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Our work applies equally well to any category of threat that concerns DHS enough to warrant investments so significant they cannot be hidden from our taxpayers, and thus not from terrorists, either. Such threats cover biological, tadioactive, chemical, and conventional attacks on our infrastructure and citizens, as well as sealing our borders against illegal immigration, and a host of military topics.

The modeling presented here has been motivated and validated by more than one hundred worldwide infrastructure vulnerability analyses conducted since 9/11 by the military-officer students and the faculty of the Naval Postgraduate School (Brown et al., 2005a, 2006a). Some of these studies have been developed into complete decision-support systems:

  • Salmerón et al. (2004) have received DHS and Department of Energy support to create the Vulnerability of Electric Grids Analyzer (VEGA), a highly detailed, optimization-based decision-support system. VEGA can evaluate, on a laptop computer, the vulnerability and optimal defense of electrical generation and distribution systems in the United States, where risk is measured as expected unserved demand for energy during any repair-and-recovery period.

  • We have developed a decision-support system to advise policy makers regarding the interdiction of a proliferator’s industrial project to produce a first batch of nuclear weapons (Brown et al., 2006b, 2007).

  • The U.S. Navy has developed a decision-support system to optimally pre-position sensor and defensive interceptor platforms to protect against a theater ballistic missile attack (Brown et al., 2005b).

The message here is that, with experience, we have gained confidence that these new mathematical methods produce results that exhibit the right level of detail, solve the right decision problems, and convey useful advice and insight to policy makers. Such capabilities have not been available before.


The Biological Threat Risk Assessment (BTRA) uses a descriptive model. Our focus is prescriptive, rather than descriptive: our models suggest prudent investment and mitigation plans for biodefense, and we strive to provide a realistic representation of the attack decisions made by an intelligent adversary.

As the defender, we seek to allocate a limited budget among biodefense investment options to form a defense strategy that minimizes the maximum risk from the actions of a terrorist attacker. We might define risk as the expected number of fatalities, or as the expected 95th percentile of fatalities, or as any other gauge that appeals. Risk is a somewhat ambiguous term when used to discuss our bilateral view of conflict between intelligent adversaries, so we hereafter substitute “expected damage to the defender.” We assume that an intelligent adversary will attempt to inflict maximum expected damage. The following, simplified model minimizes a reasonable upper bound on expected damage; we discuss generalizations later.

  • Indices

defense strategy, e.g., stockpile vaccines A and B, but not C

attack alternative, e.g., release infectious agent V

after-attack, mitigation activity, e.g., distribute vaccine A

mitigation activities enabled by defense option d, e.g., distribute vaccine A, distribute vaccine B

defense strategies that enable mitigation activity m

resource types used by mitigation activities, e.g., aircraft for distributing vaccine, personnel for administering vaccine

  • Data


expected damage if defense strategy d and attack alternative a are chosen, given no mitigation


expected damage reduction of after-attack mitigation effort m, given investment strategy d and attack a (assumes additive reduction and )


total mitigation resource of type k available if defense strategy d is chosen


consumption of mitigation resource k provided by defense option d for mitigation activity m

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