At Boeing, a major aerospace company, a team leader and his R&D group recently found themselves in uncharted territory as they faced a new project. They needed to create a leadership infrastructure to bridge the learning that happens in the workplace with more structured classroom learning. The framework would span multiple organizations, missions, locations, and personnel. The temptation to leap into action was hard to resist. But the project team realized that taking the time to develop an implementation strategy would help them to be more effective in the long run. In order to do so in a systematic way, they chose to develop an Operational Strategy Map to guide their efforts.

The Operational Mapping Methodology

Developing a map of strategy isn’t a new idea. Most organizational improvement methodologies (such as total quality management, reengineering, and the balanced scorecard) recommend some form of mapping in order to facilitate understanding of an organization and its processes. All mapping methodologies have benefits as well as limitations. Because maps are necessarily a representation of reality — and not the reality itself — it’s important to choose a framework that captures the essence of the system in a way that helps the organization most effectively navigate through the unfolding strategy.

The Operational Strategy Mapping (OSM) framework synthesizes elements from three disciplines — system dynamics, skilled facilitation, and balanced scorecard—to create a process and product that can enhance the creation and implementation of organizational change efforts (see “Operational Strategy Mapping”). Using OSM, a strategic planning and implementation team clearly articulates what the strategy should accomplish, how it works, and what unintended consequences might result. In the process of developing the map, team members generate understanding of, and commitment to, the overall plan.

System Dynamics. OSM uses system dynamics mapping and its underlying paradigm of the world. System dynamics incorporates two different visual languages: causal loop diagrams and stock and flow maps. In order to quickly get up to speed on the terminology and launch into the mapping process, groups may begin with causal loop diagrams. Causal loops can be extremely useful for eliciting important interdependencies that will impact and be impacted by the strategy.

Because OSM requires exploring questions such as “How does/will it work?” the strategy team will eventually need to build stock and flow maps to generate this “operational” focus. Although doing so may initially require a little more effort than creating causal loops, the value derived from this additional effort of differentiating between conditions and activities that change those conditions will dramatically increase the rigor and quality of any strategy discussions. Using stock and flow maps, groups can look at the factors inherent in the strategy that may contribute to unintended consequences during implementation.

OPERATIONAL STRATEGY MAPPING

The Operational Strategy Mapping (OSM) framework synthesizes elements from three disciplines — system dynamics, skilled facilitation, and balanced scorecard—to create a process and product that can enhance the creation and implementation of organizational change efforts.

The paradigm of system dynamics asks us to move from thinking about our organizations in terms of one-time events and isolated functions to considering them in terms of continuous, dynamic, integrated processes. To implement OSM, a team needs to look at the strategy as something that will unfold over time, with natural ebbs and flows, and will likely require adjusting in terms of the magnitude and timing of different elements. The system dynamics approach also suggests the need to identify forces that might slow or impede implementation. It offers guidance in predicting natural delays in the system; knowing about these delays is vital to generating an effective implementation plan.

Skilled Facilitation. Skilled facilitation, based on the work of Roger Schwarz, provides the framework for the process of building OSMs. It offers tools for assessing if the appropriate stakeholders are involved, how effective the group dynamics are, and how to facilitate conversations around building and testing the usefulness of the map. Because skilled facilitation applies an explicit approach to developing shared mental models (both about the content of the project and the group’s process), it is a natural fit with the system dynamics approach to mapping.

The Balanced Scorecard. The third discipline built into the OSM methodology, Kaplan and Norton’s Balanced Scorecard (BSC), has become popular for helping businesses and public-policy organizations build and revise visual strategic “bubble maps” as part of an ongoing, iterative learning process. The BSC’s four quadrant perspective — Financial, Customer, Internal Processes, and Learning — provides a useful guide for ensuring that the strategy map covers the organization’s different facets. (Although not all OSMs cover the four quadrants, groups should be conscious about choosing to eliminate one or more quadrants from the map.) However, the stock and flow language is better able to depict how processes work than “bubble maps” and can serve as the basis for computer simulation at a point in the future if the team finds this additional step helpful.

