The Role of Mental and Mathematical Models in the Debate of Control vs. Eradication of Diseases

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 • Modeling control vs. eradication of polio • Modeling heuristics for resource allocation • Insights and questions

3. Polio eradication • Poliomyelitis causes by virus • 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 • 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: • Globally, risk factors positively correlated: • 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 • Surveillance • Polio-specific: • Large number of asymptomatic infections • Poor vaccine performance in some areas • Vaccine-derived polioviruses • Concerns about bioterrorism after eradication (since 2001) • Rumors and conspiracy theories • Not to mention the financing …

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

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

9. Tough questions • Why spend so much on a disease that is so rare? • 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 • Must prioritize “cost-effective” interventions (CI - CSQ) Cost-Effectiveness Ratio = ---------- (HSQ - HI) where CI = Cost of intervention CSQ = Cost of status quo HI = Health outcome of intervention (e.g. # cases, # deaths, amount of disability) HSQ = Cost of status quo • Low CE ratio is good, high CE ratio is bad

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

12. What does SD have to do with polio? • Virus spread involves stocks (susceptible people, infected people, etc.), flows (infection, recovery), feedbacks, and delays • So does policy • 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 • Model poliovirus transmission in Northern India • Compare 2 policies • Control: commitment to intense vaccination activities “wavers” when CE ratio perceived too high • Eradication: 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 • Realistic control and post-eradication scenarios  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 Figure from Thompson and Duintjer Tebbens (2007)

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

20. Renewed commitmentsquotes 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) • Yellow fever: 1915 – 1930s (abandoned) • Yaws: 1954 – 1965 (abandoned) • Malaria: 1955 – 1969 (abandoned) • Smallpox: 1958 - 1980 (successful) • Polio: 1988 - ?? • Dracunculiasis (Guinea worm): 1991 - ?? • 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: • Single population • Two hypothetical eradicable diseases with equal properties • Begin with both diseases at endemic equilibrium • Assume given budget for managing both diseases • Evaluate different heuristics (decision rules) for resource allocation

24. Modeling issue • Continuous time ODE models assume: • Infinitely dividable stocks • Deterministic “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 numbers • Transition times are stochastic  Method of Gillespie (1976)

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

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

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

28. Model inputs - based on Edmunds et al. (1999) Budget equals 1.5 times budget needed to eradicate one of the two diseases

29. Consider 5 heuristics • Decision rules for “control” policies: • C1: Even resource allocation • C2: Full resource allocation towards most pressing disease • C3: Resource allocation proportional to perceived incidence • Decision rules for “eradication” policies: • E1: Cease vaccination after infection prevalence reaches 0 • E2: 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 “Fire-fighting” First stochastic iteration shown

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

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 Averaged over 100 iterations

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

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

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

39. Conclusions • In public health and beyond, decisions really are based on models • Mental models subject to poor heuristics, which can lead to sub-optimal decisions • Mathematical models also imperfect, but positively contribute to debates because… • They require explicit assumptions • They can adequately deal with stocks, flows, feedbacks, and delays • They 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