Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia

Rajivganthi Chinnathambi; Fathalla A. Rihan; Rajivganthi Chinnathambi; Fathalla A. Rihan

doi:10.3934/mbe.2022520

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11154-11171. doi: 10.3934/mbe.2022520

Previous Article Next Article

Research article Special Issues

Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia

Rajivganthi Chinnathambi ^{1
,
,},
Fathalla A. Rihan ^{2
,
,}

1.
Division of Mathematics, School of Advances Sciences, Vellore Institute of Technology, Chennai, Tamilnadu-600 127, India
2.
Department of Mathematical Sciences, College of Science, United Arab Emirats University, Al-Ain 15551, UAE

Academic Editor: Wenrui Hao

Received: 26 May 2022 Revised: 22 July 2022 Accepted: 25 July 2022 Published: 04 August 2022

Combining Sterile and Incompatible Insect techniques can significantly reduce mosquito populations and prevent the transmission of diseases between insects and humans. This paper describes impulsive differential equations for the control of a mosquito with Wolbachia. Several interesting conditions are created when sterile male mosquitoes are released impulsively, ensuring both open- and closed-loop control. To determine the wild mosquito population size in real-time, we propose an open-loop control system, which uses impulsive and constant releases of sterile male mosquitoes. A closed-loop control scheme is also being investigated, which specifies the release of sterile mosquitoes according to the size of the wild mosquito population. To eliminate or reduce a mosquito population below a certain threshold, the Sterile insect technique involves mass releases of sterile insects. Numerical simulations verify the theoretical results.

Keywords:

Citation: Rajivganthi Chinnathambi, Fathalla A. Rihan. Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11154-11171. doi: 10.3934/mbe.2022520

Related Papers:

[1]	Zairong Wang, Xuan Tang, Haohuai Liu, Lingxi Peng . Artificial immune intelligence-inspired dynamic real-time computer forensics model. Mathematical Biosciences and Engineering, 2020, 17(6): 7221-7233. doi: 10.3934/mbe.2020370
[2]	Hui Yao, Yuhan Wu, Shuo Liu, Yanhao Liu, Hua Xie . A pavement crack synthesis method based on conditional generative adversarial networks. Mathematical Biosciences and Engineering, 2024, 21(1): 903-923. doi: 10.3934/mbe.2024038
[3]	Jiajia Jiao, Xiao Xiao, Zhiyu Li . dm-GAN: Distributed multi-latent code inversion enhanced GAN for fast and accurate breast X-ray image automatic generation. Mathematical Biosciences and Engineering, 2023, 20(11): 19485-19503. doi: 10.3934/mbe.2023863
[4]	Hao Wang, Guangmin Sun, Kun Zheng, Hui Li, Jie Liu, Yu Bai . Privacy protection generalization with adversarial fusion. Mathematical Biosciences and Engineering, 2022, 19(7): 7314-7336. doi: 10.3934/mbe.2022345
[5]	Jinhua Zeng, Xiulian Qiu, Shaopei Shi . Image processing effects on the deep face recognition system. Mathematical Biosciences and Engineering, 2021, 18(2): 1187-1200. doi: 10.3934/mbe.2021064
[6]	Song Wan, Guozheng Yang, Lanlan Qi, Longlong Li , Xuehu Yan, Yuliang Lu . Multiple security anti-counterfeit applications to QR code payment based on visual secret sharing and QR code. Mathematical Biosciences and Engineering, 2019, 16(6): 6367-6385. doi: 10.3934/mbe.2019318
[7]	Dehua Feng, Xi Chen, Xiaoyu Wang, Xuanqin Mou, Ling Bai, Shu Zhang, Zhiguo Zhou . Predicting effectiveness of anti-VEGF injection through self-supervised learning in OCT images. Mathematical Biosciences and Engineering, 2023, 20(2): 2439-2458. doi: 10.3934/mbe.2023114
[8]	Si Li, Limei Peng, Fenghuan Li, Zengguo Liang . Low-dose sinogram restoration enabled by conditional GAN with cross-domain regularization in SPECT imaging. Mathematical Biosciences and Engineering, 2023, 20(6): 9728-9758. doi: 10.3934/mbe.2023427
[9]	Xiao Wang, Jianbiao Zhang, Ai Zhang, Jinchang Ren . TKRD: Trusted kernel rootkit detection for cybersecurity of VMs based on machine learning and memory forensic analysis. Mathematical Biosciences and Engineering, 2019, 16(4): 2650-2667. doi: 10.3934/mbe.2019132
[10]	Sonam Saluja, Munesh Chandra Trivedi, Ashim Saha . Deep CNNs for glioma grading on conventional MRIs: Performance analysis, challenges, and future directions. Mathematical Biosciences and Engineering, 2024, 21(4): 5250-5282. doi: 10.3934/mbe.2024232

