Epidemic dynamics with awareness cascade of positive and negative information on delayed multiplex networks

Human behavioral awareness is usually socially relevant, decisions are made based on the behavior of individuals, and this dynamic process of human awareness with herd effects is called awareness cascade. Based on the complexity of modern information dissemination, information is not monolithic. Individuals choose the type of epidemic-related information to accept, i.e., whether it is positive or negative information, according to the awareness cascade, and then take the corresponding measures to cope with the epidemic. In this paper, we use the microscopic Markov chain approach to model an information-virus dual network, where the information layer has a threshold model with awareness cascade of positive and negative information, and on the virus layer is a susceptible-infected-recovery model with epidemic infection time delay and recovery time delay. The time delay is also a non-negligible modeling factor as the complete infection of an individual and the complete recovery of an individual require sufficient time. An explicit formula for the critical threshold of epidemic spread for this model is derived. We find that positive and negative information and time delay have a significant effect on the critical threshold, and the recovery time delay is the time delay that mainly affects the epidemic size. Experiments show that the local acceptance rate of positive information has a threshold point for the spread of epidemics under awareness cascade, and that this point is significantly affected by the mass media. The local acceptance rate of negative information also divides the spread of epidemics into two stages.