<p>In this paper, we develop a system of fractional-order differential equations to model epidemics that accommodates inhibition from the behavioral adaptation of the susceptible individuals as the number of infective individuals grows large. Furthermore, the proposed model accommodates reinfection due to incomplete (or ineffective) treatment at home and in hospital. Crucial properties such as positivity, boundedness, and the existence of a unique solution are shown. The basic reproduction number is derived and expressions for the average dwell time of individuals in the infected compartments, transferred from the exposed compartment are obtained. The stability of the disease-free equilibrium is studied. To demonstrate the model, a numerical scheme based on the nonstandard finite difference method is developed which preserves the properties of the fractional-order derivative model. The disease transmission dynamics are demonstrated for scenarios where the disease dies out as well as where it persists in the population. Furthermore, the effects of the fractional order, saturated incidence rate and incomplete treatment are investigated.</p>