Pandemic Risk: Developing a Probabilistic View of...
Transcript of Pandemic Risk: Developing a Probabilistic View of...
Pandemic Risk: Developing a Probabilistic View of Possible Life Insurance Losses Dominic Smith LifeRisks
EBOLA HAS BEEN A WAKE UP CALL
HOW DOES A DISEASE LIKE EBOLA SPREAD?
t = 1 t = 2 t = 3 t = 4
WE USED A STOCHASTIC “SEIR” MODEL WITH INTERVENTIONS
S E I R σ γ
New cases are imported at rate μ Transmission rate per person per day β (starts at β0 and falls to β1 gradually after interventions with decay rate q) Transition rates from state to state Continuous Time Markov Chain (CTMC) model
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μ
SHOULD JAPAN BE WORRIED ABOUT CASES AT HOME?
NO
EMERGING INFECTIOUS DISEASE IS EVERYONE’S PROBLEM
EMERGING INFECTIOUS DISEASE IS EVERYONE’S PROBLEM
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EMERGING INFECTIOUS DISEASE IS EVERYONE’S PROBLEM
WHAT DOES AN EBOLA END-GAME LOOK LIKE?
PROBABILISTIC MODELING OF INFECTIOUS DISEASE
• 4,500 strategically sampled scenarios
• Every scenario identifiable in detail
• Distribution sets extreme tail risk (beyond 1-in-10,000)
• Well populated in the region of 1-in-200
• Based on verifiable parameters of virology and epidemiology
RMS EPIDEMIOLOGICAL MODEL
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0.5% Annual Probability (200 year return period)
RMS Synthetic Universe of Disease Scenarios
RMS INFECTIOUS DISEASE MODEL A probabilistic model of infectious disease risk, parameterized using an epidemiologic SIR model
to develop two event trees producing 2,016 flu events and 2,520 infectious disease events
Path
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Transmissibility and Virulence
Demographic Impact
Pharmaceuticals
Vaccine Production
Counter-Measures Public health countermeasures: quarantine, school closings, etc.
Vaccine timing and effectiveness
Effectiveness of antivirals and antibiotics
Matrix of Transmissibility / Fatality Rate Combinations
Age impact: seasonal, pandemic, residual immunity
Antibody
VirusHA
Insured Lives Mortality Differences Underwriting Differences
INFECTIOUS DISEASE MODEL DEVELOPMENT PROCESS
• Model development is an iterative process with model choices based on: • Historical calibration • Epidemiological and
statistical data and judgment • SIR modeling
• Cutpoints for various input parameters were chosen at inflection points in modeled SIR results to provide best representation of the spectrum of modeled outcomes
Historical DataData/literature from prior events
Medical DataResearch and publications from
leading specialists
SIR ModelStochastic model confirms
historic / medical data
Event SetCreates the Optimal Event set
• Annual probability of pandemic occurrence, parameterized by examining historical record
• Influenza (~3.6% per year) • Five influenza pandemics
in the past 120 years and 11 in the past 300 years
• Emerging infectious diseases (~1% per year) • ~1 emergent ID per
century
PANDEMIC FREQUENCY
Century Influenza Emerging Infectious Disease
14th ? Bubonic Plague 15th ? Typhus
16th 1510
Smallpox 1557-1558 1580
17th ? Measles
18th
1729-1730, 1732-1733
Yellow Fever 1761-1762 1780-1782 1788-1790
19th 1830-1831, 1832-1833,
1836-1837 Cholera 1889-1893
20th
1918-1919
HIV/AIDS 1957-1958 1968
1977-1978 21st 2009 Ebola. ??
