The influence of a transport process on the epidemic threshold

Abstract

By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the transport process that gives rise to a multiplex network model. In addition to a static layer, the (multiplex) epidemic network consists of a second dynamic layer in which any two individuals are connected for the time they occupy the same site during a random walk they perform on a separate transport network. We develop a mean-field description of the stochastic network model and study the influence the transport process has on the epidemic threshold. We show that any transport process generally lowers the epidemic threshold because of the additional connections it generates. In contrast, considering also random walks of fractional order that in some sense are a more realistic model of human mobility, we find that these non-local transport dynamics raise the epidemic threshold in comparison to a classical local random walk. We also test our model on a realistic transport network (the Munich U-Bahn network), and carefully compare mean-field solutions with stochastic trajectories in a range of scenarios.

Version as to appear in the Journal of Mathematical Biology with revised figures

References in corpus (13)

• Understanding individual human mobility patterns
• The structure and dynamics of multilayer networks
• The scaling laws of human travel
• Inferring change points in the COVID-19 spreading reveals the effectiveness of interventions
• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• Lévy walks
• Characterizing Human Mobility Patterns in a Large Street Network
• Phase transitions in contagion processes mediated by recurrent mobility patterns
• Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights
• Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading
• Analytical parameter estimation of the SIR epidemic model. Applications to the COVID-19 pandemic
• Nonlocal network dynamics via fractional graph Laplacians
• Fractional random walk lattice dynamics