In this paper, we introduce the non-dualism (by non-dualism, we mean the information is neither absolutely accurate nor absolutely not but partially accurate) 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 and to explore the trade-offs among corresponding strategies. Our experiments highlight that:For information disclosing, governments face a trade-off between speed and accuracy. A better medical understanding of the virus and an inadequate public health awareness make accuracy outweigh speed; otherwise, a quick one is better. For information blocking, the optimal strategy is contingent on varying conditions: no blocking is usually optimal for a well-known virus and a higher public health awareness; otherwise, blocking is preferred. The optimal combination of disclosing and blocking is highly sensitive to the government preference and its governance capability. A government that is only responsible for the outcome of intervention will focus unilaterally on accuracy at the expense of speed; a risk-averse government that intends to minimize the maximum infection rate in uncertain scenarios will impose a more restrictive blocking; and the most restrictive blocking strategy might be best for governments with lower capability and credibility.