1. The Role of Mental and Mathematical Models in the Debate of Control vs. Eradication of Diseases Radboud Duintjer Tebbens (Kid Risk, Inc.) Institute on Systems Science and Health Pittsburgh, PA, May 24, 2011

2. Topics Polio eradication – successes and challenges Polio eradication – successes and challenges Modeling control vs. eradication of polio Modeling control vs. eradication of polio Modeling heuristics for resource allocation Modeling heuristics for resource allocation Insights and questions Insights and questions

3. Polio eradication Poliomyelitis causes by virus Poliomyelitis causes by virus Virus ubiquitous and major cause of paralysis prior to use of vaccines (1955) Virus ubiquitous and major cause of paralysis prior to use of vaccines (1955) Eliminated and forgotten in most industrialized countries by 1980s, but still endemic in many developing countries Eliminated and forgotten in most industrialized countries by 1980s, but still endemic in many developing countries In 1988, World Health Assembly resolved to eradicate polio globally by year 2000 In 1988, World Health Assembly resolved to eradicate polio globally by year 2000

4. Images from WHO, Rotary International

5. Polio cases, 2011 (http://www.polioeradication.org/Dataandmonitoring.aspx)

6. Challenges to eradication Generic: Generic: Globally, risk factors positively correlated:Globally, risk factors positively correlated: High population density, high birth rates, hot & humid climate, poor hygiene all increase virus transmission High population density, high birth rates, hot & humid climate, poor hygiene all increase virus transmission War or political instability, poor health infrastructure all complicate access War or political instability, poor health infrastructure all complicate access SurveillanceSurveillance Polio-specific: Polio-specific: Large number of asymptomatic infectionsLarge number of asymptomatic infections Poor vaccine performance in some areasPoor vaccine performance in some areas Vaccine-derived poliovirusesVaccine-derived polioviruses Concerns about bioterrorism after eradication (since 2001)Concerns about bioterrorism after eradication (since 2001) Rumors and conspiracy theoriesRumors and conspiracy theories Not to mention the financing … Not to mention the financing …

7. circulating Vaccine-Derived Poliovirus Outbreaks (cVDPVs), 2000-2007* Type 1 2000-01 21 Cases Type 1 2005 46 Cases Type 3 2005-06 3 Cases Type 1 2004 2 Cases Type 1 2001 3 Cases Type 2 2001-02 5 Cases 2005 3 Cases Type 3 2005 1 Case 7 Contacts Type 2 2005 1 Case 2 Contacts Type 2 2005-07 84 cases Type 1 2006-07 4 Cases * data as of 20 November 2007

8. What about those costs? Polio eradication is a major project: Polio eradication is a major project: > 7 billion in donor funding (plus about as much by recipient countries)> 7 billion in donor funding (plus about as much by recipient countries) 20 million volunteers for National Immunization Days20 million volunteers for National Immunization Days Worldwide laboratory network and field surveillanceWorldwide laboratory network and field surveillance

9. Tough questions Why spend so much on a disease that is so rare? Why spend so much on a disease that is so rare? Don’t we need these resources to fight HIV, malaria, measles, etc? Don’t we need these resources to fight HIV, malaria, measles, etc?  “So far, it has cost $4 billion in international assistance and it has been estimated that eradication (including 3 years of follow up) could cost another $1.2 billion”  “We are concerned that international assistance for polio could have negative effects on other public health efforts.”  “We believe the time has come for the global strategy for polio to be shifted from ‘eradication’ to ‘effective control.’”  “As soon as the annual global number of cases is less than 500 and the number of nations with polio less than 10, all polio eradication elements should…[shift to control]. This strategy would sustain the benefits so far gained…”

10. Cost-effectiveness thinking Limited resources for health interventions Limited resources for health interventions Must prioritize “cost-effective” interventions Must prioritize “cost-effective” interventions (C I - C SQ ) Cost-Effectiveness Ratio = ---------- (H SQ - H I ) where C I = Cost of intervention C SQ = Cost of status quo H I = Health outcome of intervention (e.g. # cases, # deaths, amount of disability) H SQ = Cost of status quo Low CE ratio is good, high CE ratio is bad Low CE ratio is good, high CE ratio is bad