Abstract

References

[1]	H. Hughes, N. F. Britton, Modelling the use of Wolbachia to control dengue fever transmission, Bull. Math. Biol., 75 (2013), 796–818. https://doi.org/10.1007/s11538-013-9835-4 doi: 10.1007/s11538-013-9835-4
[2]	Y. Hui, J. Yu, Global asymptotic stability in a non-autonomous delay mosquito population suppression model, Appl. Math. Lett., 124 (2022), 107599. https://doi.org/10.1016/j.aml.2021.107599 doi: 10.1016/j.aml.2021.107599
[3]	M. Z. Ndii, R. I. Hickson, D. Allingham, G. N. Mercer, Modelling the transmission dynamics of dengue in the presence of Wolbachia, Math. Biosci., 262 (2015), 157–166. https://doi.org/10.1016/j.mbs.2014.12.011 doi: 10.1016/j.mbs.2014.12.011
[4]	P. A. Bliman, M. S. Aronna, F. C. Coelho, M. A. H. B. Silva, Ensuring successful introduction of Wolbachia in natural populations of Aedes Aegypti by means of feedback control, J. Math. Biol., 76 (2018), 1269–1300. https://doi.org/10.1007/s00285-017-1174-x doi: 10.1007/s00285-017-1174-x
[5]	L. Multerer, T. Smith, N. Chitnis, Modeling the impact of sterile males on an Aedes Aegypti population with optimal control, Math. Biosci., 311 (2019), 91–102. https://doi.org/10.1016/j.mbs.2019.03.003 doi: 10.1016/j.mbs.2019.03.003
[6]	B. Zheng, L. Chen, Q. Sun, Analyzing the control of dengue by releasing Wolbachia infected male mosquitoes through a delay differential equation model, Math. Biosci. Eng., 16 (2019), 5531–5550. http://dx.doi.org/10.3934/mbe.2019275 doi: 10.3934/mbe.2019275
[7]	F. A. Rihan, Delay Differential Equations and Applications to Biology, Springer, Singapore, 2021. https://doi.org/10.1007/978-981-16-0626-7
[8]	A. Aghriche, R. Yafia, M. A. A. Alaoui, A. Tridane, F. A. Rihan, Oscillations induced by quiescent adult female in a reaction-diffusion model of wild Aedes Aegypti mosquitoes, Int. J. Bifurcation Chaos, 29 (2019), 1950189. https://doi.org/10.1142/S021812741950189X doi: 10.1142/S021812741950189X
[9]	S. P. Sinkins, Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochem. Mol. Biol., 34 (2004), 723–729. https://doi.org/10.1016/j.ibmb.2004.03.025 doi: 10.1016/j.ibmb.2004.03.025
[10]	I. Iturbe-Ormaetxe, T. Walker, S. L. O'Neill, Wolbachia and the biological control of mosquito-borne disease, EMBO Rep., 12 (2011), 508–518. https://doi.org/10.1038/embor.2011.84 doi: 10.1038/embor.2011.84
[11]	X. Zhang, S. Tang, R. A. Cheke, H. Zhu, Modeling the effects of augmentation strategies on the control of dengue fever With an impulsive differential equation, Bull. Math. Biol., 78 (2016), 1968–2010. https://doi.org/10.1007/s11538-016-0208-7 doi: 10.1007/s11538-016-0208-7
[12]	Y. Li, X. Liu, A sex-structured model with birth pulse and release strategy for the spread of Wolbachia in mosquito population, J. Theor. Biol., 448 (2018), 53–65. https://doi.org/10.1016/j.jtbi.2018.04.001 doi: 10.1016/j.jtbi.2018.04.001
[13]	B. Zheng, M. Tang, J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equations, SIAM J. Appl. Math., 74 (2014), 743–770. https://doi.org/10.1137/13093354X doi: 10.1137/13093354X
[14]	D. Li, H. Wan, The threshold infection level for Wolbachia invasion in a two sex mosquito population model, Bull. Math. Biol., 81 (2019), 2596–2624. https://doi.org/10.1007/s11538-019-00620-1 doi: 10.1007/s11538-019-00620-1
[15]	Z. Zhang, B. Zheng, Dynamics of a mosquito population suppression model with a saturated Wolbachia release rate, Appl. Math. Lett., 129 (2022), 107933. https://doi.org/10.1016/j.aml.2022.107933 doi: 10.1016/j.aml.2022.107933
[16]	Y. Dumont, J. M. Tchuenche, Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, J. Math. Biol., 65 (2012), 809–854. https://doi.org/10.1007/s00285-011-0477-6 doi: 10.1007/s00285-011-0477-6
