Risk Assessment for the
National Emerging Infectious
Diseases Laboratories
Damon Toth, Ph.D.
Math 3600 – Mathematics
for Physicians
February 26, 2013
NEIDL Background: Basics

What?
―

Where?
―

B.U., funded by NIH
Why?
―

South Boston
Who?
―

National Emerging Infectious Diseases Labs
Study pathogens up to BioSafety Level 4
When? Good question…
2/30
NEIDL Background: Controversy

Fear of biological weapons
―

Bio-defense vs. Bio-offense
Location in downtown Boston
Population density
― Transportation accidents
― Terrorist target
―

Environmental justice
―

Impact on low-income / minority populations
Health of local population
3/30
NEIDL Background: Risk Assessment
2005/6:
RISK
ASSESSMENT
#1
2007:
RISK
ASSESSMENT
#2
20082012:
LAWSUITS
#1
REJECTED
BY COURTS
#2
REJECTED
BY NRC
RISK
ASSESSMENT
#3
4/30
NEIDL Background: Risk Assessment
Problems with previous risk assessments:
 Failure to evaluate “worst case scenario”
Release scenario severity
― Pathogen transmissibility
―

Failure to compare risk at other locations
―
Alternate sites were suburban or rural
5/30
Approach: Events + Consequences
Lab Accidents
Facility Failure
Natural
Disasters
Exposures
Initial
Infections
Secondary
Transmission
Transportation
Accidents
Malevolent
Actions
Event Sequence Analysis
Health Effects Analysis
6/30
Approach: Events + Consequences
Lab Accidents
Facility Failure
Natural
Disasters
Exposures
Initial
Infections
Secondary
Transmission
Transportation
Accidents
Malevolent
Actions
Event Sequence Analysis
(last week’s topic)
Health Effects Analysis
7/30
Approach: Events + Consequences
Lab Accidents
Facility Failure
Natural
Disasters
Exposures
Initial
Infections
Secondary
Transmission
Transportation
Accidents
Malevolent
Actions
Event Sequence Analysis
(this week’s topic)
Health Effects Analysis
8/30
Approach: Considered Pathogens

BSL-3 Bacteria
Bacillus anthracis
― Francisella tularensis
― Yersinia pestis
―

BSL-3 Viruses
Rift Valley fever virus
― SARS-associated
coronavirus
― 1918 influenza virus
―

BSL-4 Viruses
Andes hantavirus
― Ebola virus
― Lassa fever virus
― Marburg virus
― Nipah virus
― Junin virus
― Tick-borne
encephalitis complex
viruses
―
9/30
Transmission: Modeling Pathogens

SARS-associated coronavirus
―

1918 H1N1 influenza virus
―

Low transmission, high fatality, local vectors
Rift Valley fever virus
―

Highly transmissible, lower fatality (today!)
Yersinia pestis (plague bacterium)
―

Highly transmissible, high fatality
Mosquito-borne, risk of U.S. endemicity
Ebola virus
―
BSL-4, high fatality, scary!
10/30
Transmission: Small Outbreaks
Relatively likely event sequence:
Lab event
occurs
One worker
exposed
Event
undetected
or unreported
Exposure
leads to
infection
Worker
interacts with
contacts
Big question: Then what happens?
11/30
Number of Transmissions: Average
Basic Reproduction Number (R0)
“Average number of secondary cases a
typical primary case will cause in a fully
susceptible population”
If R0 >1
Infection will spread in the population
If R0 <1
Infection will die out in long run
12/30
Number of Transmissions: Variation
Problems with R0 for small outbreak:

Random effects are important
Individual transmissions differ from R0
― Outbreak can extinguish even if R0 >1
―

What if infected individual isn’t typical?
“Individual reproductive number” may differ
― Important for “worst case scenario”
―
Very high reproductive number = superspreader
13/30
Number of Transmissions: Factors

Biological factors
―
―

Sociological factors
―
―
―

Pathogen
Host (infected person and contacts)
Contact network of infected person
Behavior of infected person and contacts
Cultural factors (e.g. contact norms)
External factors
―
―
Environmental influences (e.g. weather)
Hospital and public health policies
14/30
Number of Transmissions: Math
Number of
transmissions
x
Transmissions
per unit time
Contacts per
unit time
x
Length of time
infectious
Length of time
infectious
x
=
=
Transmissions
per contact
15/30
Number of Transmissions: Factor 1
x
Length of time
infectious

x
Transmissions
per contact
Value influenced by
―
―
―
―

Contacts per
unit time
Biology of pathogen
Biology of infected person
Behavior of infected person
Treatment
Relatively easy to quantify
―
―
Data based on symptoms
Fit distributions to variation
16/30
Number of Transmissions: Factor 2
x
Length of time
infectious

