Department of Homeland Security Bioterrorism Risk Assessment: A Call for Change

R code implementing this algorithm follows.

ms1p <- (0.5)*(0.8)
ms2p <- (0.5)*(0.2)
ms3p <- (0.5)*(0.6)
ms4p <- (0.5)*(0.4)

nsampc <- 1000

cs1 <- rgamma(nsampc,8000,2)
cs2 <- rgamma(nsampc,4500,1)
cs3 <- rgamma(nsampc,10000,2)
cs4 <- rgamma(nsampc,5500,1)

bh1 <- hist(cs1,breaks=seq(3500,6000,length=101),plot=F)$density
bh2 <- hist(cs2,breaks=seq(3500,6000,length=101),plot=F)$density
bh3 <- hist(cs3,breaks=seq(3500,6000,length=101),plot=F)$density
bh4 <- hist(cs4,breaks=seq(3500,6000,length=101),plot=F)$density

erd <- ms1p*bh1 + ms2p*bh2 + ms3p*bh3 + ms4p*bh4

x <- seq(3512.5,5987.5,by=25)
points(x,erd,type=”b”,pch=2)

The estimated risk distribution from this approach is given as the line with triangles in Figure C.2.

If the conditional consequence distributions are given in parametric form, or in numerical look-up tables, calculation of the risk distribution can be done exactly, without resorting to estimating these distributions from the outputs of Monte Carlo simulations. This method is simply:

Calculate the expected arc probabilities; and
Calculate the weighted average of the consequence distributions.

ms1p <- (0.5)*(0.8)
ms2p <- (0.5)*(0.2)
ms3p <- (0.5)*(0.6)
ms4p <- (0.5)*(0.4)

x <- seq(3512.5,5987.5,by=25)
points(x,ms1p*dgamma(x,8000,2) + ms2p*dgamma(x,4500,1) + ms3p*
dgamma(x,10000,2) + ms4p*dgamma(x,5500,1),type=”b”,pch=4)

The risk distribution (exact, and not an estimate) obtained using this approach is given as the line with crosses in Figure C.2. This computation is both trivial and fast.

Table of Contents

Front Matter R1-R14

Summary 1-5

1 Introduction 6-10

2 The Critical Contribution of Risk Analysis to Risk Management and Reduction of Bioterrorism Risk 11-19

3 Description and Analysis of the Department of Homeland Security's Biological Threat Risk Assessment of 2006 20-33

4 Department of Homeland Security Decision Requirements for Risk Management 34-41

5 Risk Assessment for Unknown and Engineered Biothreat Agents 42-46

6 Improving Bioterrorism Consequence Assessment 47-50

7 Improving the Department of Homeland Security's Biological Threat Risk Assessment and Adding Risk Management 51-60

Appendix A: Lexicon 61-77

Appendix B: Mathematical Characterization of the Biological Threat Risk Assessment Event Tree and Risk Assessment 78-79

Appendix C: Computational Example Illustrating the Replacement of a Joint Distribution of Arc Probabilities with Marginal Expected Values of Individual Arc Probabilities 80-84

Appendix D: Bioterrorism Risk Analysis with Decision Trees 85-89

Appendix E: Optimizing Department of Homeland Security Defense Investments: Applying Defender-Attacker (-Defender) Optimization to Terror Risk Assessment and Mitigation 90-102

Appendix F: Combining Game Theory and Risk Analysis in Counterterrorism: A Smallpox Example 103-110

Appendix G: On the Quantification of Uncertainty and Enhancing Probabilistic Risk Analysis 111-115

Appendix H: Game Theory and Interdependencies 116-121

Appendix I: Review of BTRA Modeling 122-125

Appendix J: Reprinted Interim Report 126-148

Appendix K: Meeting Agendas 149-152

Appendix L: Biographies of Committee Members 153-156

Appendix M: Acronyms 157-158