Time-nonlocal modeling of khat addiction networks in Dire Dawa and Hararghe: Cultural persistence and economic feedback loops
DOI:
https://doi.org/10.14295/bjs.v6i2.937Keywords:
khat addiction, fractional derivatives, nonlocal influence, poverty trap, social network interventionAbstract
Khat (Catha edulis) use in Ethiopia, particularly in the Dire Dawa and Hararghe regions, represents a major public health challenge driven by neuroadaptive dependence, social reinforcement, and economic vulnerability. This study develops an integrated mathematical model combining Caputo fractional derivatives, nonlocal social influence, and economic feedback to describe addiction dynamics. The model was calibrated using cessation data (N = 87), household expenditure records (N = 423), and occupational social networks (387 nodes, 1,842 edges). Results indicate that persistent memory prolongs relapse periods and sustains higher long-term abstinence than conventional models, while nonlocal social influence accelerates the spread of consumption norms. Economic analysis identifies a poverty trap when khat expenditure exceeds 20% of household income. Key social influencers include cafe owners, elders, and taxi drivers, highlighting their central role in community-level transmission. Simulation results show that early preventive interventions combined with targeted economic support are substantially more effective and cost-efficient than delayed strategies. These findings demonstrate that long-term khat addiction is maintained by the interaction of neurobiological memory, social contagion, and economic constraints, emphasizing the importance of early intervention, community engagement, and timely economic assistance to prevent progression into persistent addiction-poverty cycles.
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