Indirect information propagation model with time-delay effect on multiplex networks

Epidemics pose a significant threat to humanity. During the early stages of an outbreak, individuals often lack comprehensive or timely access to disease-related information. The primary mode of information propagation is indirect, primarily originating from friends or their extended networks. The primary mode of information propagation is indirect, primarily originating from friends or their extended networks. Additionally, the spread of information is influenced by the incubation period of infected individuals. In this study, we develop a novel information–disease coupled propagation model, integrating both indirect information transmission and individual disease incubation periods into the dynamics of information–disease interaction on multiplex networks. It is called time-delay ID-CIP. We derive the epidemic outbreak threshold using a microscopic Markov chain approach and compare our model with classical pairwise interaction propagation and recent higher-order models. The findings suggest that the proposed information propagation mechanism is more effective in suppressing disease spread. Numerical simulations reveal that prior to an outbreak, awareness density converges to zero in the steady state, helping prevent epidemic-related rumor propagation. The disease’s incubation period has no effect on the density of the infected population in the steady state; however, it significantly impacts the density of individual’s epidemic-related awareness.