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

μ

μ

SHOULD JAPAN BE WORRIED ABOUT CASES AT HOME?

NO

EMERGING INFECTIOUS DISEASE IS EVERYONE’S PROBLEM

EMERGING INFECTIOUS DISEASE IS EVERYONE’S PROBLEM

0

1000

2000

3000

4000

5000

6000

4!-Nov 14!-Nov 24!-Nov 4!-Dec 14!-Dec 24!-Dec 3!-Jan

New Daily Cases

Date

Very pessimistic

Pessimistic

Optimistic

Very Optimistic

Realistic

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

0.0%

1.0%

2.0%

3.0%

4.0%

$ Billions

Annual Prob of

Exceedance

10 20 30 40 50

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

ogen

C

hara

cter

istic

s R

espo

nse

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

Rat

io o

f ave

rage

age

gro

up m

orta

lity

to to

tal p

opul

atio

n m

orta

lity

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

Young&Old

Middle Aged

Rat

io o

f ave

rage

age

gro

up m

orta

lity

to to

tal p

opul

atio

n m

orta

lity

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