Dynamics in A Stage-Structured Model for Biocontrol of Sea Lice

Prof. Yuan Yuan Memorial University of newfoundland, Canada

Sea lice infection is one of the major threats in marine fishery, especially for farmed salmon.So the treatment of sea lice become one of the top priorities in aquaculture research, due to their responsibility for most disease outbreaks on salmon farms and causing enormous monetary losses.In this talk, we proposea mathematical model for the growth and biological control of sea lice.We classify the growth of sea lice population into three stages and introduce cleaner fish as a predator to discuss the interaction between sea lice and cleaner fish by using the theory and methods in dynamics. Throughmathematical analysis, weaddressthreshold dynamics with respect to the adult reproduction numberfor sea lice $\mathcal{R}_s$ andthe net reproductive number of cleaner fish $\mathcal{R}_f$, including the global stability of the trivial steady state when $\mathcal{R}_s<1$, global attractivity ofthe predator-free equilibrium point when $\mathcal{R}_s>1$ and $\mathcal{R}_f<1$, persistence and existence of a unique positive steady statewhen $\mathcal{R}_s>1$ and $\mathcal{R}_f>1$. We further discuss the local stability of thepositive equilibrium point and investigate the Hopf bifurcation. Numerical simulations and case study are provided to assert the theoretical predictions.