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The contact process is an emblematic model of a non-equilibrium system,containing a phase transition between inactive and active dynamical regimes. Inthe epidemiological context, the model is known as thesusceptible-infected-susceptible (SIS) model, and widely used to describecontagious spreading. In this work, we demonstrate how accurate and efficientrepresentations of the full probability distribution over all configurations ofthe contact process on a one-dimensional chain can be obtained by means ofMatrix Product States (MPS). We modify and adapt MPS methods from many-bodyquantum systems to study the classical distributions of the driven contactprocess at late times. We give accurate and efficient results for thedistribution of large gaps, and illustrate the advantage of our methods overMonte Carlo simulations. Furthermore, we study the large deviation statisticsof the dynamical activity, defined as the total number of configuration changesalong a trajectory, and investigate quantum-inspired entropic measures, basedon the second R\'enyi entropy.

Efficient simulations of epidemic models with tensor networks: application to the one-dimensional SIS model