The steps for building an OSM are the same as those described for the BSC. In their book, The Strategy Focused Organization (Harvard Business School Press, 2000), Kaplan and Norton describe strategy management as following four principles:

1. Translate the Strategy to Operational Terms
2. Align the Organization to the Strategy
3. Make Strategy Everyone’s Everyday Job
4. Make Strategy a Continual Process

As you’ll see, the distributed learning team at The Boeing Company followed these steps as they developed and used an OSM.

Building an OSM at Boeing

The Boeing Company is an organization widely distributed across geographies, business segments, and product lines; it also includes several engineering disciplines. The decision to sponsor a leadership initiative in the company reflected an understanding that, although the culture focused primarily on formal learning events, more than 80 percent of learning and leadership development occurred on the job. The “Workplace Leadership Initiative” would integrate formal and informal learning and would support participants in pursuing their individual learning agendas on their own time. In turn, employees would contribute their own content/expertise through a personalized web site and a community space that would be integrated into the leadership program’s learning experience. Putting together the various pieces of the program was a challenging opportunity. The development team decided to create an Operational Strategy Map to help them “mentally simulate” how they might execute the initiative.

Translating the Strategy to Operational Terms. The first phase of developing the OSM was to get background information on the project and develop a “strawman” map of the strategy. Getting background information usually requires phone interviews with a few stakeholders/experts. This interviewing process serves two purposes: (1) Gathering information from throughout the system of interest, and

(2) Generating understanding and commitment from the stakeholders for the process and subsequent map.

For this project, the team leader possessed the knowledge to provide enough input for the initial map.

The team leader was concerned about the following areas of execution: creating the initial workplace leadership system, generating enthusiasm among potential users, and building support among senior managers (who might not be users, but who would likely encourage or discourage the use of the system among their staff). He had several hypotheses about how the system might work, but felt that the OSM process would force him to better articulate those assumptions, integrate the team’s assumptions more effectively, test the accuracy of the combined assumptions, and ultimately communicate them to management.

Based on initial conversations, the group chose to focus the core structure of the map on the system’s end users. In this case, the core structure (often referred to as the spinal cord or main chain of the model) assumes that users can move from being Unaware of the WL (abbreviation for “Workplace Leadership System”) to being Aware of and May Use WL. (See the section labeled “Core Structure” in the diagram “A Virtuous Cycle” on p. 4.) After experiencing the Workplace Leadership System, they might become an Advocate for WL — or they might become Resistant to WL.

The stocks and flows visually represent the movement of people from one state to another. The stocks (boxes) are the accumulation of people (how many in each state at any point in time), and the flows (circles) are the processes that advance people through the various stocks. The initiative would need to carefully manage the movement from Unaware to Aware and then ensure Advocates were generated while simultaneously limiting the flow into Resistant to WL. The team spent hours further defining attributes associated with the stocks: What type of person was in each stock? Is there a better name for the stock? Is there anything missing in the main chain?

After focusing on the stocks, the team was ready to begin thinking through strategic implications by analyzing what might drive each of the flows. They quickly realized that they couldn’t directly affect the stocks — they needed to design policies directed toward the processes that move people from one state to another. The group determined that they could have a direct impact on awareness by having focus groups and other public relations-type events. People would move into the Advocates stock through word-of-mouth; their experience with the WL system would influence the level of Advocates and Resistant folks, because the more positive the experience, the faster the rate of acquiring new Advocates.

As always happens, the team identified weaknesses in the draft map’s assumptions. Foremost among these was the map’s aggregation of the learning initiative’s attributes into a single stock. The team suggested three categories of attributes: Useful Content, Features, and Ease of Use. The discussion around the development of these features was heated. Through it, the team found an appreciation for the level of precision that OSMs bring to what’s often a fuzzy process.

As a result of the conversations to improve the assumptions in the map, the team identified a virtuous cycle they wanted to set in motion. An important element of the Workplace Leadership System is users’ ability to add their own content, wisdom, and expertise—and Advocates would likely contribute the most. The greater the content that the program has to offer, the greater participants’ overall satisfaction will be (the team called this the “Wow!” effect). High levels of satisfaction in turn create more Advocates. A nice loop to get going! The team realized, however, that a limit to growth for this loop would be the ease of use. If it’s not easy to add content, then Advocates probably will not do so, making it difficult to set the cycle into motion.

