A research of pest management SI stochastic model concerning spraying pesticide and releasing natural enemies

Lan Guijie, Fu Yingjie, Wei Chunjin, Zhang Shuwen

Abstract


In this paper, we study the dynamics of the stochastic SI epidemic model for pest management concerning spraying pesticide and releasing natural enemies. Existence of a unique global positive solution is proved firstly. And we show that the positive solution to the stochastic system is stochastically bounded. Third, by using Khasminshii's method and Lyapunov function, we derive the sufficient conditions for the existence of the nontrivial stochastically positive T-periodic solution. Then, by comparison theorem for stochastic differential equation, the sufficient conditions for existence and global attraction of the boundary periodic solution are obtained. Finally, Numerical simulations are carried out to substantiate the analytical results.

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Published: 2018-03-15

How to Cite this Article:

Lan Guijie, Fu Yingjie, Wei Chunjin, Zhang Shuwen, A research of pest management SI stochastic model concerning spraying pesticide and releasing natural enemies, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 5

Copyright © 2018 Lan Guijie, Fu Yingjie, Wei Chunjin, Zhang Shuwen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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