Table 1 Summary table of noteworthy notation introduced

G_A=(V_A,E_A)

Graph for layer A.

N _A

Number of nodes in layer A.

F ₀

Set of initial spreaders afflicted at the start of propagation.

\(F_{0}^{A}\)

Set of initial spreaders in layer A afflicted at the start of propagation.

M _AA

Adjacency matrix representing layer A.

M _AB

Adjacency matrix representing inter-edges directed from layer A to layer B.

\(U_{A}^{intra}(i)\)

Set of intra-neighbors for node i in layer A.

\(U_{A}^{inter}(i)\)

Set of inter-parents for node i in layer A.

α(i)

Fraction of intra-neighbors of node i that are afflicted.

β(i)

Fraction of inter-parents of node i that are afflicted.

π(i)

Probability of affliction by an intra-neighbor of node i.

π^′(i)

Probability of affliction by an inter-parent of node i.

T

Time horizon (or number of time-steps) considered for experiments.

Φ

Percentage of nodes in the M-IDN selected to be initial spreaders.