In this study, a mosquito population suppression model that integrates stage structure is introduced, which serves as the foundation for exploring various strategies for the periodic impulsive release of sterile mosquitoes, including those that either incorporate or disregard population state feedback, as well as a composite control approach. We identify release thresholds under different strategies that ensure the complete eradication of the wild mosquito population. Numerical analyses are conducted to evaluate the performance of these release strategies. Our findings reveal that integrating state feedback mechanisms can effectively prevent the blindness of release behaviors. Key factors such as the release interval, frequency of population assessments, and control intensity significantly influence the reduction of the cumulative release quantity of sterile mosquitoes, the shortening of control duration, and the decrease in effective release events. The influence of these factors on control outcomes across different strategies and scenarios is also examined.
Shouzong LIU
,
Yang XU
,
Mingzhan HUANG
. THRESHOLD ANALYSIS OF IMPULSIVE CONTROL IN A MOSQUITO POPULATION SUPPRESSION MODEL WITH SPARSE STATE FEEDBACK[J]. Acta mathematica scientia, Series B, 2026
, 46(2)
: 897
-919
.
DOI: 10.1007/s10473-025-0219-x
[1] Strugarek M, Bossin H, Dumont Y. On the use of the sterile insect release technique to reduce or eliminate mosquito populations. Appl Math Model, 2019, 68: 443-470
[2] Bliman P A, Cardona-Salgado D, Dumont Y, Vasilieva O. Implementation of control strategies for sterile insect techniques. Math Biosci, 2019, 314: 43-60
[3] Zheng X, Zhang D, Li Y, et al. Incompatible and sterile insect techniques combined eliminate mosquitoes. Nature, 2019, 572(7767): 56-61
[4] Lees R S, Gilles J R, Hendrichs J, et al. Back to the future: the sterile insect technique against mosquito disease vectors. Current Opinion in Insect Science, 2015, 10: 156-162
[5] Cai L M, Ai S B, Li J. Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes. SIAM J Appl Math, 2014, 74(6): 1786-1809
[6] Li J. New revised simple models for interactive wild and sterile mosquito populations and their dynamics. J. Biol Dynam, 2016, 11(S2): 316-333
[7] Li J, Cai L M, Li Y. Stage-structured wild and sterile mosquito population models and their dynamics. J Biol Dynam, 2016, 11(S1): 79-101
[8] Li Y, Li J. Stage-structured discrete-time models for interacting wild and sterile mosquitoes with Beverton-Holt survivability. Math Biosci Eng, 2019, 16(2): 572-602
[9] Huang M Z, Liu S Z, Song X Y. Study of the sterile insect release technique for a two-sex mosquito population model. Math Biosci Eng, 2021, 18(2): 1314-1339
[10] Huang M Z, You L, Liu S Z, et al. Impulsive release strategies of sterile mosquitos for optimal control of wild population. J Biol Dynam, 2021, 15(1): 151-176
[11] Yu J S, Li J. Global asymptotic stability in an interactive wild and sterile mosquito model. J Differ Equations, 2020, 269(7): 6193-6215
[12] Zheng B, Yu J S, Li J. Existence and stability of periodic solutions in a mosquito population suppression model with time delay. J Differ Equations, 2022, 315: 159-178
[13] Zheng B, Yu J S. At most two periodic solutions for a switching mosquito population suppression model. J Dyn Differ Equations, 2023, 35: 2997-3009
[14] Jiang G R, Lu Q S, Qian L N. Complex dynamics of a Holling type II prey-predator system with state feedback control. Chaos Solitons Fractals, 2007, 31: 448-461
[15] Zhang Q Q, Tang S Y, Zou X F. Rich dynamics of a predator-prey system with state-dependent impulsive controls switching between two means. J Differ Equations, 2023, 364: 336-377
[16] Yang J, Tang G Y, Tang S Y. Holling-Tanner Predator-Prey Model with State-Dependent Feedback Control. Discrete Dyn Nat Soc, 2018, 2018: Art 3467405
[17] Xu H, Zhang T H, Cheng H D. Nonlinear control ecological model with complex discrete map. Commun Nonlinear Sci Numer Simulat, 2023, 118: Art 107019
[18] Tian Y, Gao Y, Sun K B. Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy. Chaos Solitons Fractals, 2022, 164: Art 112597
[19] Tian Y, Gao Y, Sun K B. Qualitative analysis of exponential power rate fishery model and complex dynamics guided by a discontinuous weighted fishing strategy. Commun Nonlinear Sci Numer Simulat, 2023, 118: Art 107011
[20] Guan L K, Yang J, Tan Y S, et al. Bifurcation analysis of a tumour-immune model with nonlinear killing rate as state-dependent feedback control. Int J Bifurcat Chaos, 2022, 32(10): Art 2250155
[21] Huang M Z, Li J X, Song X Y, et al. Modeling impulsive injections of insulin: towards artificial pancreas. SIAM J Appl Math, 2012, 72(5): 1524-1548
[22] Jia J, Zhao Z, Yang J G, et al. Parameter estimation and global sensitivity analysis of a bacterial-plasmid model with impulsive drug treatment. Chaos Solitons Fractals, 2024, 183: Art 114901
[23] Huang M Z, Song X Y, Li J. Modelling and analysis of impulsive release of sterile mosquitoes. J Biol Dyn, 2017, 11(1): 147-171
[24] O'Connor L, Plichart C, Sang A C, et al. Open release of male mosquitoes infected with a Wolbachia biopesticide: Field performance and infection containment. PLOS Negl Trop Dis, 2012, 6(11): 1-7
[25] Almeida L, Duprez M, Privat Y, et al. Optimal control strategies for the sterile mosquitoes technique. J Differ Equations, 2022, 311: 229-266
[26] Almeida L, Duprez M, Privat Y, et al. Mosquito population control strategies for fighting against arboviruses. Math Biosci Eng, 2019, 16: 6274-6297