Coupled Dynamic Model of Resource Diffusion and Epidemic Spreading in Time-Varying Multiplex Networks

Ping Huang,Xiao-Long Chen,Shi-Min Cai,Ming Tang,Ye Wu

doi:10.1155/2021/6629105

Abstract

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.

Highlights

Most real networks are not isolated and the spreading dynamic processes on such real networks described by classical models such as the susceptible-infected-susceptible model (SIS) [1, 2] and susceptible-infected-recovery model (SIR) [3] may be interrelated and interactive with each other [4,5,6]
We perform the investigations by assuming a good abstraction from a real scenario, where the diseases spread on a physical contact network, the individual resources diffuse on an online social network, and they dynamically interact with each other
Considering such two networks are temporal due to the time-varying physical contacts or social relationships of individuals, we first construct the time-varying two-layer network by using two AD network models with different parameters. e AD model encodes the connectivity pattern of individuals in the distribution of activity potential following a power-law function empirically measured in realworld networks. is function allows the definition of a simple dynamic process based on the nodal activity level, providing a time-dependent description of the connectivity pattern

Summary

Introduction

Most real networks are not isolated and the spreading dynamic processes on such real networks described by classical models such as the susceptible-infected-susceptible model (SIS) [1, 2] and susceptible-infected-recovery model (SIR) [3] may be interrelated and interactive with each other [4,5,6]. As the resource diffusion and epidemic spreading on dynamic social networks synchronously happen in real society, the present work uses the AD model to construct a generic time-varying multiplex network representing the active contacts (or social relationships) of social networks. Ese two dynamic models are coupled into the RNR-SIS model by interlayer links of the time-varying multiplex network better to understand the interactions between resource diffusion and disease spreading. Considering the similarity between awareness propagation and resource diffusion, we make efforts to apply the MMCA for constructing a theoretical framework of the coupled resource-epidemic dynamic model (i.e., coupled RNR-SIS model) on a time-varying multiplex network. (iii) At time t + Δt (we set Δt 1), all edges of the previous network in each layer are deleted and we repeat the construction of AD networks. e coupled dynamic process continuously evolves according to the rules and is terminated when it converges to the stable state

Theoretical Analysis Based on Microscopic Markov Chain Approach

Results

Conclusion