We present a stochastic epidemic model with vectorial transmission and multi-host structure. To include environmental noise, we stochastically perturb biting rates with general state functional intensities. So, we derive a stochastic differential equation (SDE) which describes a vector disease with two types of hosts – humans and animals – and give conditions to assure disease extinction and persistence. Finally, via numerical experiments, we extend and illustrate our results using literature parameters for Chagas.