Asian Basic and Applied Research Journal

This paper develops a fractional-order model for an infectious disease in a population divided into susceptible, exposed, symptomatic infectious, asymptomatic infectious, hospitalized, and recovered classes. A Caputo derivative is used to represent the influence of past epidemic states on present transmission and recovery. Vaccination moves susceptible people directly to the recovered class, treatment increases the recovery of symptomatic cases, and public-awareness activity reduces effective contact. We establish non-negativity, boundedness, and well-posedness of the model, derive the disease-free equilibrium and the basic reproduction number, and give threshold conditions for disease elimination. An optimal-control problem balances reductions in symptomatic infection and hospitalization against the costs of the three interventions. An illustrative parameter study shows that the uncontrolled reproduction number exceeds one, whereas treatment or awareness alone can move it below one; the largest reduction is obtained when the controls are combined. The formulation separates what follows analytically from the model from what must ultimately be checked against disease-specific data.