Pair quenched mean-field approach to epidemic spreading in multiplex networks

Abstract

• A pair-quenched mean-field approach to epidemic spreading on multiplex networks is developed. • The condition for the epidemic threshold in a static multiplex network is derived. • Gillespie algorithm-based simulations staged on various multilayered network topologies were conducted. • Theoretical results are in agreement with numerical simulations on 2-layer and 3-layer complex networks. • Our findings highlight the efficiency of the presented approach for assessing epidemic thresholds in multiplex networks. Using the law of total probability, we extend the pair quenched mean-field approach for epidemic spreading in monoplex networks to the scenario of contagion outbreaks in multiplex networks. By means of the quasi-static approximation, we derive the condition for the epidemic threshold in a static multiplex network overlapped by the randomly connected subnetwork without clustering. Our theoretical results are in good agreement with continuous-time Gillespie algorithm-based simulations for 2-layer and 3-layer multiplex networks, revealing the advantage of our model in the prediction of epidemic spreading relative to the quenched mean-field (QMF) approach. Importantly, our study demonstrates that unlike the standard QMF approach, the pair QMF model can be used to assess the influence of the link overlap on the epidemic threshold, thereby carrying vital implications for future epidemiological research and policy development.