1.
Risk Analysis and Game Theory
David Banks
U.S. Food and Drug Administration
Game theory offers a set of tools for decision-making in adversarial
situations. Statistical risk analysis offers tools that provide estimates
of the payoffs needed as inputs to either the extensive (tree) form or the
normal (matrix) form of a two-person non-zero-sum game. This talk describes
efforts at the Center for Biologics Evaluation and Research to develop a
general methodology to support policy-making and resource allocation in
counter-terrorism, especially with regard to specific kinds of bioterrorism.
2.
Core Groups, Cooperative Behavior and Peer Pressure: The Dynamics of Fanaticism
by Ultra-ideologically Driven Individuals
(Joint presentation with Baojun Song, Cornell University)
Carlos Castillo-Chavez
Cornell University
The concept of core group was introduced in epidemiology by Hethcote and Yorke
(1984) in the context of gonorrhea dynamics. It has played a fundamental role
in the study of disease dynamics and in the development of health policy ever
since. In 1995, Hadeler and Castillo-Chavez introduced a dynamic concept of
Core Group. In their model, the size of the core group was allowed to vary.
The rate of recruitment from the non-core into the core depended heavily on the
state of infection within the core, that is, it was driven by the local (within
core) disease dynamics. The model has been recently extended by Huang and
Castillo-Chavez (2002) to populations structured by age. These models,
supported subcritical bifurcations a troublesome epidemiological behavior.
This early work represents the starting point for the development of a
simple model for the dynamics of fanatic behavior in ultra-ideologically
driven populations. From the formation of a very simple model, it
becomes evident that the resulting dynamics (subcritical bifurcations) are
typical of peer-driven structures and, in this sense, the results may be
general and troubling.
In classical epidemiology, the concept of basic reproductive number, R0,
plays a dominant role. R0 gives the number of secondary "conversions" generated by
a "typical" extreme individual in a population of susceptible non-converts. The
classical result says that R0 > 1 is a necessary and sufficient (local condition)
for the spread of extremism, that is, for the population of individuals with extreme
behaviors to grow and become established.
In this lecture, a simple model with compartments for core and non-core
subpopulations is introduced. Th dynamics of individuals with extreme behaviors
(I-class) are analyzed within this simple framework. Two types of R0 are found:
Rd ("demographic" R0) and R0 ("epidemiological R0). It is shown that the establishment
of a core-group subpopulation is not possible when Rd< 1. Furthermore, it is also
shown that multiple extreme populations, within the core subpopulation, may become
established when Rd> 1 and R0 < 1.
The results are quite troublesome because they point out the tremendous impact
that "invading" small subpopulations of individuals with extreme behavior may
have on the establishment of exremist groups when the conditions are not
"ideal" (Rd > 1 and R0< 1).
Some possible scenarios will be discussed as well as potential strategies for
reducing the impact of individuals with extreme behaviors.
For a more detailed description of this work, please go to the Introduction.
3.
