Context Seminar on March 15, 2011

1. Olga JonasAvian and Human Influenza Operational Response Coordinator ContextSeminar on March 15, 2011 www.worldbank.org/flu Substantial impact – severe pandemic case cost 4.8% of GDP or $3 trillion … not “if”, but “when”… small probability, possibly catastrophic event … “once-in-40 years”? Effective & efficient measures to reduce impact: ** Prevention - especially control at the animal source (externally financed expenditures $0.3b/year and falling) ** Mitigation - seminar today Global/international … national … local

2. Policy Response to Pandemic Influenza: The Value of Collective Action Maureen Cropper, RFF and UMd Georgiy Bobashev, RTI Joshua Epstein, Johns Hopkins Stephen Hutton, UMd and WBG Michael Goedecke, RTI Mead Over, CGD

3. Motivation for the Research • Concern in the World Bank following SARS and H5N1 • That a pandemic (such as human-to-human transmission of H5N1) would begin in developing countries • How high would attack rates be in developing countries? • How effective would measures to reduce transmission be? • Desire to compensate developing countries for measures taken to prevent influenza transmission • Can be justified on basis of externalities—how large are they? • How much does treatment in one country (e.g., using anti-virals) reduce the attack rate in other countries?

4. Research questions • In the event of an influenza pandemic: • What would happen to poor countries in a world in which only rich countries have stockpiles of anti-virals (AVs) sufficient to treat their populations ? • What are the effects of rich countries providing AV stockpiles to poor countries: • On the Gross Attack Rates in poor countries? • On the Gross Attack Rates in rich countries? • How do these answers vary depending on how stockpiles are distributed (to many countries or to outbreak country)? • Are the benefits to rich countries sufficient to justify these actions—or must they be motivated by altruism?

5. Methods • Simulation of flu epidemics using two approaches: • A two-region model (rich region – poor region) • Look at size of externalities from treatment in poor region on rich region (and vice versa) • Look at Anti-viral stockpiles each region will choose to hold • A detailed global model (GEM) that includes 4 age groups, 106 countries and regions, rural and urban populations, 283 airports, 7831 airline connections and seasonal variation in human susceptibility • Use to examine plausible stockpile scenarios

6. Preview of answers • In a Two-Country Model: • Poor country may rationally choose a zero stockpile • It may benefit the rich country to pay for an AV stockpile in the poor country • In a Global Epidemiological Model : • Plausible scenarios of antivirus stockpiles can significantly reduce 1-year global attack rates • Results sensitive to start date, virulence, AV efficacy, proportion of people who can be treated • Rich countries can reduce own attack rates by paying for additional antivirus doses in poor/outbreak countries

7. Overview of talk • Begin with single-country influenza model • Review dynamics of influenza and optimal AV stockpile • Look at two-country (“poor-rich”) model of flu transmission • Present global epidemic model (GEM)

8. One city model

9. SIR models • Core epidemiological model has Susceptible, Infected, Removed. These evolve over time by: • Key parameter: Reproductive rate R0 = β/δ

10. SIR Model Continued • Pandemic develops if and only if dI/dt > 0 at t=0 dI(t)/dt = βS(0)I(0) – δI(0) > 0 βS(0) – δ > 0 Since S(0) = 1 need β/δ ≡ R0 > 1 for pandemic to develop • Higher is R0, greater the gross attack rate, R(∞) = 1 - S(∞) • Nextslide shows example ofR0 = 1.5

12. Treatment with anti-virals Anti-virus (AV) treatment: • AVs used to treat infectious cases • Reduces infectiousness (lower effective β) by efficacy e for Infected cases who receive treatment • What is optimal proportion of cases (p) to treat?

13. Optimal AV Policy in an SIR Model • Suppose that the proportion of infectious people receiving an AV must be chosen before the epidemic begins: • β′ = β(1-p*e) where e is the proportionate reduction in β from AV treatment • The marginal benefits from increasing p are increasing in p • This follows from the fact that reducing R0 increases S(∞) at an increasing rate • If cost per AV is constant, choose either p = 0 or p = 1

14. There are increasing returns to reductions in the reproductive rate Gross Attack Rate (1 – S(∞)) 1 0.8 0.6 0.4 LN(1 - GAR) = R0·(GAR) 0.2 0 1 2 3 Reproductive Rate R0

15. Optimal stockpile size in an SIR model • Suppose that there is some upper limit on p, the proportion of infected people who can be treated, such as 60%. • This reflects limits to health delivery system and ability to identify infected people • Suppose that stockpile must be acquired before pandemic • Optimal stockpile is either to have stockpile sufficient to treat 60% of people for the entire pandemic, or zero. • In current example (β = 0.3 and δ = 0.2) when e = 0.4, maximum stockpile that will be used is roughly 15% • 15% stockpile reduces GAR from 58.4% to 24.1%

