Environmental Measurements for Complex System Models of Infection Transmission

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Environmental Measurements for Complex System
Models of Infection Transmission

• James S. Koopman MD MPH
• University of Michigan
• Dept. of Epidemiology

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Talk Outline

• Integrating Microbial Risk Assessment and
  Transmission System Analysis to analyze
  Environmental Transmission Systems
• A path to productive ETS science
• ETS models (simple less simple) to help analyze
  non-pharmacologic influenza interventions
• Cumulative Dose-Response models

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Traditional Microbial Risk Assessment Models
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Traditional Infection Transmission System Models

• Diverse model types
• Deterministic compartmental
• Stochastic compartmental
• Individual event history
• Fixed network
• Dynamic network

Susceptible
Diverse natural histories of infection, encounter
processes, network linkage processes,
transmission probabilities by type of contact,
etc.
Infectious
Immune
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Traditional Infection Transmission System Models
Left out of traditional Infection Transmission
System Models
Diverse natural histories of infection, encounter
processes, network linkage processes,
transmission probabilities by type of contact,
etc.
Dead Pathogen in Environment
Susceptible
Microbial fate transport models plus
dose-response models
Infectious
Live Pathogen in Environment
Immune
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Environmental Transmission System (ETS) Models
Dead Pathogen in Environment
Susceptible
Infectious
Live Pathogen in Environment
Immune
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Why Model Pathogen Passage Through the
Environment?

• Many interventions act on environment we need
  to now when, where, how to use interventions
  cost-effectively
• Much ignorance about modes of transmission
• Environmental measurement of pathogens should
  provide powerful data for analyzing infection
  transmission systems

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Are Simpler Models Better?

• Yes if inferences from them are robust to
  realistic relaxation of assumptions
• Simple models make unrealistic assumptions
• Inference robustness must be assessed by
  comparing to more realistic model
• Yes if their parameters are more estimable
• No if they ignore available data theory

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Why Environmental Transmission Models are Better

• Place of pathogen identification can be more
  informative than contact history
• Contact is hard define measure so contact
  parameters are rarely separately estimable
• Transmission systems are spatial place of
  pathogen identification is more tightly related
  to transmission than histories of places visited
• Environmental pathogen data statistically
  identifies more key parameters of ETS models than
  history data does for contact models

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Path to Building ETS Science that Serves Public
Health

• Focus inference robustness assessment on key
  public health decisions
• Effects of interventions to block routes of
  transmission in specific places (respiratory
  hygiene, air or surface decontamination, air flow
  change, masks, changing human flow, hand washing,
  gloves, many more)
• Cost-benefit decisions
• Models must encompass intervention effects

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build series of nested (dockable) ETS models with
  increasing realism
• Deterministic compartmental
• Stochastic compartmental
• Individual based
• Dynamic network
• Increasing spatial and behavioral detail

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest model forms from which robust
  inferences can be made specify most influential
  parameters in these
• Find problematic simplifying assumptions by
  comparing models that relax assumptions
• Assess sensitivity of outcomes of PH significance
  to parameter values that may be extrinsically or
  intrinsically estimated

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest models for valid inferences
• Specify extrinsically estimable parameters
• Link up with a group of scientists enthusiastic
  about conducting studies to estimate those
  parameters in a Center like CAMRA

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest models for valid inferences
• Specify extrinsically estimable parameters
• Find data that provides statistical
  identifiability for parameters needing intrinsic
  estimation
• Test parameter identifiability with IBM data
• Find data that varies most with parameters having
  large effects on public health decisions

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest models for valid inferences
• Specify extrinsically estimable parameters
• Find data that identifies key parameters
• Develop new intrinsic parameter estimation
  methods for key parameters
• Least squares, MCMC, filtered likelihood
• Use simpler models for estimation test methods
  on data from more detailed models

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest models for valid inferences
• Specify extrinsically estimable parameters
• Find data that identifies key parameters
• Develop parameter estimation methods
• Use most detailed and realistic models available
  to design studies
• Maximize inference robustness for key PH decisions

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Path to Building ETS Science that Serves Public
Health

• Focus on key public health decisions
• Build model series with increasing realism
• Find simplest models for valid inferences
• Specify extrinsically estimable parameters
• Find data that identifies key parameters
• Develop parameter estimation methods
• Design studies for robust PH decisions

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Environmental Transmission System (ETS) Models
Dead Pathogen in Environment
Susceptible
Infectious
Live Pathogen in Environment
Immune
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Simple ETS Model

• pickup rate
• p linear dose response
• g recovery rate
• deposit rate
• m pathogen death rate

S
ED
I
EA
R
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Epidemics when pathogen die off is negligible
Higher Pickup Rate
Lower Pickup Rate
Fraction Infected
EA
I
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Simple ETS Behavior

• Identical to classic Kermack-McKendrick SIR model
  when pickup rate is high
• Density dependent infection process when pathogen
  die off rate is high
• Number of transmissions from infected individual
  is proportional to population size
• Frequency dependent when pathogen die off rate is
  low
• Number of transmissions from infected individual
  doesnt change with population size

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Airborne vs. Hand-Fomite Transmission of Influenza

• Both routes transmit infection experimentally
• Role of either in transmission system is not
  established
• Mucosal ID50 dose is 10 times alveoli ID50 dose
• Contamination and exposure rates poorly studied
  for either route
• CDC is supporting numerous studies of mask
  wearing vs. alcohol hand wipe effects as well as
  studies of droplet size production to help
  pandemic influenza control decisions

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Dormitory Study at University of Michigan

