A Stochastic Model for Evaluating Interconnected Critical Infrastructure Decontamination and Recovery Barrett Richter1, Tanvi Joshi1, Ryan James1, Timothy Boe2, Worth Calfee2, Leroy Mickelsen2, Paul Lemieux2, Joe Wood2 1. Battelle Memorial Institute 2. United States Environmental Protection Agency o w. PRO^ 1 BATTELLE It can be done Background Critical infrastructure assets are vulnerable to the effects of natural disasters and CBRN terrorism events (e.g., a biological attack) The EPA has a need to evaluate and prioritize critical infrastructure remediation options for biological contamination events The complex and interconnected nature of critical infrastructure systems is vital to response planning ¦ Modeling these interactions as a system of systems can inform response activities such as decontamination, sampling, and waste management Model Overview Model Objective. Simulate the recovery of an interconnected system of infrastructure sectors in the aftermath of an adverse contamination event Model Inputs. Initial infrastructure sector operating efficiencies Infrastructure sector interaction network Remediation factors ¦ Model Approach. Gillespie Algorithm^ - stochastic models dependent on component interactions ¦ Model Outputs. Time-dependent sector operating efficiency values used to inform decontamination strategies Model Data - Infrastructure Interactions to System of Equations The model is based on the DHS list of critical infrastructure sectors, literature search, and operational feedback A network diagram of infrastructure sector interdependencies is used to develop the system of interaction equations Interaction diagram from PATH/AWAREI2! provides a large set of infrastructure dependencies between 70+ subsectors The number of defined "Parent * Child" relationships between each are used to determine the infrastructure sector interactions Interaction coefficients are set as the number of child sub-sectors Remediation factors (RF) model the rate at which external resources (e.g., government) are used to provide remediation to a contaminated infrastructure sector Sample Equation Development Infrastructure Network Diagram w T2 2E + 3T -> (5 + RFw)W Developed Rate Laws for Sectors illSIIIHy :;333E!^B r0 = k0*Es*T*M/w rl = k.-c-;c - k/W9*W6*T2*C5*A2/G Model Framework - Gillespie Algorithm Originally developed to stochastically model concentration profiles of coupled kinetic chemical reactions Extensible to any situation where species are converted from one to another via "reactions" of the form A + B > C Ex: healthy person + sick person ~ 2 sick people, water + transportation + money > food Algorithm executes single, discrete interactions, randomly selecting which one occurs at each iteration ¦ Advantages over deterministic methods Flexibility of applying discrete effects to the data (e.g., setting a maximum or minimum value of a component, using variable stoichiometric coefficients) Ability to generate distributions and statistical conclusions on parameters and outcomes Next Steps Use data from historical events to fit model parameters and validate model outputs Validate network of infrastructure sector interconnectivity with SMEs Apply results to prioritize infrastructure sector decontamination Disclaimer The U.S. Environmental Protection Agency, through its Office of Research and Development, is funding and managing the research described here under Contract # EP-C-16-014 to Battelle Memorial Institute. Final publications will be subject to the Agency's review process. Questions should be addressed to Timothy Boe (boe.timothv@epa.gov, 919-541-2617). References 1. Gillespie, D.T. Exact stochastic simulation of coupled chemical reactions. The journal of physical chemistry, 81(25):2340-2361, 1977. 2. Knowlton, R.G., et al. "Quick Start Users Guide for the PATH/AWARE Decision Support System." 2013, doi:10.2172/1090216. Model Algorithm Example | r5 = k5*W*E*T/M | pR = kfi*T2*G2/A ElEBEHgEBEaai = ve«SSS Food and Agriculture Plume over Union Station efficiency values based Dupbnt Gtrcfej . I Washington JMCfjSj Energy Transportation Government Operational Viability Time (days) water energy transport communications Efficiency (%) Infrastructure Efficiency Time Profiles government food emergency waste management Remediation Factor www.battelle.org ------- |