【10月15日下午】袁沅 教授：Dynamics In the Growth of Sea Lice and Control

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 propose a 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. Through  mathematical analysis, we  address  threshold dynamics with respect to the adult reproduction number  for sea lice $\mathcal{R}_s$ and  the 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 of  the predator-free equilibrium point when $\mathcal{R}_s>1$ and $\mathcal{R}_f<1$, persistence and existence of a unique positive steady state  when $\mathcal{R}_s>1$ and $\mathcal{R}_f>1$. We further discuss the local stability of the  positive equilibrium point and investigate the Hopf bifurcation. Numerical simulations and case study are provided to assert the theoretical predictions.