Disease spreading with social distancing: a prevention strategy in disordered multiplex networks

Perez, I. A.; Muro, M. A. Di; Rocca, C. E. La; F'isica, L. A. Braunstein Instituto de Investigaciones F'isicas de Mar del Plata -Departamento de; FCEyN,; Plata-CONICET, Universidad Nacional de Mar del; Plata, Mar del; Argentina,; Department, Physics; University, Boston; Boston,; MA,; USA.,

The continue emerging of diseases that have the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and COVID-19, makes it relevant to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are very rare to find in any context, specially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers that are interconnected through a fraction $q$ of shared individuals. We model the interactions between individuals in each layer through a weighted network, because person-to-person interactions are diverse (or disordered); weights represent the contact times of these interactions and we use a distribution of contact times to assign an individual disorder to each layer. Using branching theory supported by simulations, we study a social distancing strategy where we reduce the average contact time in one layer (or in both of them, if necessary). We find a set of disorder parameters - associated with average contact times - that prevents a disease from becoming an epidemic. When the disease is very likely to spread, the system is always in an epidemic phase, regardless of the disorder parameters and the fraction of shared nodes. However we find that it is still possible to protect a giant component of susceptible individuals, which is crucial to keep the functionality of the system composed by the two interconnected layers.