A pest control model with birth pulse and residual and delay effects of pesticides

Jinyang Li,Qingdao Huang,Bing Liu

doi:10.1186/s13662-019-1978-7

Jinyang Li, Qingdao Huang + Show 1 more

Open Access

https://doi.org/10.1186/s13662-019-1978-7

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Abstract

Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed time in a year. So a pest control model with birth pulse and spraying pesticides is proposed. Using the limit system of the developed model, we analyze the dynamics of the system. The stability of the trivial equilibrium and the positive equilibrium of the model is analyzed, and the threshold conditions of pest eradication and permanence of the system are given. We obtain the optimal frequency of spraying pesticides by numerical simulations. The important parameters related to the pest eradication or permanence of the system are given by analyzing the sensitivity of the parameters. Finally, biological explanations are provided.

Highlights

The economic development of China has been advancing rapidly
Considering the delayed and residual effects of the pesticide, the pollution emission model is employed to simulate the mathematical function of pesticide effects
Ricker and Beverton–Holt birth functions are investigated in our study. This is the first study in which a mathematical function based on pesticide effects has been incorporated into a pest management model with stage structure and birth pulse

Summary

Introduction

The economic development of China has been advancing rapidly. Methods to increase crop yield are highly desired and are critical to the economic growth of the nation. Wei [9] analyzed the dynamics of the pest control models with birth pulse under the assumptions that pesticides killed adult pests or larvaes or both of them, respectively. Based on the above biological background, in this paper, we study a pest management model with stage structure and birth pulse, and only chemical control is applied. Assuming the adult population reproduce at the fixed time in a year, the model considering stage structure and birth pulse constructed by Tang [23] is as follows:. Based on the above birth pulse model and the assumption that the pesticide is applied at fixed time in a birth cycle, Liu [6] built the following pest management model:.

The solution for the positive equilibrium is

Conclusion