We study the class of SIS epidemics on temporal networks and propose a new activity-driven and adaptive epidemic model that captures the impact of asymptomatic and infectious individuals in the network. In the proposed model, referred to as the A-SIYS epidemic, each node can be in three possible states: susceptible, infected without symptoms or asymptomatic and infected with symptoms or symptomatic. Both asymptomatic and symptomatic individuals are infectious. We show that the proposed A-SIYS epidemic captures several well-established epidemic models as special cases and obtain sufficient conditions under which the disease gets eradicated by resorting to mean-field approximations. In addition, we highlight a potential inaccuracy in the derivation of the upper bound on the decay ratio in the activity-driven adaptive SIS (A-SIS) model in (Ogura et. al., 2019) and present a more general version of their result. We numerically illustrate the evolution of the fraction of infected nodes in the A-SIS epidemic model and show that the bound in (Ogura et. al., 2019) often fails to capture the behavior of the epidemic in contrast with our results.