Stage-structured discrete-time models for interacting wild and sterile mosquitoes with beverton-holt survivability

Yang Li; Jia Li; Yang Li; Jia Li

doi:10.3934/mbe.2019028

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 572-602. doi: 10.3934/mbe.2019028

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Research article

Stage-structured discrete-time models for interacting wild and sterile mosquitoes with beverton-holt survivability

Yang Li ^{1
,
,},
Jia Li ^2,3

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
2.
Center for Applied Mathematics, Guangzhou University, Guangzhou 51006, China
3.
Department of Mathematical Sciences, The University of Alabama in Huntsville, Huntsville, AL 35899, USA

Received: 18 June 2018 Accepted: 03 October 2018 Published: 11 January 2019

The sterile insect technique (SIT) is an effective weapon to prevent transmission of mosquito-borne diseases, in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population. To study the impact of the sterile insect technique on the disease transmission, we formulate stage-structured discrete-time models for the interactive dynamics of the wild and sterile mosquitoes using Beverton-Holt type of survivability, based on difference equations. We incorporate different strategies for releasing sterile mosquitoes, and investigate the model dynamics. Numerical simulations are also provided to demonstrate dynamical features of the models.
- mathematical modeling,
- beverton-holt survivability,
- discrete-time models,
- sterile mosquitoes,
- vector-borne diseases,
- numerical simulations
Citation: Yang Li, Jia Li. Stage-structured discrete-time models for interacting wild and sterile mosquitoes with beverton-holt survivability[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 572-602. doi: 10.3934/mbe.2019028

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Abstract

The sterile insect technique (SIT) is an effective weapon to prevent transmission of mosquito-borne diseases, in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population. To study the impact of the sterile insect technique on the disease transmission, we formulate stage-structured discrete-time models for the interactive dynamics of the wild and sterile mosquitoes using Beverton-Holt type of survivability, based on difference equations. We incorporate different strategies for releasing sterile mosquitoes, and investigate the model dynamics. Numerical simulations are also provided to demonstrate dynamical features of the models.

References

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