Global dynamics in sea lice model with stage structure

Sea lice infection is one of the major threats in the marine fishery, especially for farmed salmon. In this paper, we propose a mathematical model for the growth of sea lice with a three-stage structure: non-infectious immature, infectious immature and adults where the level of non-infectious immature development depends on the size of the adult population. We first describe the nonlinear dynamics by a system of partial differential equations, then, by mathematical techniques and an appropriate change of variables transform it into a system of delay differential equations with constant delay. We address the system threshold dynamics in the established model with respect to the adult reproduction number Rs, including the global stability of the trivial steady state when Rs<1, persistence and global attractivity of the unique positive steady state when Rs>1. Numerical simulations are provided to confirm the theoretical results.