Cage culture, as a kind of aquaculture, is increasingly becoming the main way to provide aquatic products due to its merits of high output and easy management. However, the main issue for the fishermen to be concerned about is the determination of the reasonable amount of casting bait since excess feeding bait will not only deteriorate water quality but also increase farming costs while too little bait casting cannot meet the demand for capture. To this end, in this letter, we formulate a diffusive bait-fish model with advection term, aiming to determine the bait casting threshold that meets the demand for the breeding and causes less pollution to the water environment. We first prove the well-posedness of the proposed model. Then we define the net reproductive rate $R_0$ determining the survival of the model and reveal the relationship between $R_0$ and the bait casting rate. Besides, we show that the proposed model undergoes a forward supercritical transcritical bifurcation when the bait casting rate is equal to the critical value. Finally, we resort to a numerical example to support our theoretical results.

网箱养殖作为水产养殖的一种，以其产量高、管理方便等优点，日益成为水产品供应的主要方式。但是，渔民们关心的主要问题是如何确定合理的投饵量，因为投饵过多不仅会恶化水质，还会增加养殖成本，而投饵过少则不能满足捕捞需求。为此，在这封信中，我们制定了一个带有平流项的扩散饵鱼模型，旨在确定满足养殖需求且对水环境污染较小的饵料投放阈值。我们首先证明了所提出模型的适定性。然后我们定义净繁殖率$R_0$确定模型的生存和揭示之间的关系$R_0$和诱饵投放率。此外，我们表明，当诱饵投放率等于临界值时，所提出的模型经历了前向超临界跨临界分叉。最后，我们借助一个数值例子来支持我们的理论结果。