Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Jerry Magaña - University of North Georgia
Co-Author(s): J. Alanis1,2, M.M. Brown1,3, J. Kitchens1,4, J. Magaña1,5, C. Velastegui1,6, M. Thakur1, B. Espinoza1, A. Murillo1, M. Rodriguez Messan1, R. Koester7, C. Castillo-Garsow1,8 1Simon A. Levin Mathematical, Computational, and Modeling Sciences Center: Mathematical & Theoretical Biology Institute. Arizona State University, Tempe AZ, United States 2San Joaquin Delta College, Stockton CA, United States 3Scripps College, Claremont CA, United States 4Warren Wilson College, Swannanoa NC, United States 5University of North Georgia, Dahlonega GA, United States 6Yachay Tech University, San Miguel de Urcuquí Imbabura, Ecuador 7Kingston University London, London, United Kingdom 8Eastern Washington University, Cheney WA, United States
Search and Rescue (SAR) operations are critical to the safety and well-being of individuals who visit state and national parks. Rescue time is crucial as survival rates dramatically decrease each day, and the cost of each mission increases proportionally. It is estimated that approximately 2000 individuals get lost every year, and the average cost of a SAR operation is $1,375 per person. There is a need to incorporate a mechanistic mathematical model that takes a parameter of human behavior into consideration also. Data from resources such as the International Search and Rescue Incident Database (ISRID) are analyzed to identify patterns in human behaviors and key geographic environmental influences to develop a mechanistic model of missing persons. We use a discrete-time Markov Decision Process (MDP) where the lost individual’s state determines a strategy for being found. The individual then interacts with the environment, where a utility function for that strategy over the geographic environment determines direction of travel. We compare data from various national parks against our model. Implications are discussed for SAR, hiker survival training, and other areas. The proposed model might be extended for other groups of people, including experienced hikers or individuals who suffer from mental illnesses. Presentation: This presentation will focus on determining the probability of a hiker selecting a specific path to a destination. We use concepts from Dynamic Programming, specifically the development and application of an appropriate Bellman Equation to the Markov Decision Process framework.
Funder Acknowledgement(s): This research was conducted as part of 2019 MTBI at the Simon A. Levin Mathematical, Computational and Modeling Sciences Center (MCMSC) at Arizona State University (ASU). This project has been partially supported by grants from the National Science Foundation (NSF Grant MPS-DMS-1263374 and NSF Grant DMS1757968), the National Security Agency (NSA Grant H98230-J8-1-0005), the Office of the President of ASU, and the Office of the Provost of ASU.
Faculty Advisor: Dr. Carlos Castillo-Garsow, firstname.lastname@example.org
Role: I was mainly responsible for developing the appropriate Bellman Equation, the associated value and cost functions, and coding this portion of the framework. I did additional work on preparing the geographic data using GIS tools, and am working with my team to compare results to available data.