Predicting disease outbreak in models of aquaculture

Infectious Salmon Anemia (ISA) virus (ISAv) is an Orthomyxovirus which causes ISA in a variety of finfish including Atlantic salmon (Salmo salar L.).  The disease has resulted in large mortality events and associated economic losses to the salmon culture industries in nearly all major salmon producing countries.  We recall results deterministic analysis including equilibria and thresholds for the persistence of the virus.  We introduce related stochastic models and utilize numeric and analytic techniques to approximate the probability of outbreak for each model.  We show the threshold for this probability being greater than zero is equal to the threshold for persistence in the deterministic setting.