Modeling the Economic Impact of Muguka Addiction: A Deterministic Approach That Integrates Economic Burden Cost

Muguka, a variant of miraa (khat), significantly influences the socio-economic dynamics of regions where it is widely cultivated and consumed. Despite its economic importance, addiction to Muguka has led to substantial health and economic challenges, yet limited research has quantified these impacts comprehensively. To address this gap, this study develops a deterministic compartmental model that integrates health costs to analyze the dynamics of Muguka addiction. The aim is to quantify and evaluate the economic and health consequences of Muguka addiction, providing insights for effective public health interventions. The methodology involves formulating a system of ordinary differential equations (ODEs) to capture the dynamics of addiction and health costs across defined compartments. Key aspects of the analysis include deriving the reproduction number, examining equilibrium points and their stability, and performing sensitivity analysis to explore how changes in critical parameters influence addiction prevalence and associated costs. Numerical simulations are employed to assess health cost dynamics and to design optimal, cost-effective control strategies. The findings reveal that Muguka addiction imposes significant economic burdens, including substantial income loss and escalating healthcare costs. The model provides policymakers and public health officials with a valuable tool for designing targeted interventions to mitigate the adverse effects of Muguka addiction.