The team found that the mapping process surfaced a dark side of implementation that they hadn’t consciously discussed before: the buildup of folks resistant to the initiative. At first, the group was dismayed to think about the potential for Resisters to develop in

A VIRTUOUS CYCLE

An important element of the Workplace Leadership System is users’ ability to add their own content, wisdom, and expertise. The greater the content that the program has to offer, the greater participants’ overall satisfaction will be. High levels of satisfaction in turn will create more Advocates.

the organization. But after some discussion, they realized that because they now knew the possibility existed, they could look out for it.

Further, they decided that if budding Resisters were identified early enough and were listened to, two things would happen. First, they would likely have feedback that would improve the overall system. More importantly, they might move over into the stock of Advocates. The team believed that people who cared enough to be Resisters could become strong Advocates — the energy would just be directed differently. The team referred to this as an aikido approach to resistance: Rather than push directly back against critical feedback (the natural tendency of a design team), they would redirect the energy behind the criticism — and apply it to improving the product. The team also strongly believed that the process of listening would generate Advocates.

The group developed a large wall hanging with crisp high-resolution graphics. Over the course of a couple of weeks, they used the map in their meetings and presented it to managers and other stakeholder groups within Boeing. In discussions and presentations, team members were able to walk up to the map, point directly at the area of strategy they were describing, and quickly get everyone’s reactions.

As a result of these meetings, the map was modified slightly — yet the core structure remained the same. The team found they could present the map without the aid of the project consultant. In that sense, they owned the map, its assumptions, and the implications it had for their strategy — it provided a common framework that guided their discussions.

Aligning the Organization to the Strategy. The second step in the process is to align the organization to the strategy. The team did so by using the map to develop a team project plan. They focused on the flows in the map and assigned tasks to different individuals. Although the group could have used sophisticated project planning software, for this effort they imported snapshots of map segments into Excel worksheets and added roles and responsibilities (see “The Project Plan”).

Results from the Initiative

The project is still underway, but the team has already reaped several benefits from developing the OSM. The most significant impact is that the team focused their early effort on a seven-day process to set in motion a virtuous cycle around the project. The goal of this experiment was to learn as quickly as possible about potential Advocates and Resisters. The team tested the initiative’s ease of use, features, and useful content in order to assess the “Wow!” factor, identify the number of individuals in various categories, and analyze the quality of their experience in moving to being an Advocate or a Resister.

As a result of this exploration, the team reconceptualized the project’s web interface. If they hadn’t learned from this experiment with setting a virtuous cycle in motion, they might have wasted a large portion of their 2005 budget in trying to implement a system without thoughtful consideration of Advocates and Resisters.

The team was pleased to find that the map was still valid even after the shift in emphasis. This process confirmed that the level of aggregation was sufficiently useful, that is, it allowed them to examine the implications of their implementation strategy at a high level, without becoming so specific that they needed to modify the map every time they made minor modifications to the actual program.

Making Strategy Everyone’s Everyday Job. Another result of the OSM process was that the team developed a shared language. This terminology improved the quality of conversations, because it made implicit assumptions about the strategy explicit. It created an environment for making

THE PROJECT PLAN

The team developed a project plan by focusing on the flows in the map and assigning tasks to different individuals. They imported snapshots of map segments into Excel worksheets and added roles and responsibilities.

strategy everyone’s everyday job. When people pointed to a piece of the map to describe the impact of a certain proposal, everyone understood what they were referring to. Having a shared language also had the unintended benefit of increasing camaraderie.

In most cases of strategy development, management knows the underlying assumptions, but the implementation team is left in the dark. The OSM process integrates assumptions from the entire team. The group as a whole owns the strategy, the implementation, and of course, the results. Talk about empowerment!

