Information diffusion can be controlled by disconnecting user accounts (nodes) in online social networks, as well as in real-world networks. To identify the most influential links to remove while minimizing diffusion, previous studies have proposed upper bounds for spreading processes in SIR and SIS models, using supermodularity and weighted matrices to identify critical links in contact networks. However, in some cases, existing upper bounds are not sufficiently tight to accurately capture the effect of important edges, as in the SDIR model of \cite{Khanh2026}. We therefore propose a tighter upper bound for controlling diffusion in the SDIR model by directly analyzing the dynamics of the two state vectors D and I in a $2N$-dimensional space. This approach yields an improved spectral-radius convergence condition and outperforms the previous method. Simulations on the real-world Haslemere dataset using a Greedy edge-deletion algorithm demonstrate its effectiveness for influence minimization on social networks.

SDIR epidemic models,complex networks; influential nodes identification; spanning tree; redundant ties,Complex Networks,discrete optimization,Markov chains,edge deletion,Greedy Algorithm,mean-field approximation