Multiscale dynamics of epidemic-information coupling model on duplex networks: Role of environmental transmission

Nowadays, with the development of Internet technology and the change of climate and environment, the spread of epidemics has become more and more complex. This paper considers a multiscale model coupling epidemics, information and environment, where we adopt the UAU (unaware-aware-unaware) process for information propagation and the modified SIS (susceptible-infective-susceptible) model with environmental infection for epidemic spreading. To describe the differences in epidemic and information transmission pathways and speeds, we use a duplex network framework and introduce a relative timescale parameter. Under a homogeneous mixing hypothesis, we utilize the mean-field approach to reduce the dimension of the model and analyze its dynamics, including epidemic thresholds and the existence and stability of disease-free equilibria. In the case of heterogeneous networks, we conduct a similar analysis. Numerical simulations are performed to confirm the existence of positive equilibria and show that information dissemination [especially the reactions of AS (aware and susceptible) and AI (aware and infected) individuals] and environmental cleanup are crucial. However, rapid information dissemination is not conducive to reducing the final scale of epidemics. A preliminary understanding of the relationship among environment, information, and epidemics in multiscale context is of great significance for preventing and controlling the spread of epidemics in real life.