11. Mental models From Table 3 in Shiffman (2006) Sunk costs: Too much spent already Sunk costs: Too much spent already Static perception of CE ratio: Polio eradication looks cost-ineffective if you ignore the dynamics Static perception of CE ratio: Polio eradication looks cost-ineffective if you ignore the dynamics

12. What does SD have to do with polio? Virus spread involves stocks (susceptible people, infected people, etc.), flows (infection, recovery), feedbacks, and delays Virus spread involves stocks (susceptible people, infected people, etc.), flows (infection, recovery), feedbacks, and delays So does policy So does policy Literature suggests our mental models deal poorly with stocks, flows, feedbacks and delays Literature suggests our mental models deal poorly with stocks, flows, feedbacks and delays  SD-type simulation model useful

13. Wavering commitment Negative feedback loop with time delay

14. Modeling “static perception of CE ratio” Critical assumption: Eradication is technically feasible given sufficient political will Critical assumption: Eradication is technically feasible given sufficient political will Model poliovirus transmission in Northern India Model poliovirus transmission in Northern India Compare 2 policies Compare 2 policies Control: commitment to intense vaccination activities “wavers” when CE ratio perceived too highControl: commitment to intense vaccination activities “wavers” when CE ratio perceived too high Eradication: sustained commitment to intense vaccination until prevalence drops below 1Eradication: sustained commitment to intense vaccination until prevalence drops below 1

15. The poliovirus transmission model

16. Polio in Northern India “Control” policy: intense vaccination if perceived cost- effective, less intense vaccination if perceived CE ratio above “tolerable” threshold $10,000/case (Red line) “Eradication” policy: intense vaccination until no more infectious people (Blue line)

17. Full economic analysis All low-income countries; 20-year time horizon All low-income countries; 20-year time horizon Realistic control and post-eradication scenarios Realistic control and post-eradication scenarios Figure from Thompson and Duintjer Tebbens (2007)  Low-cost, low-cases option does not exist  Policy of control leads to either more cases, more costs, or both  Eradication best for public health, not just for polio

18. Bottom line  Economic justification to investing > $3 billion more to finish eradication  Much more if we include any WTP  Much, MUCH more if we include benefits to middle and high- income countries

19. pp. 362-363 … Follow up to our study

20. Renewed commitments quotes from http://www.cidrap.umn.edu/cidrap/content/other/news/jun1808polio.html Jun 18, 2008 (CIDRAP News) – The international coalition of health agencies dedicated to ending polio yesterday declared a "final push" toward the long-delayed goal of eradicating the disease. But its members coupled the announcement with a plea for millions of dollars in donations to fill shortfalls, and with an admission that the 20-year-old campaign continues to face stubborn challenges. "The greatest danger we have now is the danger of stopping too soon," Dr. Robert Scott, chair of The Rotary Foundation, said at a press conference. "We have to keep after this virus and finally eradicate it." Dr. Margaret Chan, the WHO director-general, said she is "committing the entire [WHO] to putting polio as our top operational priority,“ Yesterday's event showcased the launch of a "$100 Million Challenge," an effort to raise matching funds for a 3-year $100 million challenge grant given to Rotary in November 2007 by the Bill and Melinda Gates Foundation. The challenge is aimed at Rotarians, but the organization is also seeking contributions from nonmembers. "We cannot afford to not eradicate polio," Dr. Julie Gerberding, the director of the CDC, said at the press conference. "It's an economic imperative for us on a global basis. It's also a moral imperative."