Another benefit of the process was that the team found it easier to be brutally honest during implementation. For example, as word of the Workplace Leadership Initiative spread during the development of the map, the team not only heard from folks with a favorable impression of the project but also from those with an unfavorable view. In other circumstances, the group might have filtered out the negative input. But because the map suggested that they pay attention to potential resisters, and that by doing so they could generate a positive trend, the team accepted the early criticism and incorporated some of the constructive comments in their implementation plan.

Making Strategy a Continual Process. As part of continual learning, the Boeing team may choose to go into more detail in some areas of the map. They are exploring the potential benefits of developing simulation models of certain aspects. Further, the group may build additional maps or revise the current one. Even so, they will continue to use the OSM they’ve developed in building and implementing strategy for months to come.

Using the Methodology in Your Organization

If you’d like to use an Operational Strategy Map to help guide your strategic planning and implementation, here are a few things we’ve learned:

• You won’t get the map perfect the first time. The process of building the map is where the learning is. Create a prototype (what we’ve called the “strawman map”) as quickly as you can. Then let the strategy development team critique, modify, and ultimately own it. The process of their owning it will make it better. Trust us!
• Identify as quickly as possible the “main chain” of the map. Use the main chain to ask questions about how the system in question works and what might be some unintended consequences of any activities.
• Focus on analyzing the major dynamics in the map. In the case described here, the team focused on the major virtuous cycle for a week. They asked questions about it, tested its usefulness and likelihood of occurrence — and in the end, they developed a whole new approach to the overall project.
• Fit the map on one page if you can. The Boeing team struggled on occasion as it tried to add nuances to the map that added complexity. The understanding generated from these incremental add-ons was usually minimal. You can always create separate maps of more detailed processes at a later date.
• Once the strawman map has been developed, modify it only in the presence of the whole team. Otherwise, you will not have the buy in needed to implement any new insights. Plus, you’ll likely miss something important when making the change.
• Develop simulation models only to the point where doing so provides an adequate return for the time and money invested. The process of simulation modeling is often a laborious one; it may take months to develop a reasonably sophisticated computer model of the strategy. The siren call of “We’ll find the answer” often tempts teams to try to develop the Mother of All Models. But this quest can become a journey of diminishing returns, in that simulation modeling may not generate enough additional insight to be worth the investment. The team in this article will develop a few small models to deepen and refine their understanding of implementation dynamics.

The OSM methodology holds potential for all organizations. The process of developing a simple, one page stock and flow map of the organization’s strategy generates strategic insight and commitment to implementation. If your organization has been struggling to execute its strategy — or even to develop a good one — you will find building an OSM useful. It’s a perfect tool to get everyone on the same page so that when you come to a fork in the road, you’ll be more likely to take the better path.

Chris Soderquist (chris.soderquist@pontifexconsulting.com) is the founder of Pontifex Consulting. He consults to organizations and communities in order to build their capacity to create and implement sustainable, high-leverage solutions to their most strategic challenges. Mark Shimada (mark.s.shimada@boeing.com) is a program manager in The Boeing Company’s Leadership Development and Functional Excellence Group. He supports his peers to accelerate business results through extraordinary leadership development programs.

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Anticipating System Behavior

School districts are made up of many components, including district staff, individual schools, teachers and administrators within those schools, parent councils, and students. The sheer number and variety of these actors make it difficult to see their interdependence and to notice how an action in one part of the system affects the others. Add to this complexity policies originating from agencies outside the district, such as state education departments and the U. S. Department of Education, and the task of assessing how best to direct resources to meet students’ needs becomes almost hopelessly confusing.

Systems thinking and system dynamics tools, including casual loop diagrams, stocks and flows, and computer simulation, can shed light on the interrelationships among components and, perhaps more important, illustrate how outcomes may result from feedback loops rather than from simple, linear chains of cause and effect. These tools also make explicit the delays that often occur between a change in one component of a system and its effect on others. The interplay of feedback and delays can produce unanticipated system behavior, as shown by the mandating of smaller class sizes in California. When the legislature passed the new law, schools had to increase the number of classes they offered at each grade level to accommodate the same number of students. To do so, they needed to hire more teachers. Because becoming a teacher through traditional means requires at least four years of pre-service training, the number of teachers available fell short of meeting the needs of all schools. Suburban districts with greater resources filled their spots by recruiting teachers from urban districts, leaving those schools woefully understaffed. Proponents of the new law had failed to anticipate this unfortunate outcome of the change in class size.

