HIV/AIDS compartmental model analysis with drug resistance treatment, vertical transmission, and optimal control theory

This study develops a novel HIV/AIDS compartmental model that integrates the critical, interconnected challenges of drug resistance emergence from treated individuals, healthcare constraints via a saturating treatment function, and persistent vertical transmission. The objective is to provide a comprehensive mathematical framework for analyzing these complex dynamics and designing effective intervention strategies. Our analysis reveals that treatment saturation can induce a backward bifurcation, complicating disease eradication efforts, while optimal control simulations demonstrate that a combined strategy of enhanced screening, accelerated treatment initiation, and adherence support significantly reduces infection pools and minimizes disease progression compared to isolated interventions.