Learning the probability of activation in the presence of latent spreaders

Abstract

When an infection spreads among members of a community, an individual's probability of becoming infected depends on both his susceptibility to the infection and exposure to the disease through contact with others. While one often has knowledge regarding an individual's susceptibility, in many cases, whether or not an individual's contacts are contagious and spreading the infection is unknown or latent. We propose a new generative model in which we model the neighbors' spreader states and the individuals' exposure states as latent variables. Combined with an individual's characteristics, we estimate the risk of infection as a function of both exposure and susceptibility. We propose a variational inference algorithm to learn the model parameters. Through a series of experiments on simulated data, we measure the ability of the proposed model to identify latent spreaders, estimate exposure as a function of one's spreading neighbors, and predict the risk of infection. Our work can be helpful in both identifying potential asymptomatic carriers of infections, and in identifying characteristics that are associated with an increased likelihood of being an undiagnosed source of contagion.