Optimal Response to Deliberate Reintroduction of Smallpox: Design
via Mathematical Modeling
(Joint presentation with M. Reynolds, M.I. Meltzer, B. Schwartz, J.M. Lane,
S.O. Foster, J.D. Millar and W.A. Orenstein)
John Glasser
CDC
Events of late have rekindled interest in smallpox. Accordingly, we have
modeled this ancient scourge to evaluate possible responses to deliberate
re-introductions of arbitrary magnitude, including emergency mass or contact
vaccination, with or without isolation, and isolation alone. Our current model
comprises sixteen states: susceptible, S, naive or partially-immune people
whose respiratory tracts are colonized, CN and CM, naive ones within whose
reticuloendothelial cells virus is replicating, E, or in whom virus is
disseminating, H, people with residual immunity within whom virus is replicating
or disseminating, RM, ones with normal or modified disease spectra, DN and DM,
who are isolated, QN and QM, naturally or artificially immune, IN and IA,
susceptible to boosting, BN and BA, or who have residual naturally-acquired or
artificially-induced immunity, RN and RA. Population biologists compare hosts
and pathogens via several interrelated quantities, among them R0, secondary
infections on the introduction of newly infectious people to wholly susceptible
populations, Nc, susceptible people required for outbreaks, and pc, population
immunity necessary to prevent them. We report these analytical results and
estimates for Bangladesh in the aftermath of the 1971 civil war, which
underlie the relative ineffectiveness - for smallpox control - of mass
vaccination, and necessity for search and containment, throughout the Indian
Sub-Continent. Currently, we are fitting other historical time-series (e.g.,
Stockholm, 1963; Yugoslavia, 1972) to validate or improve our model and learn
how transmission varies with density, movement, social structure, and other
population phenomena. Given a range for R0, we will evaluate possible official
responses. In particular, we will simulate emergency campaigns differing in
intensity and timeliness post-introductions differing in magnitude. Entire
communities or only those likely incubating virus (i.e., contacts) may be
targeted for vaccination, and possibly isolation, but with varying success. We
will estimate public health resources (e.g., doses of vaccine, contact tracers
or vaccinators) required to curtail spread. We are also developing age-specific
and planning spatially distributed models.
4.
The Role of Migration and Contact Distributions in the Spread of Deliberately
Released Infectious Agents
K. P. Hadeler
Biomathematics, University of Tuebingen
There are several scenarios for the deliberate release of
infectious agents. The main distinctive features are the following.
The infectious agent is either communicable from host to host or
only from the environment to the host. The agent is released locally
from one or several sources, or it is released locally and then it
spreads by wind or water, or the agent itself is spread out over a wide
area. Combination of these features lead to a few basic scenarios some
of which are more likely to happen than others. For some, e.g. the
local emission of a non-communicable agent, mathematical modeling seems
restricted to a statistical analysis and estimates for prevention
policies.
For the scenario where a communicable agent is released at one or few
spots, the possible spread of the disease depends on the rate of
transmission from infecteds to susceptibles, the rate of removal of
infecteds, and the contacts between individuals which are localized at
different space positions.
Traditionally, these contacts have been described either by contact
distributions or by stochastic proesses for the movements of individuals.
These two approaches lead to qualitatively similar results, e.g.
with respect to the speed of epidemic spread. There seems to be few
attempts to relate these modeling approaches analytically or to put
the parameters of the different models into correspondence. In a sense,
there is a problem of book-keeping. Does one think of a partly
infective population where infecteds migrate at some average rate?
Or does one consider individuals essentially fixed at given positions
and making contacts to close and also to more distant neighbors?
In this presentation we describe the essential features of this
spatial transmission problem, we apply appropriate scalings of parameters
and variables and we unify the two approaches. We identify the key
parameters and thus indicate where vaccination, control and education
policies can be successfully applied.
5.
Challenges in NJ's Ongoing Surveillance: A Discussion Of Current
Activities
Teresa Hamby
NJ Dept of Health & Senior Services
When the cases of anthrax in New Jersey were identified in October, 2001,
the NJ Dept of Health & Senior Services with CDC implemented a 60-day
Active Surveillance System in 40 hospital emergency departments in NJ, PA
and DE to monitor for possible additional cases. Once the sixty days
passed, NJ continued to request ED info from the original seven counties
and expanded the data collection to all NJ hospitals. This brief
discussion will outline the challenges in maintaining a vigilant and
effective ongoing surveillance system.
6.
