Bacteria of the Salmonella genus are intracellular pathogens, which cause gastroenteritis and typhoid fever in animals and humans, and are responsible for millions of infections and thousands of deaths across the world every year. Furthermore, Salmonella has played the role of a model organism for studying host-pathogen interactions. Taking these two aspects into account, enormous efforts in the literature are devoted to study this intracellular pathogen. Within epithelial cells, there are two distinct subpopulations of Salmonella: (i) a large fraction of Salmonella, which are enclosed by vacuoles, and (ii) a small fraction of hyper-replicating cytosolic Salmonella. Here, by considering the infection of epithelial cells by Salmonella as a discrete-state, continuous-time Markov process, we propose a stochastic model of infection, which includes the invasion of Salmonella into the epithelial cells by a cooperative strategy, the replication inside the Salmonella-containing vacuole, and the bacterial proliferation in the cytosol. The xenophagic degradation of cytosolic bacteria is considered, too. The stochastic approach provides important insights into stochastic variation and heterogeneity of the vacuolar and cytosolic Salmonella populations on a single-cell level over time. Specifically, we predict the percentage of infected human epithelial cells depending on the incubation time and the multiplicity of infection, an d the bacterial load of the infected cells at different post-infection times.Competing Interest StatementThe authors have declared no competing interest.