Modeling the impact of prevalence-driven public awareness on dengue dynamics and optimizing multi-intervention...

Dengue fever, a rapidly expanding mosquito-borne viral disease, poses a significant global public health challenge due to complex transmission dynamics influenced by human behavior and environmental factors and continues its relentless global expansion, with approximately 390 million annual infections straining health systems across endemic regions, yet conventional models persistently overlook the critical feedback loop wherein rising case numbers trigger public awareness that subsequently alters transmission behavior. This study develops and rigorously analyzes a novel mathematical framework that elevates prevalence-driven public awareness from an absent or static parameter to a dynamic state variable, fundamentally advancing beyond existing approaches that unrealistically assume innate awareness at birth. We construct a deterministic compartmental model using seven ordinary differential equations, stratifying human populations into unaware susceptible, aware susceptible, infected, and recovered classes coupled with susceptible and infected mosquito compartments, while implementing a biologically grounded acquisition mechanism where all newborns enter the unaware class and gain awareness through baseline educational programs at rate ν and prevalence-driven campaigns at rate [Formula: see text]. The methodological approach proceeds through four integrated phases: derivation of the basic reproduction number [Formula: see text] via the next-generation matrix method with rigorous stability analysis of the disease-free and endemic equilibria; comprehensive local sensitivity analysis using elasticity indices and global sensitivity analysis employing Partial Rank Correlation Coefficients with [Formula: see text] Latin Hypercube samples to identify the most influential transmission parameters; formulation of an optimal control problem with four time-dependent interventions comprising vector control [Formula: see text], surge awareness campaigns [Formula: see text], treatment acceleration [Formula: see text], and personal preventive measures [Formula: see text]; and numerical solution of the optimality system using Pontryagin's maximum principle with forward-backward sweep implementation. The principal contributions include the first integrated framework explicitly linking prevalence-driven awareness dynamics to dengue transmission with realistic newborn acquisition pathways, rigorous analytical results encompassing [Formula: see text] characterization and stability theorems, and a complete optimal control solution demonstrating synergistic effects among four simultaneous interventions. Key findings reveal that mosquito mortality rate [Formula: see text] represents the most influential parameter (elasticity [Formula: see text], PRCC [Formula: see text], [Formula: see text]), awareness parameters exhibit statistically significant negative effects (α PRCC [Formula: see text], ν PRCC [Formula: see text], [Formula: see text]), and optimal control analysis demonstrates that single interventions achieve 45-[Formula: see text] peak infection reduction while the full four-control combination attains [Formula: see text] reduction, transforming an outbreak peak of approximately [Formula: see text] cases to below 150 cases. These results provide a quantitative, mathematically rigorous roadmap for resource allocation in dengue-endemic regions, establishing that integrated multi-pronged intervention portfolios yield superior outcomes that transcend the sum of their individual components.