Pair quenched mean-field approach to epidemic spreading 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.