• Dorms randomized to masks, masks plus hand wipes,
  or control
• Students swabbed when symptomatic
• Environmental samples collected in air exposure
  only spots and hand-touched spots
• Higher CFU of both Staph aureus epidermidis
  from untouched surfaces
• Staph epidermidis much more frequent than aureus
  on touched surfaces but both are equal on
  untouched

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Analyzing Trials Without ETS

• Significance testing has lower power
• Best multi-level model capturing individual and
  herd immunity effects makes poor predictions of
  effects even within the range of attack rates
  observed in dormitories (Using data generated by
  simulations)
• No ability to generalize to other venues

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Analyzing Trials with ETS

• A couple years away from developing needed
  methods
• Should provide better power to detect differences
  in effect
• Should provide some robust inferences of effects
  in venues with differing characteristics

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Environmental Transmission Model of Influenza by
Wien

• Analysis by Larry Wien presented to Institute of
  Medicine (still unpublished) concluded only
  airborne was important
• Relative contributions of air vs. fomite not
  affected by human movement patterns or cumulative
  dose response curves in this model
• Our analysis suggests these are important factors
  that should be taken into account

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Movement Effects on Airborne vs. Hand-fomite
Transmission

• Theaters have little human movement, stores have
  more
• Fomite contamination disseminates slowly through
  space, airborne contamination disseminates more
  rapidly
• Movement increases both fomite contamination
  dissemination and number of fomites contacted

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Individual Based Model of Infection Transmission

• N agents roaming in a venue of size M (2D-grid)
• Each cell has a certain level of air and fomite
  contamination.
• Agents move to different cells with a rate m
• An agent is infected following a Beta-Poisson
  dose response.
• Dose dose from air dose from fomite
• Once infected agents shed contamination
  (aerosolized and deposited to surfaces)
• Contamination between cells is transported by air
  diffusion of by agents acting as carriers
• Contamination dies out

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Individual Based Model of Infection Transmission
1) There are 3 people, 2 susceptible and one
infected
2) The infected person sneezes. Droplets
contaminate the surface and aerosolized pathogens
start to spread.
3) The air contamination diffuses. At the same
time the fomite and air contamination die-out at
their respective rates.
4) Contamination reaches a susceptible person.
5) The contamination of the air dilutes in the
whole area. The infected people move. One
susceptible person becomes infected.
6) The contamination of the air dilutes as it
disseminates. The infected people move.
7) The remaining susceptible person moves to the
cell with fomite contamination. The contamination
of the air is fully spread throughout the venue.
8) The person is infected. The concentration of
fomite contamination in that persons cell is
much larger than air contamination.
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Transmission model
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Results the role of movement

• Interventions do not only depend on the disease
  or the venue.
• The functional characteristics (the kind of venue
  and consequently the patterns of movement in it)
  play a crucial role in the transmission.

For disease parameters modeling influenza

• Air intervention is only effective if m is lower
  than 1/180 (less than one movement in 3h)
• Fomite intervention more effective when movement
  is faster than one every hour.
• Movement helps determine which transmission route
  dominates.

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Mode of Transmission Dose Timing

• Airborne long slow low dose timing
• Hand-Fomite intermittent high doses
• Linear dose-response model gives both equal risk
  for equal total dose
• Realistic innate or acquired immune element
  replenishment dynamics in our dose-response model
  favor hand-fomite transmission
• Control inferences of Wien are not robust to
  realistic relaxation of linear dose-response
  assumptions

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Model Development Cumulative Dose Response

• Continuous time Markov chain model
• Dose has less probability of infection if the
  time of inoculation is longer.
• Need for time-dependent dose-response experiments.

System state variables and parameters P of
pathogens I of immune particles D total
dose T total inoculation time gp growth rate of
pathogens mp natural death rate of pathogens dp
deactivation rate of pathogens ai Arrival rate
of immune particles mp natural death rate of
immune particles dp deactivation rate of immune
particles
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Model Development Cumulative Dose Response
Fast immune replenishment
Slow immune replenishment

• Fast immune replenishment (c0.1)
• Shorter dosing regimes shifts Dose-response
  function to left (increased infectivity)
• Slow immune replenishment (c0.001)
• Dose-response function independent of dosing time
  periods

Blue to red transition represents longer/low
concentration dosing periods
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Model Development Cumulative Dose Response

• Dynamic response from dosing (pathogen growth in
  time)
• 22 of the trials ended up in infection (blue
  lines)
• 78 of the trial ended up in not infection (red
  lines)

Infection (Immune particles depleted)
Constant Inoculation Period
Transient Period
No Infection (Immune particles grow back to
Equilibrium)
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Dose-Response Data

• Our model generates steeper than observed rises
  given a one time dose
• Inbred mouse curves for Lassa fever Yersinia
  pestis rise much faster than outbred mouse curves
  and can be fit
• An immune element recruitment parameter also
  flattens the curve and permits the model to fit
  data

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Summary 1

• Infection transmission system science will be
  transformed by environmental data models.
• With a big contribution from CAMRA we will learn
• what modes of transmission play different roles
  in different populations
• what interventions affecting modes of
  transmission in different places will have big
  population effects
• how to study transmission in hospitals for
  emerging infections like SARS so that we can
  predict which population interventions will be
  most effective

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Summary 2

• Focusing on PH policy inference robustness will
  help our science serve Public Health
• Simple abstract and realistic ETS models should
  work together to analyze data, project
  intervention effects, assess inference
  robustness
• Cumulative dose-response models must be specified
  for a science of ETS to advance

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Thanks

• Questions?