16. Impact of stockpile size on attack rate

17. A 2-city model a a

18. Pandemic dynamics:2 city model

19. Attack rates in a 2-city modeldepend on each city’s stockpile

20. Optimization in a 2-city model • Cities act to minimize antivirus costs + morbidity costs • Cities choose P* to solve: Min: VR(∞) + cP* • V is the cost of an influenza case • c is the cost of an antivirus dose • Minimization problem gives best response functions, PA (PB) and PB(PA) • V will vary by city: if A is poor and B is rich, VA < VB • Results depend on relative sizes of VA , VB, c

21. Case A: VA = VB = 100, c = 10 Nash equilibrium = social optimum

22. Case B: VA = 3, VB = 100, c = 10Nash equilibrium = suboptimal

23. Conclusions: 2-city model • If only one city treats, it benefits, but benefits to the other city are small • If both cities treat, they do better than either treating alone • But, cities may not chose this as a private optimum • Pareto improvement can be made where rich country pays for additional antivirus stockpile in poor country • This result depends on particular parameter values; it does not hold in general, it may not hold in a larger or more realistic model

24. Global Epidemiological Model • Divides the world into 106 regions • Regions are medium-large countries or groups of small countries in the same region (e.g. “Rest of Western Africa”) • 86% of world population lives in a country that is its own region • Each region has one or more cities with an international airport and one “rural” area • Rural area includes all population in a region who do not live in one of the airport cities • In total, there are 283 cities and 103 rural areas • Total world population is roughly 6.5 billion, of which roughly 89% is allocated to a rural area.

25. Sample network with 3 regions Region 2 Region 1 C22 C21 C12 C13 R2 C11 R1 Region 3 R3 C31

26. Modeling the network • Disease spreads through internal mixing within a city and travel of exposed and asymptomatic infectious among cities • Movement between cities is based on airline passenger data (average number of seats per day between airports) • Movement between cities and rural areas is assumed to be 1% of the urban population per day • Assume no cross-border travel between regions, other than through airline travel • Uniform mixing occurs within cities; all people are identical (except by age group and disease state); contact rates differ by age

27. Disease Spread in Each City • Disease spreads according to SEIR model in each city (exposed category added) • Four age categories (0-4, 5-14, 15-64, 65+) • Contact rate matrix based on Mossong et al. (2009); varies with population density • Probability of infection given contact varies with latitude and season • Probability of infection greater near the equator • Probability of infection greater in winter • People remain exposed for 2 days, infectious for 5 days (on average)

28. Baseline (No Intervention) Results • Group countries by per capita income: • Poor countries: Below $3,000 (2.84 billion people) • Lower Middle: $3,000 - $10,000 (2.16 billion people) • Upper Middle : $10,000 - $20,000 (515 million people) • Rich countries: > $20,000 (915 million people) • Next slide shows Gross Attack Rates at end of Year 1 • Assume: • Pandemic starts in Indonesia • R0 = “moderate” (~1.7) [P(Transmission|Contact) = .0533] • Show results for January 1 and July 1 start dates

29. Baseline (No Intervention) Results

30. Seasonality assumptions

31. Implications of seasonality 1

32. High Implications of seasonality 2 Upper mid Lower mid Poor

33. Baseline (No Intervention)Dynamics

34. Anti-Virus Scenarios • Nature of anti-viral administration • AV reduces infectiousness by 60% and length of infection by 1 day • Requires stockpile, as in 2-city model • 50 percent of symptomatic infectious persons treated until stockpile exhausted • Treatment begins after 100 cases detected • Treated on second day of symptoms • Compare and contrast the following stockpiles (% of population): • 0/0/5/10 in Poor/Lower Middle/Upper Middle/Rich • 0/1/5/10 in Poor/Lower Middle/Upper Middle/Rich • 1/1/5/10 in Poor/Lower Middle/Upper Middle/Rich

35. Antivirus scenarios: Number of AV doses

36. Impact of AV scenarios depends on • Infectiousness of the flu • P(T|C) = 0.0533 [moderate R0] • P(T|C) = 0.060 [high R0] • P(T|C) = 0.045 [low R0] • Any AV control strategy will be more successful the lower the R0 • When the flu starts • Flu is much milder world-wide if it starts on January 1 than on July 1 • AV controls more effective for a flu starting in January than in July • Nature of anti-viral administration • Percent of symptomatic infectious persons treated (50% or fewer) • Whether infectiousness is reduced by 60% (or 50%)

37. Results 1: Antivirus reduceslocal attack rates

38. Results 2: High sensitivityto virulence

39. Results 3: Health infrastructure matters

40. Results 4: Payoff to rich countries from providing AVs

41. Closing questions and comments • Containment is the best solution (but rarely feasible) • Pure self-interest case for rich countries to pay for some antivirus for poor outbreak source, if this is additionalBUT: Externality size moderate • Large benefits from improving health infrastructure (increase % cases treated) • Previous results in the literature suggest larger benefits of stockpile donations • These results depend on rapid delivery of AVs to 70% of symptomatic infectious on day 1 of infection • More research on seasonality needed