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This paper introduces a methodology to extend the capabilities of the dynamic inoperability input-output model (DIIM) to account for perturbations to sectors of the economy that are time varying and probabilistic. The DIIM accounts for the interdependent nature of the economy in determining the impact of a disruption on the ability of each economic sector to satisfy the prevailing demand. While the original formulation of the DIIM only allows for a single perturbation vector, this paper extends the DIIM to allow a perturbation matrix to be utilized as inputs to the model. The underlying motivation for this paper is understanding the impact of a pandemic on a regional economy. As such, idiosyncrasies associated with a pandemic are also accounted for in the model formulation. These include translating workforce absenteeism into a measure of sector inoperability and accounting for the impact of long-term absenteeism on a sector's ability to deliver its as-planned production output.