The uncertainty associated with the evolution of new and emerging infectious diseases remains a huge impediment to the development of efficient biosecurity policies in both the developed and developing worlds.  One potentially useful tool in the estimation of risks associated with different emergence paths is multitype branching-process theory. In this talk, I'll analyze extinction and emergence probabilities in a scenario of ongoing transmission between a host population and a zoonotic reservoir, and show how.  Topics will include discussion irreversible process approximations of reversible processes, and numerical methods for the calculation of extinction probabilities and elasticities.