An improved integrated pest management model under 2 control parameters (sterile male and pesticide).

*(English)*Zbl 1120.92042Summary: The object of the present paper is to study an integrated pest management (IPM) problem in an agro-ecosystem (paddy-fish culture) through mathematical modeling and analysis, where release of sterile males and spraying of pesticide have been used as control measures for the pest population. Using optimal analysis of the model, we have shown that restricted and proper use of control measures might enhance the crop production of the system in an economically viable way. The paper also considers the vulnerability of the underlined ecosystem due to the effect of temperature on the pest growth. Using Lyapunov-like functions, we have found out a suitable range of temperature, where this IPM strategy remains effective. Some important remarks have finally been made on the basis of numerical simulations.

##### MSC:

92D40 | Ecology |

93C95 | Application models in control theory |

49N90 | Applications of optimal control and differential games |

##### Keywords:

sterile males; vulnerability of the system; singular control; Pontryagin’s maximum principle
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\textit{S. Bhattacharyya} and \textit{D. K. Bhattacharya}, Math. Biosci. 209, No. 1, 256--281 (2007; Zbl 1120.92042)

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##### References:

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