arXiv 2201.092302022-01math.DS

Modelling the inhibiting effect on a microbial pesticide model

Xiaoxiao Cui, Yonghui Xia

备注：: Many studies have shown that some species of microorganism A (or plant extracts) can inhibit other species of microorganism B (bacteria or fungi), and this inhibiting effect can reduce the birth rate of microorganism B. Consequently, the density of B is inversely proportional to the density of A. Thus, using an inverse proportional function to modelling the inhibiting effect is very reasonable

英文摘要：

Microbial pesticides can avoid many of negative effects of traditional chemical pesticides. To modelling the inhibiting effect, in this paper we propose a model of entomopathogenic nematodes killing the target insects, and inhibiting the birth rate of the target insects simultaneously. In the model, we achieve the purpose of restricting or eliminating pests by continuously releasing nematodes. By analyzing the stability of the equilibrium of the model and the stability of the Hopf bifurcation periodic solution, the best solution to control pests is obtained, and our conclusions are verified by examples and numerical simulations.

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