x
Transmissions
per contact
Value influenced by
―
―
―

Contacts per
unit time
Network of infected person
Behavior of infected person, contacts
Public health measures
Open area of research
―
―
―
Demography, surveys, prox. sensors (!)
Network models, agent-based simulations
Virtual game worlds?
Lofgren & Fefferman, Lancet Infect Dis 2007
17/30
Number of Transmissions: Factor 3
x
Length of time
infectious

x
Transmissions
per contact
Value influenced by
―
―
―
―
―

Contacts per
unit time
Biology of pathogen (symptoms, viability)
Biology of infected person (shedding)
Behavior of infected person
Intimacy of contacts
Environmental factors
Difficult to quantify
―
―
Some experimental evidence
Contact tracing and surveys
18/30
Number of Transmissions: So How?
Higher-level approach
Use contact
tracing data
Fit distribution
to data
Number of
transmissions by
each infected
Draw “individual
reproductive
numbers”
Simulate chain
of transmissions
From best fitted
distribution
(mean R0)
Ref: Lloyd-Smith et al., Nature 2005
19/30
Number of Transmissions: Distribution
Variation for individual reproductive number
Use Gamma distribution
Mean R0
― Shape parameter k
―
k infinite
No variation
k =1
Exponential dist.
k <1
High variation;
Extremes more likely
k<1 best fit to data
Ref: Lloyd-Smith et al., Nature 2005
R0 = 3 for all
20/30
Number of Transmissions: Simulation

For each infected individual:
Draw individual reproductive number v
― Use v to draw number of transmissions Z
―
Z ~ Poisson(v) or Z ~ NegBin(R0,k)

Use branching process
Z=1
Z=2
Z=0
Z=3
Z=0
Index Case
Z=0
Z=0
21/30
Modeling for NEIDL Risk Assessment
Benefits of branching process approach
―
Captures stochastic extinction
o
―
Rarity of one person starting outbreak
Quantifies likelihood of “worst case scenario”
o
Superspreader in early generations
Straightforward way to capture variation
― Amenable to adding important details
―
o
o
Effect of public health intervention
Demographic characteristics
22/30
Modeling Example: Event Sequence
Lab event
occurs
One worker
exposed
Event
undetected
or unreported
Exposure
leads to
infection
Worker
interacts with
contacts
23/30
Example: SARS-CoV parameters



Early case(s): Transmissions from Negative
Binomial distribution: R0 = 3.0, k0 = 0.16
Later cases: switch to Rc = 0.7, kc = 0.071
Simulation results (# of public infections)
1 or more: 38%
― 10 or more: 21%
― 100 or more: 8.8%
― 1,000 or more: 0.2%
―
24/30
Approach: Events + Consequences
Lab Accidents
Facility Failure
Natural
Disasters
Exposures
Initial
Infections
Secondary
Transmission
Transportation
Accidents
Malevolent
Actions
Event Sequence Analysis
(this week’s topic)
Health Effects Analysis
25/30
Importance of exposure to infection

Lab accidents
E.g., centrifuge aerosol release
― Given number of organisms inhaled, what’s
the probability of infection?
―

Large scale event leading to “plume”
E.g., earthquake, faulty exhaust filter
― Given x people inhaling y particles, how many
develop infection?
― Important for site differences
―
26/30
Quantifying Dose Response

Key parameter: ID50 (Infectious Dose-50)
Dose at which 50% of exposed population
would develop infection
― Often based on animal experimental data
―

Extrapolate p(d) curves (probability of
infection given dose)
p(ID50) = 0.5,
― p(ID10) = 0.1,
― p(ID1) = 0.01, etc.
―
27/30
Dose Response Curve Formulas
Model
Lognormal or
“Log-probit”
Exponential
Details
 Traditional model in toxicology
 Parameter 1: ID50
 Parameter 2: probit slope m
 Parameter: r is the probability
that one organism establishes
infection
Equation
p(d )   m l og(d / ID50))
Ф is the c.d.f of the
standard normal
distribution
p(d) = 1 – exp{– r d}
r = ln(2)/ID50
28/30
Sverdlovsk anthrax leak, 4/2/1979



Leak from Russian military facility
Approximately 100 deaths resulted
Data used by Wilkening (2005) to assess
dose-response functions…
Wilkening, 2005. Sverdlovsk revisited:
Modeling human inhalation anthrax. PNAS 103
29/30
Wilkening models (A and D best)
A: Lognormal
D: Exponential
B: Lognormal
C: Lognormal
with agedependent
ID50
30/30