Syndromic Surveillance of Emergency Department Visits, New York City
Rick Heffernan
New York City Department of Health, Communicable Disease Program
Since September, 2001, the New York City Department of Health has
monitored emergency department (ED) visits daily for evidence of
intentional or natural disease outbreaks. Currently, 33 sites
participate, representing two-thirds of ED visits in NYC. Each morning,
electronic files containing demographic information and chief complaints
from the previous day are transmitted to the Department of Health by
email or FTP. No personal identifying information is collected. A
text-string search algorithm codes chief complaints into key syndromes
(eg. respiratory, fever, diarrhea, vomiting). Citywide temporal trends
and geographic clustering by ED address or patient's home zip code are
assessed with the temporal and spatial scan statistics. In what is
arguably the most challenging step, telephone and field investigations
are carried out to determine whether aberrations represent
epidemiologically-related illnesses of public health concern. Results
to date will be presented. Computer simulations could provide insight
into the size, timing and geographic distribution of epidemics that
might be identified through ED surveillance systems.
7.
Comparing and Combining Agent Based and Differential Equation Models
for the Spread of Epidemics
Mac Hyman
Los Alamos National Laboratory
To devise effective strategies to minimize the impact and spread of
infectious diseases, we must use all of the tools available to
advance epidemic models from qualitative insight to quantitative
predictions. I will describe a flexible, stochastic agent-based
decision simulation model for understanding the spread of a disease
within a major city and compare it with a class of deterministic
differential equation models. Although the agent-based model can
include far more detail than the differential equation model, we
have fewer analysis tools to understand the underlying dynamics in
the detailed simulation. I will describe an approach to define a
simple differential equation model that captures the average course
of an epidemic as defined by an agent-based model of a million
people and over ten thousand locations. The differential equation
model uses the same parameters and initial conditions as the agent
based model, and then can be analyzed directly to predict the course
of the epidemic in the more complex agent based model.
8.
Modeling Bioterror Response Logistics: The Case of Smallpox
(Joint presentation with David Craft and Larry Wein)
Edward Kaplan
Yale University
To evaluate existing and alternative proposals for emergency
response to a deliberate smallpox attack, we embed the key
operational features of such interventions into a smallpox disease
transmission model. Such modeling highlights the importance of
variables such as the number of personnel available for contact
tracing and vaccination, the rates with which the population can be
vaccinated, and the accuracy of contact tracing in addition to
standard epidemiological parameters such as the reproductive rate
of infection and disease progression rates. We explicitly model the
tracing/vaccine queues and quarantine requirements that would
result from the existing policy for smallpox response, in addition to
the number of smallpox cases, deaths, and persons vaccinated that
result from this and alternative proposals. The use of probabilistic
reasoning within an otherwise deterministic epidemic framework is
featured throughout.
9.
Basing Surveillance On Infection Transmission System Theory Rather Than
Sampling Theory
Jim Koopman
University of Michigan
The Tecumseh study demonstrated that patterns of infection dissemination have
local regularities related to contact patterns. These regularities involve
illnesses that seemed not to justify tight surveillance and control of
transmission either because they were too mild, like those due to rhinoviruses
and caliciviruses, or too difficult to control, like influenza. New potential
for bioterrorist dissemination of virulence modified highly transmissible
agents, for influenza control, and for transmission model based surveillance
have changed this situation. A surveillance system using some Tecumseh like
data along with institutional and health system based data now has the
potential to generate transmission model based infection pattern predictions
rather than just sampling theory based predictions. This would detect and give
early warning of emerging infection and bioterrorist problems that might
otherwise go undetected for long periods. It would also enable transmission
control of influenza and many other common infections. Three technological
advances make this possible: 1) Web based real time surveillance systems like
those under development by Biomedware Inc. with an SBIR grant from NIH, 2)
Infection transmission system modeling software that allows easy transition
between model forms like the MTSA software under development by Biomedware Inc.
with an SBIR grant from NIH, and 3) Nucleotide sequencing capacity that can
provide data with the complexity level needed to test hypotheses regarding the
underlying contact patterns of a transmission system and to estimate
transmission system parameters.
10.
Mathematical Challenges Posed by Bioterrorism
Simon Levin
Princeton University
The rich mathematical literature in epidemiology provides a natural framework
for addressing many of the problems posed in fighting bioterrorism, but these
are only a subset of the ways in which mathematical approaches can be of value.
