A zoonotic disease is a disease that can be passed from animals to humans. 
Zoonotic viruses may adapt to a human host eventually becoming endemic in 
humans, but before doing so punctuated outbreaks of the zoonotic virus may be 
observed. The Ebola virus disease (EVD) is an example of such a disease. The 
animal population in which the disease agent is able to reproduce in sufficient 
number to be able to transmit to a susceptible human host is called a reservoir. 
There is little work devoted to understanding stochastic population dynamics in 
the presence of a reservoir, specifically the phenomena of disease extinction 
and reintroduction. Here, we build a stochastic EVD model and explicitly 
consider the impacts of an animal reservoir on the disease persistence. Our 
modelling approach enables the analysis of invasion and fade-out dynamics, 
including the efficacy of possible intervention strategies. We investigate 
outbreak vulnerability and the probability of local extinction and quantify the 
effective basic reproduction number. We also consider the effects of dynamic 
population size. Our results provide an improved understanding of outbreak and 
extinction dynamics in zoonotic diseases, such as EVD.