In a fast evolving major public health crisis such as the COVID-19 pandemic, multiple pieces of relevant information can be posted sequentially in a social media platform. The interval between subsequent posting times may have different impact on the transmission and cross-propagation of the old and new information to result in different peak value and final size of forwarding users of the new information, depending on the content correlation and whether the new information is posted during the outbreak or quasi steady state phase of the old information. To help in designing effective communication strategies to ensure information is delivered to the maximal number of users, we develop and analyze two classes of susceptible-forwarding-immune information propagation models with delay in transmission, to describe the cross-propagation process of relevant information. We parametrize these models using real data from the Sina-Microblog and use the parametrized models to define and evaluate mutual attractiveness indices, and we use these indices and parameter sensitivity analyses to inform strategies to ensure optimal strategies for a new information to be effectively propagated in the microblog.