In the real world, individual resources are crucial for patients when epidemics outbreak. Thus, the coupled dynamics of resource diffusion and epidemic spreading have been widely investigated when the recovery of diseases significantly depends on the resources from neighbors in static social networks. However, the social relationships of individuals are time-varying, which affects such coupled dynamics. For that, we propose a coupled resource-epidemic (RNR-SIS) dynamic model (coupled model for short) on a time-varying multiplex network to synchronously simulate the resource diffusion and epidemic spreading in dynamic social networks. The equilibrium analysis of the coupled model is conducted in a general scenario where the resource generation varies between susceptible and infected states and the recovery rate changes between resourceful and noresource states. By using the microscopic Markov chain approach and Monte Carlo simulations, we determine a probabilistic framework of the intralayer and interlayer dynamic processes of the coupled model and obtain the outbreak threshold of epidemic spreading. Meanwhile, the experimental results show the trivially asymmetric interactions between resource diffusion and epidemic spreading. They also indicate that the stronger activity heterogeneity and the larger contact capacity of individuals in the resource layer can more greatly promote resource diffusion, effectively suppressing epidemic spreading. However, these two individual characters in the epidemic layer can cause more resource depletion, which greatly promotes epidemic spreading. Furthermore, we also find that the contact capacity finitely impacts the coupled dynamics of resource diffusion and epidemic spreading.
Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network