By showing the potential behavior over time of multiple scenarios based on specific inputs, computer modeling offers policymakers and administrators the ability to visualize the long-term effects of specific decisions before those decisions are implemented. We can also use models to identify unexpected interactions between system components; ask “what if questions about changes in system parameters; run no-cost experiments that compress time and space; and reflect on, expose, test, and improve the mental models upon which we rely to make decisions about difficult problems. Thus, computer modeling could allow school-system leaders to make more effective decisions by building their understanding of long-term consequences of resource decisions in a complex environment.

Evaluating Professional Development Programs

To illustrate how a district can use computer modeling to analyze its options, I have created a simulation that explores the impact of professional development programs for teachers. Many school districts have responded to the call for better educational performance by implementing a standards-based curriculum. They offer professional development workshops to increase teachers’ ability to communicate this new curriculum to their students. The workshops are often formatted as multi-week summer programs.

Research has shown that teachers can learn to communicate the new curriculum through professional development training, so the question for a district is not whether summer workshops can build capacity, but whether they can do so for a critical mass of teachers in a reasonable time period. What factors play a role in this issue? Which workshops are most effective? What are the costs associated with this form of professional development? These questions are amenable to modeling because we can determine quantitative values for most of the important variables — such as the number of teachers in training and the turnover rate of teachers — and reasonable estimates for the qualitative variables — such as the effectiveness of the workshops and the relationship between the length of the workshop and the willingness of teachers to enroll in it.

I followed these steps to build the model:

1. Define the teacher stocks. All the teachers in the district fall into three stocks: Those who are not familiar with the standards; those who are attending a workshop to learn about the standards; and those who are familiar with the standards.

2. Establish the flow between stocks. Teachers who aren’t familiar with the standards can take a workshop to gain familiarity; teachers in the workshop may become familiar with the standards and move into the “familiar” stock or may not gain much from the workshop and return to the “unfamiliar” stock; and both “familiar” and “unfamiliar” teachers may leave the system each year.

3. Identify and assign values to the important system parameters and variables.

4. Incorporate funding components.

The model is based on the following assumptions:

• The number of teachers in the system remains constant at 10,000, and at the starting point, 10 percent of the teachers are already familiar with the standards-based curriculum. Workshops vary in length from one day to five weeks.
• Ten percent of the teachers leave and are replaced each year (with 10 percent of new teachers entering in the “familiar” stage), and the rate at which teachers leave the system is higher for teachers in the “unfamiliar” pool than in the “familiar” pool.
• In the baseline simulation, 1,000 teachers participate in the three-week workshop; this number can vary up or down by a factor of three.
• Fewer teachers participate in longer workshops, more in shorter ones. However, longer workshops are more effective. The initial success rate for teachers reaching the “familiar-with-standards” stage in a three-week workshop is 30 percent. This base rate increases linearly over time as more and more teachers (those for whom training was not effective the first time) retake the workshop.
• There are 25 teachers in each workshop. The cost of the workshop includes a stipend of $300/week/ teacher for each of 25 participating teachers and an additional cost of $2,500/week for the instructor, supplies, and space.

“Modeling Professional Development” illustrates the model’s basic features.

Analyzing Results

The simulation yields several non-intuitive results, the most important being that these workshops alone cannot adequately deal with the problem of building the necessary capacity in the teacher workforce. Even after 10 years of providing three-week workshops, only 52 percent of the teachers are skilled in presenting a standards-based curriculum — and this number includes teachers who were capable before they enrolled in the workshops. The results clearly show that the workshops do not produce a critical mass of teachers with the desired capabilities in a reasonable amount of time.

Another unexpected result of this analysis is that the five-week workshops result in the largest number of trained teachers over a 10-year period, even though the smallest number of teachers enrolls in them. Holding all else constant, approximately 5,200 teachers achieve the desired level of ability after participating in a five-week workshop, while only about 2,800 teachers reach this stage through one week workshops. The longer workshop is also the most cost-effective per teacher trained: $2,300 per teacher for a five-week workshop; $2,635 for a three-week workshop; and $3,100 for a one-week workshop.

