A Game-Theoretic Model of Optimal Clean Equipment Usage to Prevent Hepatitis C Among Injecting Drug Users

Kristen Scheckelhoff, Ayesha Ejaz and Igor V. Erovenko ()
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Kristen Scheckelhoff: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
Ayesha Ejaz: Department of Chemistry and Biochemistry, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
Igor V. Erovenko: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA

Mathematics, 2025, vol. 13, issue 14, 1-18

Abstract: Hepatitis C is an infectious liver disease which contributes to an estimated 400,000 deaths each year. The disease is caused by the hepatitis C virus (HCV) and is spread by direct blood contact between infected and susceptible individuals. While the magnitude of its impact on human populations has prompted a growing body of scientific work, the current epidemiological models of HCV transmission among injecting drug users treat risk behaviors as fixed parameters rather than as outcomes of a dynamic, decision-making process. Our study addresses this gap by constructing a game-theoretic model to investigate the implications of voluntary participation in clean needle exchange programs on the spread of HCV among this high-risk population. Individual drug users weigh the (perceived) cost of clean equipment usage relative to the (perceived) cost of infection, as well as the strategies adopted by the rest of the population, and look for a selfishly optimal level of protection. We find that the spread of HCV in this population can theoretically be eliminated if individuals use sterile equipment approximately two-thirds of the time. Achieving this level of compliance, however, requires that the real and perceived costs of obtaining sterile equipment are essentially zero. Our study demonstrates a robust method for integrating game theory with epidemiological models to analyze voluntary health interventions. It provides a quantitative justification for public health policies that eliminate all barriers—both monetary and social—to comprehensive harm-reduction services.

Keywords: game theory; hepatitis C; injecting drug use; Nash equilibrium; public health; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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