A stochastic modelling approach to describing the dynamics of an experimental furunculosis epidemic in Chinook salmon, Oncorhynchus tshawytscha (Walbaum).

Abstract

A susceptible-infected-removed (SIR) stochastic model was compared to a susceptible-latent-infectious-removed (SLIR) stochastic model in terms of describing and capturing the variation observed in replicated experimental furunculosis epidemics, caused by Aeromonas salmonicida. The epidemics had been created by releasing a single infectious fish into a group of susceptible fish (n = 43) and progress of the epidemic was observed for 10 days. This process was replicated in 70 independent groups. The two stochastic models were run 5000 times and after every run and every 100 runs, daily mean values of each compartment were compared to the observed data. Both models, the SIR model (R(2) = 0.91), and the SLIR model (R(2) = 0.90) were successful in predicting the number of fish in each category at each time point in the experimental data. Moreover, between-replicate variability in the stochastic model output was similar to between-replicate variability in the experimental data. Generally, there was little change in the goodness of fit (R(2)) after 200 runs in the SIR model whereas 500 runs were necessary to have stable predictions with the SLIR model. In the SIR model, on an individual replicate basis, approximately 80% of 5000 simulated replicates had R(2) = 0.7 and above, whereas this ratio was slightly higher (82%) with the SLIR model. In brief, both models were equally effective in predicting the observed data and its variance but the SLIR model was advantageous because it differentiated the latent, i.e. infected but not having the ability to discharge pathogen, from the infectious fish.