Dynamics of a novel fractional-order model for autism spectrum disorder perspective propagation with optimal control

Abstract

This study addresses the propagation of negative societal perspectives toward Autism Spectrum Disorder (ASD) through a novel fractional-order mathematical model that captures the critical memory effect in individuals' attitude formation, where historical experiences continuously shape current perceptions. By analyzing intervention strategies combining media awareness campaigns and therapeutic programs, we demonstrate that fractional calculus reveals significantly slower attitude transitions (30-50 percent reduction in rate) compared to classical models, with therapeutic interventions proving three times more effective than media campaigns alone in rehabilitating negative perspectives of individuals. Our optimal control problem identifies a strategy that achieves a 75 percent reduction in negative perspectives, while cost-effectiveness analysis confirms the economic viability of the proposed combined approaches. These findings suggest that integrated interventions utilizing both media and therapy control measures yield the most efficient path to mitigating negative perspectives towards Autism Spectrum Disorder, with fractional-order modeling providing essential insights into the persistent nature of social attitudes that traditional integer-order models cannot capture.