease.
• Policy option #2 – Quarantine: Place in quarantine those individuals showing disease symptoms. The quarantine would last until they recover (or die).
• Policy option #3 – Social Distancing: Promote social distancing (self-quarantine) by providing daily updates on news media and by distributing to the public resources such as face masks and antiseptic hand cleansers. This effectively reduces the contact rate for those who participate in the social distancing effort.

Monitoring Stakeholder Interests via the Balanced Scorecard

The final step is to add features to the model that will account for the interests of the stakeholders and that will provide information that can be used to construct a balanced scorecard by which Dr. Constantine can evaluate the various policies she considers.

The core stock and flow structure you’ve developed so far is shown in Figure 39 below. We will refer to this diagram to flesh out the next steps in the model building process. In order to keep things readable, this diagram omits many causal links and variables that are in that full model up to this point.

It is clear from the above exercise that we have to add some features to the model to account for the cost of the public health response to an outbreak, as well as features that account for the flow of people into and out of the hospital during the outbreak.

Creating an interface with a balanced scorecard

Now it is time to build an interface that allows your decision maker, Dr. Constantine to explore policy options, and evaluate them using the balanced scorecard. In general, your interface should provide two types of control knobs.  One type corresponds to those policies that the decision maker wishes to evaluate. Let’s call these control knobs the policy knobs.  By adjusting these, the policymaker can turn certain policies “on” or “off” and can conceivable adjust parameters that are potentially under their control to fine tune those policies.

The other type of control knob are those that represent external conditions or assumptions about the system whose exact values are unknown. Let’s call these external condition knobs.  The policy maker wishes to know if the policies they choose are unnecessarily dependent on assumptions or values that are not known with great precision. Policies that meet this requirement are said to be robust with respect to external conditions.  For example, consider these two cases:

• Case 1: Policy A gives outstanding results under a particular set of assumptions, but gives terrible results if any of those assumptions are off by even a little bit.
• Case 2: Policy B gives good conditions (but not as good as A under some conditions). In addition, the benefits from this policy (compared to others) are reliable, regardless of the external conditions.

In this situation, Policy B is more robust with respect to the external conditions than is Policy A. Hence, it would clearly be preferred over Policy A.

It’s now time to create a user interface for your client, Dr. Constantine. This interface should allow Dr. Constantine to do the following:

• Try out the following three policies (or combinations of them) for responding to an H5N1 outbreak in Smallville. This will be done by providing policy control knobs for Dr. Constantine to adjust.

1. 1. Inoculation: Develop a vaccine for H5N1 (estimated cost: $200 million) and use it to inoculate the population. You will provide the following policy control knobs:
      1. Inoculation switch (to turn the policy on or off)
      2. Deployment time (can be shorter or longer by subtracting or adding resources to the team responsible for inoculating the citizens)
      3. Vaccine effectiveness (can be raised through a more expensive vaccine development program)
   2. Quarantine: Place in quarantine those individuals showing disease symptoms. The quarantine would last until they recover (or die). The policy control knobs for this are:
      1. Quarantine switch (to turn the policy on or off)
      2. Quarantine delay time (can be shorter or longer, depending on how many resources are applied)
   3. Social distancing: Promote social distancing (self-quarantine) by providing daily updates on news media and by distributing to the public resources such as face masks and antiseptic hand cleansers. Here are the policy control knobs:
      1. Social distancing switch (to turn the policy on or off)
      2. Effect of Total deaths on daily contacts. This is a graphical function whose shape can be affected by changing how aggressive are the media campaigns to update the public and by changing the resources dedicated to distributing tools like face masks and disinfectant cleaners to avert spread of the disease. More aggressive efforts and more resources will lead to a steeper curve in this graphical function.

• Evaluate each policy (or combinations of those policies) against a balanced scorecard. From an earlier activity we learned that the balanced scorecard should be comprised of the following collection of BOTGs. In each case, we describe the relevance of the BOTG, the stakeholders who are interested in it, and what they would like to see (i.e. their “hopes” for this BOTG).
  • 1. #H5N1 cases each day: BOTG of the total Exposed + Infected stocks. This shows how fast the disease is spreading and how long an epidemic might last.  A rapidly-spreading disease is much more difficult to handle than a slower-spreading epidemic.
    2. Total #H5N1 cases so far: BOTG of the sum of Exposed, Infected, Quarantined, Hospitalized, Recovered, and Total Deaths. This is an overall measure of how severe the epidemic was. At the end of the day, the more people who got the disease, the worse things are for the town. Dr. Constantine would like to keep this value as low as possible.
    3. #Deaths: BOTG of the Total Deaths. Dr. Constantine and all the stakeholders are concerned about this and want to keep deaths to a minimum.
    4. #Requiring hospitalization: BOTG of the Hospitalized stock. Recall that the Smallville Director of public health is worried that the two hospitals in town may not have the capacity to handle the number of patients during a disease outbreak. The two hospitals have 520 beds between them. Hence, if the #requiring hospitalization exceeds 520, there will be a problem.
    5. Cost: BOTG of Total Healthcare Cost. The Blue Diamond/Blue Square health insurance company is concerned about high healthcare costs from an epidemic, and would support policies that keep these costs as low as possible.
    6. #Inoculated: BOTG of the Inoculated stock. The Medicine No More citizen group is opposed to vaccinations in general. The higher this BOTG goes, the more concerned they will be.
    7. #Quarantined: BOTG of the Quarantined stock. The citizens of Smallville are concerned that a heavy-handed quarantine policy will infringe on their freedom of movement.
• Test how robust her best policies are against changes in those conditions or assumptions that we don’t know for certain. This will be done by providing several external condition knobs that Dr. Constantine can adjust and see how the policies do under differing conditions. For the purposes of this case study, we will provide the following external condition knobs on the interface.
  1. Infectivity. How will the policies do if the infectivity of the H5N1 virus is higher or lower? Use a default value of 0.05, but allow this to be adjusted from 0.01 to 0.9
  2. Baseline Contact Rate. What if this is higher or lower? How would that impact the relative effectiveness of the policies? Use a default of 5 contacts per person each day, but allow it to be adjusted between 1 and 10 contacts.
  3. Daily Death Fraction. What if the disease were more deadly? Less deadly? Use a default of 0.05, but allow it to be adjusted between 0.02 and 0.2
  4. Incubation Time. What if it takes shorter or longer for someone to begin to show symptoms after they have contracted the disease? Use a default of 3 days and allow this to be adjusted between 2 and 12 days.
  5. Daily Fraction Quarantined Who are Hospitalized. Use a default of 0.05 and allow it to be adjusted between 0.1 and 0.5.
  6. Daily Fraction Infected Who are Hospitalized. Use a default of 0.2 and allow it to be adjusted between 0.1 and 0.5.
  7. Dosage Cost. Use a default of $200, but allow to vary between $50 and $300.
  8. Per Patient Hospital Cost. Use a default of $3,500 and allow to vary between $1,500 and $10,000.

5. Stages 3 and 4 Exploring Options and Building Alignment

The worksheet below corresponds with the different BOTGs you have created. The critical information is in those BOTGs, reflecting how behavior has changed over time. Use Table 1 to track whether the policy has improved, stayed the same, or worsened based on the key variables you identified.