In this presentation, I will try to survey a variety of challenges, from
agent-specific reactive mechanisms, to generic approaches that are relevant
before the fact. Ultimately, what is needed is a system-level immune system,
and hence a flexible and adaptive framework for responding.
11.
Disease Spread on Networks: Analogies between Biological and Computer Viruses
(Joint presentation with Ira Schwartz and Lora Billings)
Alun L. Lloyd
Program in Theoretical Biology, Institute for Advanced Study
Communication networks (such as the internet or WWW) play an ever greater
part in our lives. It is important to understand how the patterns of
connectivity in these networks affect the spread of computer viruses
within them and their ability to handle attack or component failure.
Many models for communication can be formulated in terms of networks,
in which nodes represent individuals (such as computers, people or species)
and edges represent contacts between individuals (network links, social or
sexual contact, or species interactions). The study of communication networks,
therefore, has important and interesting parallels with both epidemiology
and ecology. In this introductory talk, I shall introduce basic epidemiological
concepts and discuss some of the models used to describe real-world networks.
The impact of network structure on disease outbreaks-- and their
prevention-- will be illustrated with reference to both biological
infections and those affecting computer systems.
12.
Some Aspects of Adverse Events Detection
David Madigan, Rutgers University
We examine various ways in which statistical and computational methods
might contribute to the design of an automated or semi-automated system for
adverse events detection, recognizing that to be of value, such a system
must facilitate rapid, comprehensive, and accurate detection of such events.
Three topics that come into play are (1) the possible uses of existing data
sets concerning adverse reactions to vaccines and drugs, for the purpose of
developing and refining statistical models; (2) the use of natural language
processing tools to facilitate interactive communication of medical
observations; and (3) exploring possibilities for tapping into new sources
of environmental and other forms of potentially relevant signals.
13.
Making Models Make Sense to Policy-makers
Ellis McKenzie
NIH
Few mathematical modelers are familiar with the policy-making process, and
few policy makers or advisors are familiar with mathematical modeling, so it
is not surprising that communications are often burdened by
misunderstandings and unrealistic expectations. The models most likely to
be used in preparing for and responding to bioterrorism events will reflect
an understanding of policy-making, and may require that several different
approaches to modeling be integrated, e.g. operations-research and
epidemiological.
14.
Biological Modeling and Support to Operations
Peter Merkle
Defense Threat Reduction Agency
Mathematical models of biological phenomena have important missions on the
proving ground of support to military and law enforcement operations. There
are a variety of potential biological threats to national security at home
and abroad, and academic and technical professions are mobilizing expertise
to respond to new challenges. I will provide background on current policy
and operational support efforts using numerical models, and describe the
organizations and processes in place for development, validation, and
operational deployment of new models. I will present some examples of recent
study results and an analytical framework for understanding the biological
threat environment.
15.
Analyzing Bio-surveillance Data to Increase Vigilance to Bio-terrorism
(Joint presentation with Marco Bonetti, Karen Olson and Kenneth D. Mandl)
Marcello Pagano
Harvard School of Public Health, Harvard Medical School, and Children's
Hospital Medical Center
This talk describes the analysis of data obtained from an existing surveillance
network which virtually integrates multiple hospital emergency department
databases in real time. This network provides a real time picture of regional
population patterns of disease. Current surveillance methods are extended to
exploit the study of these patterns and increase the power of detection of an
abnormal outbreak. Early thoughts and early results of work in progress will
be discussed.
16.
Challenges for Discrete Mathematics and Theoretical Computer Science
Fred S. Roberts
DIMACS, Rutgers University
This talk will pinpoint a number of topics in discrete mathematics and
theoretical computer science which seem relevant to the defense
against bioterrorism. Topics to be covered include streaming data
analysis applied to biosurveillance, algorithms for data mining, and
combinatorial group testing. Graph-theoretical models of social
networks have been used to study the spread of opinions and ideas and
these will be discussed, in particular their relation to models for
the spread of diseases through networks. Closely related ideas from
the theory of distributed computing will also be discussed.