21. Global disease eradication projects Hookworm: 1909 – 1920s (abandoned) Hookworm: 1909 – 1920s (abandoned) Yellow fever: 1915 – 1930s (abandoned) Yellow fever: 1915 – 1930s (abandoned) Yaws: 1954 – 1965 (abandoned) Yaws: 1954 – 1965 (abandoned) Malaria: 1955 – 1969 (abandoned) Malaria: 1955 – 1969 (abandoned) Smallpox: 1958 - 1980 (successful) Smallpox: 1958 - 1980 (successful) Polio: 1988 - ?? Polio: 1988 - ?? Dracunculiasis (Guinea worm): 1991 - ?? Dracunculiasis (Guinea worm): 1991 - ?? Future targets: few clear-cut but many potential candidates Future targets: few clear-cut but many potential candidates

22. Emerging theme Smallpox: “A deficiency of resources was a continual problem, which seriously jeopardized the international effort” (Fenner et al. 1988, p. 1358) Dracunculiasis: Watts (1998, p. 808) reports “Ministry of Health officials thinking that they could take the eradication goal of December 1995 as an accomplished fact and questioning the need to continue using scarce funds for dracunculiasis surveillance”. Malaria: “The problem is one of near-success in an environment with an excess of problems clamoring for attention” (Scholtens et al. 1972, p. 20) Yaws: “Partly because of the great success of the mass campaigns of the 1950s and 1960s, [including yaws is] are widely thought under control” and that since they are “not fatal and usually restricted to poor, remote, rural populations, they are not perceived to be high- priority problems by many decision makers” (Hopkins 1985, p. S338)

23. Modeling resource allocation for multiple vaccine-preventable diseases Simple model to focus on behavior: Simple model to focus on behavior: Single populationSingle population Two hypothetical eradicable diseases with equal propertiesTwo hypothetical eradicable diseases with equal properties Begin with both diseases at endemic equilibriumBegin with both diseases at endemic equilibrium Assume given budget for managing both diseases Assume given budget for managing both diseases Evaluate different heuristics (decision rules) for resource allocation Evaluate different heuristics (decision rules) for resource allocation

24. Modeling issue Continuous time ODE models assume: Continuous time ODE models assume: Infinitely dividable stocksInfinitely dividable stocks Deterministic “average” transitions ratesDeterministic “average” transitions rates  Stocks decrease exponentially, never reach absolute 0  To adequately capture (time until) extinction, we need to transform model such that Stocks are discrete numbersStocks are discrete numbers Transition times are stochasticTransition times are stochastic  Method of Gillespie (1976)

25. Multiple-disease model Based on standard SIR model (Edmunds et al. 1999) Based on standard SIR model (Edmunds et al. 1999) Subscripted by infectious disease number (ID i ) Subscripted by infectious disease number (ID i )

26. Multiple-disease model Immunization of fraction of susceptibles Immunization of fraction of susceptibles Waning of immunity Waning of immunity

27. Multiple-disease model Decision rules (here based on perceived incidence) Decision rules (here based on perceived incidence)

28. Model inputs - based on Edmunds et al. (1999) Model input [unit]Base case value Population size [people]10,000 Birth and death rate [1/year]0.02 Recovery rate [1/year]5 R 0 [dimensionless]5 Waning rate [1/year]0.2 Incidence perception time [year]1 Costs per successful immunization [$/people]10 Budget [$/year]132,000 Budget equals 1.5 times budget needed to eradicate one of the two diseases

29. Consider 5 heuristics Decision rules for “control” policies: Decision rules for “control” policies: C1: Even resource allocationC1: Even resource allocation C2: Full resource allocation towards most pressing diseaseC2: Full resource allocation towards most pressing disease C3: Resource allocation proportional to perceived incidenceC3: Resource allocation proportional to perceived incidence Decision rules for “eradication” policies: Decision rules for “eradication” policies: E1: Cease vaccination after infection prevalence reaches 0E1: Cease vaccination after infection prevalence reaches 0 E2: Cease vaccination after perceived incidence drops below 1E2: Cease vaccination after perceived incidence drops below 1

30. Decision rule C1: Allocate resources evenly to both diseases First stochastic iteration shown

31. Decision rule C2: Prioritize all resources to the disease with highest perceived incidence First stochastic iteration shown “Fire-fighting”

