Why does scabies persist despite effective treatment? Coordination failure, Nash equilibrium, and replicator dynamics

Scabies remains a persistent global public health problem despite the availability of effective treatments, including topical permethrin, benzyl benzoate, crotamiton, and systemic ivermectin. This paper develops a formal economic-epidemiological framework using game theory to explain persistence through coordination failure and Nash equilibrium.

Household treatment decisions are modeled as a coordination game under imperfect information, treatment costs, and reinfection externalities. The analysis is further extended using an evolutionary replicator dynamics framework to examine how parameter conditions determine equilibrium stability and long-run behavioral outcomes. To illustrate the theoretical framework, I analyzed global data linking scabies disability-adjusted life years (DALYs) to household washing machine coverage.

The analytical results demonstrate that individually rational behavior can lead to inefficient equilibria, resulting in recurrent infections and elevated societal costs. The empirical analysis reveals a statistically significant negative association between scabies DALYs and household washing machine coverage that is consistent across multiple yearly specifications and stable regional patterns of household washing machine coverage.

The empirical findings should be interpreted as correlational and illustrative rather than causal, since the empirical analysis does not control for the broader socioeconomic and institutional determinants of scabies burden. Nevertheless, the results are consistent with the theoretical framework and highlight the potential role of infrastructure-based hygiene interventions, in combination with mass drug administration and health education, in aligning individual incentives with socially optimal outcomes. Sustainable scabies control requires integrated economic, epidemiological, and behavioral strategies.