The integrated sensing and communication (ISAC) has been proposed as an enabling technology for improving the network efficiency, where the wireless infrastructures and spectrum resources can be reused by co-designing the sensing and communication (S&C) functionalities. Different networks adopt the technique of ISAC to achieve the enhanced capabilities in precise localization, tracking, and imaging. To further improve the performance of cooperative detection, data dissemination can be carried out for ISAC-enabled networks. However, as sensing information sharing among S&C devices generally proceeds in a multi-hop manner, there exist various design challenges in ISAC-enabled networks, e.g., data dissemination modeling and deployment of S&C devices. Since epidemic theory has been developed as an innovative tool for modeling data dissemination, it can also be applied to design and analyze the ISAC-enabled network. In this article, we first introduce the ISAC-enabled network as well as several design challenges. Then, we present some key design issues of the ISAC-enabled network, including the sensing information dissemination, where some scenarios or use cases for practical applications of the ISAC-enabled network are given to validate the effectiveness of the epidemic theory-based modeling. Finally, the potential directions of epidemic theory on ISAC-enabled networks are discussed to motivate future works.