Context Seminar on March 15, 2011 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 Olga Jonas Avian and Human Influenza Operational Response Coordinator

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

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?

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?

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

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

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)

One city model

SIR models Core epidemiological model has Susceptible, Infected, Removed. These evolve over time by: (2) (3) Key parameter: Reproductive rate R 0 = β/δ

SIR Model Continued

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?

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 R 0 increases S(∞) at an increasing rate If cost per AV is constant, choose either p = 0 or p = 1

There are increasing returns to reductions in the reproductive rate Reproductive Rate R 0 Gross Attack Rate (1 – S(∞)) LN(1 - GAR) = R 0 ·(GAR)

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%

Impact of stockpile size on attack rate

A 2-city model  

Pandemic dynamics: 2 city model

Attack rates in a 2-city model depend on each city’s stockpile City B P* B = 0P* B = 15 City A P* A = , , P* A = , , 0.235

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, P A (P B ) and P B (P A ) V will vary by city: if A is poor and B is rich, V A < V B Results depend on relative sizes of V A, V B, c

Case A: V A = V B = 100, c = 10 Nash equilibrium = social optimum

Case B: V A = 3, V B = 100, c = 10 Nash equilibrium = suboptimal

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

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.

Sample network with 3 regions C 11 C 12 R1R1 C 13 R3R3 R2R2 C 22 C 31 C 21 Region 1 Region 2 Region 3

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

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)

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 – R 0 = “moderate” (~1.7) [P(Transmission|Contact) =.0533] – Show results for January 1 and July 1 start dates

Baseline (No Intervention) Results

Seasonality assumptions

Implications of seasonality 1

Implications of seasonality 2 High Upper mid Lower mid Poor

Baseline (No Intervention) Dynamics

Anti-Virus Scenarios Nature of anti-viral administration –A V 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

Antivirus scenarios: Number of AV doses Total doses purchased (millions) Marginal doses (millions) Baseline0.0 0/0/5/ /1/5/ /1/5/

Impact of AV scenarios depends on Infectiousness of the flu – P(T|C) = [moderate R 0 ] – P(T|C) = [high R 0 ] – P(T|C) = [low R 0 ] – Any AV control strategy will be more successful the lower the R 0 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%)

Results 1: Antivirus reduces local attack rates

Results 2: High sensitivity to virulence

Results 3: Health infrastructure matters

Results 4: Payoff to rich countries from providing AVs Rich country cases reduced per additional dose Transition Jan 1, Moderate Jan 1, High Jan 1, Low July 1, Moderate 0/0/5/10 → 0/1/5/ /1/5/10 → 1/1/5/ /0/5/10 → 0/0/5/ in Indonesia

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 additional BUT: 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