Information diffusion and disease spreading in communication-contact layerednetwork are typically asymmetrically coupled with each other, in which how anindividual being aware of disease responds to the disease can significantlyaffect the disease spreading. Many recent studies have demonstrated that humanbehavioral adoption is a complex and non-Markovian process, where theprobability of adopting one behavior is dependent on the cumulative times ofthe received information and the social reinforcement effect of thesecumulative information. We study the impact of such a non-Markovian vaccinationadoption behavior on the epidemic dynamics and the control effects. We findthat this complex adoption behavior caused from the communication layer cansignificantly increase the epidemic threshold and reduce the final infectionrate. By defining the social cost as the sum of the cost of vaccination and thecost of treatment, we show that there exists an optimal social reinforcementeffect or optimal information transmission rate allowing the minimal socialcost. We also develop a mean field based theory to verify the correctness ofthe simulation results.
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