17.
Data Mining in Public Health: Issues and Challenges
Henry Rolka
CDC
The availability of usefully summarized, representative data can be
vitally consequential to the value of programmatic and policy
decisions. This presentation is designed to emphasize issues and
challenges of data mining in public health surveillance. A sample of
data sources is described and characterized including the Vaccine
Adverse Event Reporting System (VAERS), the Vaccine Safety Datalink
(VSD), and the National Electronic Telecommunications Surveillance
System (NETSS). An overview of some applications for summarizing and
analyzing surveillance data for signals and/or patterns is provided by
examples of works-in-progress including association discovery using
the Gamma Poisson Shrinkage Estimator and enhanced surveillance of
health events in Emergency Room data with a CUSUM approach. Issues
and challenges are discussed including data sharing, system
integration, local vs. broad-based data use and relevance,
interoperability of applications. An attempt is made to move from
general issues to more specific problems that may be approachable.
18.
Mathematical Problems in Biological and Chemical Sensors
Ira B. Schwartz
Naval Research Lab
In this short talk, I will give a brief overview of some of the
open problems arising in chemical and biological sensors being designed
as well as currently in use. Sensors employing single neurons, clusters, and
neuronal tissue will be used to bring out some of the mathematical issues
of detecting biological agents. On the chemistry side, capillary flow
sensors will illustrate how fluid flow mechanics is combined with
stochastic inputs and biological mechanisms to detect minute quantities
of chemicals.
19.
The Need for Mathematical Models to Make Better Public Health Decisions:
A Few Examples from the World of Influenza Pandemic Planning
Lone Simonsen
National Institute of Allergy and Infectious Diseases (NIAID), NIH
When considering mathematical models as analytical tools for bioterrorism
defense planning, it might be useful to consider the experience with and
need for for such tools in another area of planning which has been going on
for years: influenza pandemic planning. This is an example where decisions
similar to the Bio-T defense scenario must be made, but where there is the
advantage of time (years of preparation) and where key aspects will not be a
surprise (pathogen type,likely impact on morbidity and mortality, likely
availability of vaccine, antivirals available and stock-piling possible).
I will describe two scenario's from pandemic planning: one in which decisions
are being made largely on the basis of intuition - and another where
mathematical modeling is playing a central role. One example is how to best
use antivirals in order to reduce or delay the impact of pandemic influenza on
mortality. Another example is how to prioritize sub-populations in the likely
scenario of a limited vaccine supply.
20.
The Role of Computer Science in the Defense Against Bioterrorism
Gary Strong
NSF
Computer science contributes in at least three ways to the nation's defense
against bioterrorism: spatio-temporally indexed models of events; pattern
discovery; and communications infrastructure. Models of epidemiological
spreads of disease and statistical models for incidence baselining are two
significant types of model development that are indexed spatio-temporally
and of critical need in the prediction or detection of bioterrorist events.
Computer science provides the tools for training such models, validating
them, and indexing them by space and time coordinates (e.g., geographical
location and time of season). Patterns that are revealed by data mining
over heterogeneous datasets provide keys for further extraction of data of
importance to intelligence and law enforcement in general and especially in
bioterrorism defense. Such patterns may involve characteristic signatures
of bioterrorism activities or genomic fingerprints identifiable from
intercepted biological matter. Finally, since consequence management can be
enormously complex in the case of bioterrorist events, an infrastructure for
timely sharing of appropriate information is essential. Even before such
events occur, computer science can, by virtual environment modeling, create
potential scenarios for bioterrorism and "play" them out, examining their
likelihood and implications. Computer science research supports our
nation's defense against bioterrorism in multiple, diverse ways.
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