We can generalize this kind of model to other areas of professional development, because the results are independent of the workshop content. Administrators have access to the quantitative data for their district (such as number of teachers in the system, distribution by length of service, teacher leaving rate, funding available for workshops) and can reasonably estimate values for the qualitative variables (such as percent of teachers who require specific professional development, workshop effectiveness, relationship of workshop length to teacher resistance and workshop effectiveness) from prior experience. Plugging these numbers into a computer simulation would give them a general tool for predicting the impact of a summer workshop on professional development in any content area.

Similar models could let stakeholders examine other questions, such as the impact of rationing workshop participation depending on teachers’ average time of service in the system.

Should administrators concentrate on those who will remain in the system longest, that is, younger teachers? Or is there value in offering training opportunities to experienced teachers, who can serve as opinion leaders in changing the system’s culture? This analysis could also be incorporated into an expanded model to include the use of mentors and school and web-based professional development. By exploring these variables as well, districts might come upon a formula for producing a multi-component professional development system with the capacity to bring a critical mass of teachers up to speed on new curriculum requirements in an acceptable time period.

As I hope I’ve shown here, computer modeling offers a valuable planning and decision-support tool for school districts. This approach permits “no-risk” analysis of competing policy choices and resource allocations and, while it does not offer definitive answers, it can help school-system leaders understand the impact of their decisions and guide them toward making better-informed allocations of scarce resources.

Daniel D. Burke, Ph. D., has a broad understanding of K-graduate educational systems. As deputy director for education, the CNA Corporation (CNAC), he leads the research and analysis activities of CNAC’s public education group. Before joining CNAC, Dan was a researcher in molecular biology and produced an extensive record of curriculum innovations. He also played an important role in the National Science Foundation’s K-12 education reform programs.

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A New Threat

SARS emerged this year as a previously unknown virus that is particularly virulent—it is easily spread and can be deadly. Because it kills approximately 15 percent of those infected—the rate is even higher among the elderly—health officials around the world have taken strong steps to mitigate the epidemic and to prevent the public from panicking. In Canada, the great majority of cases were concentrated in Toronto, the country’s largest city and capital of the province of Ontario. From its first news release on March 14 to the latest daily updates on the situation, the Province of Ontario’s Ministry of Health and Long-term Care (MoH, the main governmental department responsible for dealing with the outbreak) sought to inform the public about the progress of the disease and the measures taken to deal with it. Now that the outbreak in Toronto has been suppressed, we can appreciate the impact of this information on public perceptions of and reactions to this health crisis.

A clear and rigorous way to report and interpret data about the spread of infection would help people accurately assess the level of risk.

One element of the daily updates was the summary of relevant statistics on the number of cases of the disease. In keeping with the WHO’s style of reporting on epidemics, the MoH bulletins reported cumulative numbers, in this case the total numbers of probable and suspected cases and deaths to date. Each day, the media reported this cumulative total; some later reports also mentioned cumulative recoveries (referred to as discharges).

I can attest that it was difficult to know how bad the situation was becoming from the raw information being offered. Reporters did little to interpret the data, instead publishing stories about the public’s and their own reactions to the outbreak, to the problems of living under quarantine, and to the few cases of people breaking quarantine. The use of cumulative numbers of cases, discharges, and deaths—numbers that can only increase until the epidemic has run its course—was often confusing and misunderstood. Such information gave no sense of the progress of the disease for example, whether the numbers of cases or deaths per day were increasing, staying the same, or decreasing.

The MoH did eventually include the category of “active” cases in its reports, which gave the public a sense of how many people were currently infected. But confusion was heightened by occasional instances in which the MoH reported tens or even hundreds of potential cases with no clear indication of whether these numbers fell into the active or cumulative category. For the public, this confusion led to the panicked buying of high-quality respiratory masks, cancellation of several large conventions, reduced participation in social activities like sports and cultural events, and a slump in restaurant dining and tourism, with economic side-effects that are still being felt.

