Modeling resilience and survivability as stochastic processes with techno-human-economic systems under stress

This article presents a Markov-based approach that integrates technical, social, and economic aspects that describe a techno-human-economic (THE) model under disturbance. These systems replicate the complex behavior of different sectors in society and private enterprises altogether. The model incorporates resilience and survivability measures and the concepts of breaking points, referred to as divergence, and resurgence. The representation of a THE model intends to be more extensive than other representations as it evaluates systems at different performance levels and state spaces through time. The model is meant to be a tool to forecast or anticipate breaking points and resurgence events through THE's lifecycle. It is also designed as a mathematical foundation, allowing decision-makers to view multiple factors simultaneously. To prove the pertinence of the approach, the notable predicaments of Puerto Rico (PR) since 1960 have been transcribed to the mathematical dialect of a THE under stress with real historical data, socioeconomic indexes, and technological innovation indexes. The final resolved Markov chain for PR's case reveals that, for a stressed society, a contracted economy, and a survivable form of technology, the greater probabilities tend to the initial state from a survivable state (i.e., 90.32%) to survivability from a resurgent state (i.e., 86.31%), and to divergence from a resilient state (i.e., 70.69%).