Asian Journal of Pure and Applied Mathematics

Infectious-disease dynamics may retain effects associated with previous exposure, delayed behavioural responses, and earlier interventions. This study formulates a six-compartment susceptible–exposed– symptomatic–asymptomatic–hospitalised–recovered model governed by a Caputo derivative of order 0 < \(\alpha\) \(\le\) 1. Vaccination, treatment, and public awareness are represented through distinct mechanisms: removal of susceptible individuals, accelerated removal of symptomatic infectious individuals, and reduction of effective transmission, respectively. The analysis establishes positivity, boundedness, and local well-posedness; derives the disease-free and endemic equilibria; and obtains the controlled reproduction number using the nextgeneration matrix. The disease-free equilibrium is locally asymptotically stable when R₀ < 1 and unstable when R₀ > 1, while a stronger sufficient condition is provided for global disease elimination. The reproduction number is decomposed into symptomatic and asymptomatic contributions, clarifying the distinct roles of the two infectious pathways. Normalised sensitivity indices identify transmission and asymptomatic infectiousness as factors that increase R₀, whereas vaccination, treatment, recovery, hospitalisation, and awareness reduce the threshold. Reproducible predictor–corrector simulations show that the fractional order affects transient epidemic timing and peak behaviour, while combined interventions can move the illustrative system across the R₀ = 1 threshold. Because all numerical parameters are illustrative rather than estimated from a specific outbreak, the numerical findings should be interpreted as mechanistic demonstrations rather than disease-specific forecasts or empirical intervention-effect estimates.