Based on the bi-layered network model, we explore two main themes: how disease spreads affect information spreads and how information affects the efficiency of controlling the epidemic. We introduce the non-dualism of information and the heterogeneity of nodes’ behaviors into the epidemic model and conduct a simulation to reveal the information intervention dilemma faced by the government between information disclosing and blocking. We find that governments face a trade-off between speed and accuracy in information disclosing; and the optimal strategy is contingent on varying conditions in information blocking. The optimal combination of disclosing and blocking is highly sensitive to the government preference and its governance capacity. Governments that are only responsible for the outcome of intervention will focus unilaterally on the accuracy at the expense of speed; a risk-averse government that intends to minimize the maximum infection rate under uncertain scenarios will impose a more restrictive blocking; and the most restrictive blocking strategy might be the best for governments with lower capability and credibility.