  It has been shown in the past that many real-world networks exhibit community
structures and non-trivial clustering which comes with the occurrence of a
notable number of triangular connections. Yet the influence of such connection
patterns on the dynamics of disease transmission is not fully understood. In
order to study their role in the context of Susceptible-Infected-Susceptible
(SIS) epidemics we use the Triadic Random Graph (TRG) model to construct small
networks (N=49) from distinct, closed, directed triadic subpatterns. We compare
various global properties of TRGs and use the N-intertwined mean-field
approximation (NIMFA) model to perform numerical simulations of SIS-dynamics on
TRGs. The results show that the infection spread on undirected TRGs displays
very similar behavior to TRGs with an abundance of (directed) feed-back-loops,
while using (directed) feed-forward-loops as network-entities significantly
slows down the epidemic and lowers the number of infected individuals in the
endemic state. Moreover, we introduce a novel stochastic approach for modelling
the SIS-epidemics on TRGs based on characterizing nodes according to their set
of $\left(k_{in},k_{out}\right)$ within triads. Within this model, the topology
of the network is given by the number and the local structure of directed
triadic motifs and not by the adjacency matrix. Nevertheless, the outcome of
simulations is qualitatively similar to the results of the NIMFA model.