32. First stochastic iteration shown Decision rule C3: Distribute resources proportional to perceived incidence

33. Decision rule E1: Continue vaccination until number of infections reaches 0 First stochastic iteration shown

34. Decision rule E2: Continue vaccination until perceived incidence drops below 1 First stochastic iteration shown

35. Cumulative CE ratios Policy - decision ruleIncremental CE ratio after 20 years compared to no vaccination ($/prevented case) No discounting10% discount rate C1: Even resource allocation52.053.6 C2: Full resource allocation towards most pressing disease63.262.8 C3: Resource allocation proportional to perceived incidence53.054.4 E1: Cease vaccination after infection prevalence reaches 014.627.6 E2: Cease vaccination after perceived incidence drops below 141.757.7 Averaged over 100 iterations

36. Caveats Hypothetical example Hypothetical example Benefits of eradication depend on expected time until last case, which depends on: Benefits of eradication depend on expected time until last case, which depends on: Population size and heterogeneityPopulation size and heterogeneity Prior control effortsPrior control efforts Immunization intensity relative to threshold for eradication (optimal intensity exists)Immunization intensity relative to threshold for eradication (optimal intensity exists) Costs as f(vaccination rate)Costs as f(vaccination rate) Properties of actual disease are more complex and variable Properties of actual disease are more complex and variable For model of actual diseases, must address uncertaintyFor model of actual diseases, must address uncertainty

37. Insights Financing of eradication challenging despite promise of health and financial benefits Financing of eradication challenging despite promise of health and financial benefits Static perception of priorities may lead to economically sub-optimal outcomes Static perception of priorities may lead to economically sub-optimal outcomes Must remind stakeholders of long-term dynamics Must remind stakeholders of long-term dynamics Powerful analogy for other non-linear processes Powerful analogy for other non-linear processes

38. Emerging questions For what system properties do poor heuristics lead to suboptimal decisions? For what system properties do poor heuristics lead to suboptimal decisions? How do we optimally manage a “portfolio” of (dynamic) infectious disease? How do we optimally manage a “portfolio” of (dynamic) infectious disease? Dynamic optimization for this type of problem? Dynamic optimization for this type of problem? How does uncertainty affect resource allocation decisions? How does uncertainty affect resource allocation decisions?

39. Conclusions In public health and beyond, decisions really are based on models In public health and beyond, decisions really are based on models Mental models subject to poor heuristics, which can lead to sub-optimal decisions Mental models subject to poor heuristics, which can lead to sub-optimal decisions Mathematical models also imperfect, but positively contribute to debates because… Mathematical models also imperfect, but positively contribute to debates because… They require explicit assumptionsThey require explicit assumptions They can adequately deal with stocks, flows, feedbacks, and delaysThey can adequately deal with stocks, flows, feedbacks, and delays They can propagate uncertainty in a manner consistent with probability theoryThey can propagate uncertainty in a manner consistent with probability theory

40. Acknowledgements Kim Thompson TU Delft: Roger Cooke, Tom Mazzuchi, Dorota Kurowicka, Daniel Lewandowski CDC: James Alexander, Lorraine Alexander, Brenton Burkholder, Victor Cáceres, Steve Cochi, Howard Gary, John Glasser, Hamid Jafari, Julie Jenks, Denise Johnson, Bob Keegan, Olen Kew, Mark Pallansch, Becky Prevots, Hardeep Sandhu, Nalinee Sangrujee, Jean Smith, Peter Strebel, Linda Venczel, Steve Wassilak, Margie Watkins WHO: Bruce Aylward, Fred Caillette, Claire Chauvin, Esther deGourville, Hans Everts, Ulla Griffiths, David Heymann, Scott Lambert, Asta Lim, Jennifer Linkins, Patrick Lydon, Chris Maher, Roland Sutter, Chris Wolff, David Wood SDS: David Anderson, Ed Anderson, Bob Eberlein, Jay Forrester, Gary Hirsch, Jack Homer, Drew Jones, Bobby Milstein, Brad Morrison, Mark Paich, Nelson Repenning, George Richardson, Anjali Sastry, Roberta Spencer, John Sterman, Jeroen Strueben Others: Harrie van der Avoort, Francois Bompart, Laurent Coudeville, Walt Dowdle, Paul Fine, Van Hung Nguyen, Myriam Huninck, Tracy Lieu, Marc Lipsitch, Anton van Loon, Peter Wright

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42. Thank you