Failure Detection periodically detects node validity to maintain application layer network stability. The detection cycle interval value is a key parameter for detection scheme performance; there have been few studies on models of analyzing cycle interval value affecting the scheme. We propose a dynamic model of hierarchical application layer multicast tree node failure epidemic SIRS (NFE-SIRS). The NFE-SIRS analyzes statistical node failure in hierarchical application layer multicast tree structure, and models relationship between cycle interval value and detection scheme repair behavior, finally obtains the expected cycle interval value to improve detection scheme performance. Simulation shows that, the NFE-SIRS can dramatically improve detection scheme performance compared with common fixed cycle interval detection scheme.