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The addicted predator-prey model: How opioid use disorder shapes productivity and growth-cycle dynamics

Nara Chung, Marwil J. Dávila‐Fernández · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.10356 · cited by 0 works (OpenAlex) · open-access PDF

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이 논문은 Goodwin (1967)의 포식자-포식자 성장주기 모델을 사용하여 노동 생산성에 대한 오피오이드 사용 장애 (OUD)의 부정적인 영향을 통합합니다. 미국 국가 수준의 데이터를 사용하여 1998-2019 년에 대한 피드백을 확장합니다. 우리는 처음으로 노동 점유율의 악화가 약물 유발 사망률 증가로 이어집니다. 우리는 OUD의 확률이 임금 점유율과 함께 감소하는 새로운 분리 선택 메커니즘을 통해 모델에이 링크를 구축합니다. 따라서 실제 임금이 생산성 성장과 함께 속도를 유지하지 못하면 오피오이드 사용이 증가합니다.이 행동 건강 채널은 생산성 손상 기능을 통해 경제에 다시 공급됩니다. Andronov-Hopfurcation 이론의 존재 부분을 적용함으로써 우리는

Machine translation (Meta M2M100); the English original follows.

Abstract

This paper extends Goodwin's (1967) predator-prey growth-cycle model to incorporate the negative impact of Opioid Use Disorder (OUD) on labor productivity. Using U.S. state-level data for 1998--2019, we first document that deteriorations in the labor share are followed by rising drug-induced mortality. We then build this link into the model through a novel discrete-choice mechanism in which the probability of OUD decreases with the wage share, so when real wages fail to keep pace with productivity growth, opioid use rises. This behavioral health channel feeds back into the economy through a productivity damage function. Applying the existence part of the Andronov-Hopf bifurcation theorem, we show that the resulting three-dimensional nonlinear system admits a limit cycle, as confirmed by our numerical simulations. Along the cycle, rising OUD paradoxically raises the employment rate, as falling productivity requires more labor per unit of output; across steady states, however, higher OUD prevalence is associated with a lower employment rate, consistent with evidence that opioid use disorder reduces labor force participation. Moreover, our numerical experiments show that OUD sensitivity to income widens fluctuations, while productivity sensitivity to OUD counterintuitively compresses them through a self-correcting feedback that speeds the recovery of the wage share. Policies that weaken the link between income and OUD, such as stronger social safety nets, stabilize the resulting dynamics.

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Topics: Opioid use disorder, Productivity, Economics, Wage, Opioid overdose, Labour economics

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