  Information diffusion and disease spreading in communication-contact layered
network are typically asymmetrically coupled with each other, in which how an
individual being aware of disease responds to the disease can significantly
affect the disease spreading. Many recent studies have demonstrated that human
behavioral adoption is a complex and non-Markovian process, where the
probability of adopting one behavior is dependent on the cumulative times of
the received information and the social reinforcement effect of these
cumulative information. We study the impact of such a non-Markovian vaccination
adoption behavior on the epidemic dynamics and the control effects. We find
that this complex adoption behavior caused from the communication layer can
significantly increase the epidemic threshold and reduce the final infection
rate. By defining the social cost as the sum of the cost of vaccination and the
cost of treatment, we show that there exists an optimal social reinforcement
effect or optimal information transmission rate allowing the minimal social
cost. We also develop a mean field based theory to verify the correctness of
the simulation results.
