Study of the sterile insect release technique for a two-sex mosquito population model

Mingzhan Huang; Shouzong Liu; Xinyu Song; Mingzhan Huang; Shouzong Liu; Xinyu Song

doi:10.3934/mbe.2021069

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 2: 1314-1339. doi: 10.3934/mbe.2021069

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Research article

Study of the sterile insect release technique for a two-sex mosquito population model

1.
College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
2.
College of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Received: 22 October 2020 Accepted: 13 January 2021 Published: 20 January 2021

In this paper, to study the large-scale time control and limited-time control of mosquito population in a field, a two-sex mosquito population model with stage structure and impulsive releases of sterile males is proposed. For the large-scale time control, a wild mosquito-free periodic solution is given and conditions under which it is globally stable are obtained by the use of the monotone system theory. Besides, based on the stability analysis, threshold conditions under which the wild mosquito population is eliminated or not are obtained. Then we study three different optimal release strategies for the limited-time control, which takes into account both of the population control level of wild mosquitoes and the economic input. To solve technical problems in optimal impulsive control, a time rescaling technique is applied and the gradients of cost function with respect to all control parameters are obtained. In addition, by the aid of numerical simulation, we get the optimal release amounts and release timings for each release strategy. Our study indicates that the optimal release timing control is superior to the optimal release amount control. However, simultaneous optimal selection of release amount and release timing leads to the best control performance.
- large-scale time control,
- limited-time control,
- impulsive release,
- release timing,
- release amount
Citation: Mingzhan Huang, Shouzong Liu, Xinyu Song. Study of the sterile insect release technique for a two-sex mosquito population model[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1314-1339. doi: 10.3934/mbe.2021069

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Abstract

In this paper, to study the large-scale time control and limited-time control of mosquito population in a field, a two-sex mosquito population model with stage structure and impulsive releases of sterile males is proposed. For the large-scale time control, a wild mosquito-free periodic solution is given and conditions under which it is globally stable are obtained by the use of the monotone system theory. Besides, based on the stability analysis, threshold conditions under which the wild mosquito population is eliminated or not are obtained. Then we study three different optimal release strategies for the limited-time control, which takes into account both of the population control level of wild mosquitoes and the economic input. To solve technical problems in optimal impulsive control, a time rescaling technique is applied and the gradients of cost function with respect to all control parameters are obtained. In addition, by the aid of numerical simulation, we get the optimal release amounts and release timings for each release strategy. Our study indicates that the optimal release timing control is superior to the optimal release amount control. However, simultaneous optimal selection of release amount and release timing leads to the best control performance.

References

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