A Simple Model

In such public health crises, a simple stock and flow model could clarify the situation (see “Stocks and Flows of the SARS Epidemic”). The stocks would be the “Active” cases— “Probable” and “Suspect.” Their principal inflows would be “New Cases” of each sort discovered each day. The outflows would be the number of “Deaths” (a small figure; the total number in Toronto is 24 as of this writing) and the number of people who recovered from the disease each day, reported as “Discharges.” A final flow from “Suspect” to “Probable” cases would take care of the clinical difference between the two classes.

This model would define the primary data needed to represent different aspects of the outbreak:

• Its onset and its gathering speed with the number of new cases per day.
• Its control and eventual suppression when the number of new cases stays at zero for 20 days (twice the incubation period) and the number of active cases dwindles to zero.
• The requirements for treatment resources based on the number of active cases.
• The treatment success rate as shown by the number of discharges compared to the number of deaths.

All of this information is much more difficult, if not impossible, to assess directly from the current data stream provided by the standard reporting practices. It is not clear what part these difficulties in assessment played in the WHO’s unexpected and unprecedented decision to issue a travel advisory for Toronto (since rescinded). Nevertheless, confusion about the success that public health authorities were having in controlling SARS was certainly part of the issue and continues to inspire efforts to remove the stain on the city’s reputation as a safe place to visit and conduct business.

STOCKS AND FLOWS OF THE SARS EPIDEMIC

In a public health crisis, a simple stock and flow model could clarify the situation by distinguishing between the stock variables (“Suspect” and “Probable”), which give a snapshot of the situation at any given moment, and the flow (or rate) variables, which explain the day-to-day variations in the picture. For more information about stock and flow diagrams, go to www.pegasuscom.com/stockflow.html.

The discovery of a few suspect cases of SARS in Toronto on May 22 and the extension of the voluntary quarantine to a few hundred people demonstrate another element of the dynamic structure—potential but undetected cases. This category exists because of the lack of a precise test for the disease. Without an objective measure of who does or doesn’t have SARS, healthcare workers must make judgments, for example, that an elderly patient suffering from postoperative pneumonia does not have SARS, followed by a realization several days later that this patient does indeed have the disease. Unfortunately, this kind of significant delay in the discovery of problematic cases can perpetuate the epidemic and lead to large social and economic costs.

Using a simple stock and flow model to depict the course of future epidemics could better inform the public so they could make wise individual choices about how best to respond to the health threat.

Wise Choices

This model or a slightly more elaborate version could have reduced some of the confusion surrounding the raw, cumulative data reported during the outbreak. It would have clarified the important distinction between the stock variables, which give a snapshot of the situation at any given moment, and the flow variables, which explain the day-to-day variations in the picture. The usefulness of the stock and flow model is validated by the most recent news reports on the final success of the campaign. These reports include a graphical representation of the number of active cases. The diagram shows a downward trend at a varying rate since the peak of SARS cases on April 18 to May 15, the date of this writing. Such a graphic goes far in highlighting the pattern over time of the outbreak.

Finally, the stock and flow model would identify the important variables—the flows (“New Cases,” “Discharges,” and “Deaths”)—that have to be managed in order to control the outbreak and deal with its economic and social side-effects. For example, an increase in “New Cases” that is not soon matched by an increase in “Discharges” could be a signal to increase resources for treatment (“Discharges”) and quarantine (“New Cases”). Reports of decreasing numbers of active cases should be accompanied by estimates of the probable numbers of deaths or, more positively, by estimates of the probable number of recoveries so as not to give the false impression that success in suppressing the outbreak means no more casualties.

Toronto, like Vietnam before it and more recently Singapore, has shown that SARS can be contained by vigorous efforts to identify and isolate patients (in hospital or in quarantine). Using a simple stock and flow model to depict the course of future epidemics—such as the summertime threat of West Nile virus in North America—could better inform the public so they could make wise individual choices about how best to respond to the health threat.

R. Joel Rahn is recently retired as a professor in the Department of Operations and Decision Systems at Laval University. He has been active in teaching and research in system dynamics for over a quarter century.

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