The robustness of human social networks against epidemic propagation relies on the propensity for physical contact adaptation. During the early phase of infection, asymptomatic carriers exhibit the same activity level as susceptible individuals, which presents challenges for incorporating control measures in epidemic projection models. This paper focuses on modeling and cost-efficient activity control of susceptible and carrier individuals in the context of the susceptible-carrier-infected-removed (SCIR) epidemic model over a two-layer contact network. In this model, individuals switch from a static contact layer to create new links in a temporal layer based on state-dependent activation rates. We derive conditions for the infection to die out or persist in a homogeneous network. Considering the significant costs associated with reducing the activity of susceptible and carrier individuals, we formulate an optimization problem to minimize the disease decay rate while constrained by a limited budget. We propose the use of successive geometric programming (SGP) approximation for this optimization task. Through simulation experiments on Poisson random graphs, we assess the impact of different parameters on disease prevalence. The results demonstrate that our SGP framework achieves a cost reduction of nearly 33% compared to conventional methods based on degree and closeness centrality.