A single cohort time delay model of the life-cycle of the salmon louse Lepeophtheirus salmonis on Atlantic salmon Salmo salar

Abstract

A single cohort time delay differential equation model of Lepeophtheirus salmonis population dynamics was developed. The model was parameterised using data from tank infection trials, which followed a single experimental cohort of post-settlement lice through all the developmental stages. This simple mathematical model successfully predicted the timing and numbers of parasites present on the host. However, the death rates of parasitic louse stages within the tank trials were found to be highly variable despite the simplified conditions prevailing within such a system. Embryonic development, free-living nauplius stages and infection parameters were added to this model to allow the complete parasite life-cycle to be described. In addition simulations were carried out to determine the effect upon short-term salmon louse population dynamics of employing a notional chemotherapeutant having an arbitrary instantaneous efficacy of 80%. These results were used to determine the optimal timing of treatment relative to initial lice counts. This was found to be different for male and female lice stages, reflecting their respective developmental rates.