TRANSMISSIBILITY • Transmissibility (infectiousness) represents the speed at which
a pandemic will spread within a population • Function of pathogen characteristics
o Incubation period: time between infection and symptoms o Latent period: time between infection and infectiousness o Attack rate: likelihood of infecting another person on
contact • Measured by basic reproductive number (R0) for influenza and
immunity threshold (IT) for emerging infectious disease
Recovered
Susceptible
Susceptible Incubation Period
Latent
Symptomatic Period
Duration Infectious Non-infectious
Date of infection Date symptoms begin Date of recovery
VIRULENCE • Virulence is a measure of the relative ability of a pathogen to
cause disease and mortality o Measured in terms of the case-fatality rate (CFR): fraction
of deaths per case Influenza • CFR ranges from 0.01% to 30% with long tail to cover spectrum
of potential fatality rates • Pandemics since 1900 have had CFR<2.5% in developed
countries • Includes possibility for H5N1 pandemic: CFR observed ~50% Emerging Infectious Disease • CFR ranges from 0.1 % to 50%, mean CFR higher than influenza • Captures measured CFRs from wide range of diseases:
o Ebola (50-90%), SARS (10%), Salmonella (<1%)
• In general, diseases with high virulence tend to have lower transmissibility since the dead and injured are not effective transmitters of the disease
• Worst-case scenario is an infectious disease for which subset of a population suffers high death rates when infected and another subset has high infection rates but does not suffer greatly o Black plague: fleas unaffected and
spread disease while highly virulent for humans
TRANSMISSIBILITY VS. VIRULENCE
INFLUENZA DEMOGRAPHIC PROFILES
• Three demographic mortality profiles for influenza: o Seasonal: affects youngest and oldest o Pandemic: larger impact on working age lives (cytokine
storm) o Residual immunity: impact relatively flat due to residual
immunity in order ages (can also include cytokine storm) Pandemic
Seasonal
RI
Year Name Demographic mortality
Seasonal 90% >65 years
1889 Russian
1918 Spanish >95% <65 years
1957 Asian 36% <65 years
1968 Hong Kong 48% <65 years
1977 Russian majority <20 years
2009 Swine 86% <65 years
2003 Avian majority in young
Historical Influenza Pandemics
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EMERGING INFECTIOUS DISEASE DEMOGRAPHIC PROFILES
• Three demographic profiles o Young &old: affects individuals with weak immune
systems (food-borne) o Flat: all ages affected by the disease equally (Ebola,
Black Death) o Middle-aged: primarily affects the working-age population
(Hantavirus)
Flat
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Middle Aged
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PHARMACEUTICALS Influenza • Two main sources of influenza pandemic deaths
1) Viral pneumonia due to influenza virus: treat with antivirals 2) Secondary bacterial pneumonia due to compromised immune
system: treat with antibiotics • 4 pharmaceutical categories, depending on whether
antivirals/antibiotics are available/effective Emerging Infectious Disease • Many different pathogens, many different pharmaceuticals • 4 pharmaceutical categories:
• Supportive care • Antivirals and antifungals • Secondary antibiomicrobials • Primary antibiotics and antiparasitics
VACCINES • Vaccine parameter applies a discount to account for the reduction in mortality/morbidity due to effective and available vaccines • Represented by the proportion of the population with immunity
to the pathogen • Includes residual immunity from previous exposure
• Timing of vaccine is key • Identification of strain • Development of vaccine • Testing for effectiveness and safety • Distribution
• Likelihoods linked to transmissibility and virulence • Vaccines unlikely to be ready in time to impact a highly
transmissible virus • More likely to encounter problems for a highly virulent virus but
more resources likely devoted
RMS LEADS THE INDUSTRY IN EXCESS MORTALITY MODELS
Year Issuer Coverage
2009 Vita Capital IV Series I UK, US
2010 Vita Capital IV Series II UK, US
2010 Vita Capital IV Series III & IV Canada, Germany, Japan, US
2011 Vita Capital IV Series V & VI Canada, Germany, UK, US
2012 Vita Capital V Series I Australia, Canada, US
2012 Mythen Re Series II US Hurricane, UK Mortality
2013 Atlas IX Capital Series I US