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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 2000.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Outbreak dynamics
I(t)
Day
Pro
po
rtio
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
Pro
po
rtio
n
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 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*
Att
ac
k 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
Pro
po
rtio
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
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
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 m
ultip
lier
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
Att
ac
k r
ate
-50 -25 0 25 500.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
July 1 start
Latitude
Att
ac
k r
ate
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