Multi-species compartment epidemic models, such as the multi-species susceptible-infectious-recovered (SIR) model, are extensions of the classic SIR models, which are used to explore the transient dynamics of pathogens that infect multiple hosts in a large population. In this article, we propose a dynamical Bayesian hierarchical SIR (HSIR) model, to capture the stochastic or random nature of an epidemic process in a multi-species SIR (with recovered becoming susceptible again) dynamical setting, under hidden mass balance constraints. We call this a Bayesian hierarchical multi-species SIR (MSIRB) model. Different from a classic multi-species SIR model (which we call MSIRC), our approach imposes mass balance on the underlying true counts rather than, improperly, on the noisy observations. Moreover, the MSIRB model can capture the discrete nature of, as well as uncertainties in, the epidemic process.