ContextSeminar 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

www.worldbank.org/flu

Olga JonasAvian and Human Influenza Operational Response

Coordinator

Policy Response to Pandemic Influenza:The Value of Collective Action

Maureen Cropper, RFF and UMdGeorgiy Bobashev, RTIJoshua Epstein, Johns HopkinsStephen Hutton, UMd and WBGMichael 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:

(1)

(2)

• Key parameter: Reproductive rate R0 = β/δ

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(∞)

• Next slide shows example of R0 = 1.5

0 20 40 60 80 100 120 140 160 180 2000.000.010.020.030.040.050.060.07

Outbreak dynamics

I(t)

Day

Prop

ortio

n

0 20 40 60 80 100 120 140 160 180 2000.000.100.200.300.400.500.600.700.800.901.00

Cumulative Infected

Susceptible

Day

Prop

ortio

n

Treatment with anti-viralsAnti-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 R0 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 R0

Gross Attack Rate (1 – S(∞))

1 2 3

1

0.4

0.6

0.2

0.8

0

LN(1 - GAR) = R0·(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

0 0.05 0.1 0.15 0.2 0.250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Stockpile size P*

Atta

ck r

ate

A 2-city model

aa

Pandemic dynamics:2 city model

0 20 40 60 80 100 120 140 160 180 2000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Contagion dynamics: No intervention

I_AI_B

Day

Prop

ortio

n

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

City B

P*B = 0 P*B = 15

City A P*A = 0 0.588, 0.579 0.579, 0.412

P*A = 15 0.419, 0.577 0.240, 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, 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

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

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.020.040.060.080.1

0.120.140.160.180.2

BR_BBR_A

PA*

PB*

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

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

BR_BBR_A

PA*

PB*

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

C11

C12

R1

C13

R3

R2

C22

C31

C21

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– R0 = “moderate” (~1.7) [P(Transmission|Contact) =

.0533]– Show results for January 1 and July 1 start dates

Baseline (No Intervention) Results

World Poor Lower middle

Upper middle

Rich0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000 Day 365 world attack rates

January 1 start date

July 1 start date

Seasonality assumptions

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

1.2

New York SFSingapore SFSydney SF

t (assuming t0 = January 1)

Infe

ctiou

snes

s mul

tiplie

r

Implications of seasonality 1

-50 -25 0 25 500.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

Jan 1 start

Latitude

Atta

ck ra

te

-50 -25 0 25 500.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

July 1 start

Latitude

Atta

ck ra

te

Implications of seasonality 2

-50 -25 0 25 50

Latitudes by income group

Latitude

High

Upper mid

Lower mid

Poor

Baseline (No Intervention)Dynamics

0 200 400 600 800 1000 12000

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

40,000,000

January 1 start date

WorldPoorLower MidUpper MidRich

Day number

Num

ber o

f cas

es

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

Antivirus scenarios: Number of AV doses

Total doses purchased (millions)

Marginal doses (millions)

Baseline 0.0

0/0/5/10 117.3 117.3

0/1/5/10 138.8 21.5

1/1/5/10 167.2 28.4

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%)

Results 1: Antivirus reduceslocal attack rates

World Poor Lower middle

Upper middle

Rich0

0.1

0.2

0.3

0.4

0.5

0.6

Attack rates: Effect of Antivirus

No AV0/0/5/100/1/5/101/1/5/10

Results 2: High sensitivityto virulence

High P(T|C) Moderate P(T|C) Low P(T|C)0

0.1

0.2

0.3

0.4

0.5

0.6

Global attack rate

Baseline0/0/5/100/1/5/101/1/5/10

Results 3: Health infrastructure matters

World0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

0.3500

0.4000

0.4500

0.5000

Attack rate: only 30% of cases treated in poor/lower mid income

baseline - no antivirals0/1/5/10, variable prop treat0/1/5/10, standard1/1/5/10, variable prop treat1/1/5/10, standard

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 → 0/1/5/10

0.37 0.00 0.74 0.33

0/1/5/10 → 1/1/5/10

0.18 -0.17 0.29 0.83

0/0/5/10 → 0/0/5/10 + 4.2 in Indonesia

0.52 -0.58 0.90 2.17

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