In this stduy we introduce a new SIS-like model of network diffusion where the
probability rate functions can depend not only on the states of the nodes neigh-
borhoods but on the whole network state. The model allows also competitive
scenarios, where there are two states both diffusive. In this framework, we pro-
pose an efficient dynamic algorithm, Generalized Largest Reduction in Infectious
Edges (gLRIE), that enhances the counter-contagion by allocating treatments. The
algorithm is generalized to the case of network with hierarchical cluster structure.
We perform simulations for a large set of parameters on random and real networks
and compare the results with competitors from literature. The same idea was also
applied in the different setting of deterministic SIS model in metapopulation and
analysed in the framework of optimal control theory.