[17]	Y. Dumont, I. V. Yatat-Djeument, Sterile insect technique with accidental releases of sterile females. Impact on mosquito-borne diseases control when viruses are circulating, Math. Biosci., 343 (2022), 108724. https://doi.org/10.1016/j.mbs.2021.108724 doi: 10.1016/j.mbs.2021.108724
[18]	L. Almeida, M. Duprez, Y. Privat, N. Vauchelet, Mosquito population control strategies for fighting against arboviruses, Math. Biosci. Eng., 16 (2019), 6274–6297. https://doi.org/10.3934/mbe.2019313 doi: 10.3934/mbe.2019313
[19]	S. Ai, M. Fox, Four positive equilibria in a model for sterile and wild mosquito populations, Appl. Math. Lett., 121 (2021), 107409. https://doi.org/10.1016/j.aml.2021.107409 doi: 10.1016/j.aml.2021.107409
[20]	S. Xue, M. Li, J. Ma, J. Li, Sex-structured wild and sterile mosquito population models with different release strategies, Math. Biosci. Eng., 16 (2019), 1313–1333. https://doi.org/10.3934/mbe.2019064 doi: 10.3934/mbe.2019064
[21]	S. S. Lee, R. E. Baker, E. A. Gaffney, S. M. White, Modelling Aedes Aegypti mosquito control via transgenic and sterile insect techniques Endemics and emerging outbreaks, J. Theor. Biol., 331 (2013), 78–90. https://doi.org/10.1016/j.jtbi.2013.04.014 doi: 10.1016/j.jtbi.2013.04.014
[22]	R. Anguelov, Y. Dumont, J. Lubuma, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl., 64 (2012), 374–389. https://doi.org/10.1016/j.camwa.2012.02.068 doi: 10.1016/j.camwa.2012.02.068
[23]	M. Huang, X. Song, J. Li, Modelling and analysis of impulsive releases of sterile mosquitoes, J. Biol. Dyn., 11 (2017), 147–171. https://doi.org/10.1080/17513758.2016.1254286 doi: 10.1080/17513758.2016.1254286
[24]	X. Zhang, S. Tang, R. A. Cheke, Birth-pulse models of Wolbachia-induced cytoplasmic incompatibility in mosquitoes for dengue virus control, Nonlinear Anal. Real World Appl., 22 (2015), 236–258. https://doi.org/10.1016/j.nonrwa.2014.09.004 doi: 10.1016/j.nonrwa.2014.09.004
[25]	Y. Li, X. Liu, An impulsive model for Wolbachia infection control of mosquito-borne diseases with general birth and death rate functions, Nonlinear Anal. Real World Appl., 37 (2017), 412–432. https://doi.org/10.1016/j.nonrwa.2017.03.003 doi: 10.1016/j.nonrwa.2017.03.003
[26]	P. A. Bliman, D. C. Salgadob, Y. Dumont, O. Vasilieva, Implementation of control strategies for sterile insect techniques, Math. Biosci., 314 (2019), 43–60. https://doi.org/10.1016/j.mbs.2019.06.002 doi: 10.1016/j.mbs.2019.06.002
[27]	V. A. Dyck, J. Hendrichs, A. S. Robinson, The Sterile Insect Technique, Principles and Practice in Area-wide Integrated Pest Management, Springer, Dordrecht, 2006. https://doi.org/10.1201/9781003035572
[28]	B. Zheng, J. Yu, J. Li, Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression, SIAM J. Appl. Math., 81 (2021), 718–740. https://doi.org/10.1137/20M1368367 doi: 10.1137/20M1368367
[29]	X. Zheng, D. Zhang, Y. Li, S. M. White, Incompatible and sterile insect techniques combined eliminate mosquitoes, Nature, 572 (2019), 56–61. https://doi.org/10.1038/s41586-019-1407-9 doi: 10.1038/s41586-019-1407-9
[30]	D. O. Carvalho, J. A. Torres-Monzon, P. Koskinioti, N. D. A. D. Wijegunawardana, X. Liang, G. Pillwax, et al., Aedes Aegypti lines for combined sterile insect technique and incompatible insect technique applications: the importance of host genomic background, Entomol. Exp. Appl., 168 (2020), 560–572. https://doi.org/10.1111/eea.12892 doi: 10.1111/eea.12892
[31]	X. Xu, Y. Xiao, R. A. Cheke, Models of impulsive culling of mosquitoes to interrupt transmission of West Nile virus to birds, Appl. Math. Modell., 39 (2015), 3549–3568. https://doi.org/10.1016/j.apm.2014.10.072 doi: 10.1016/j.apm.2014.10.072
[32]	Y. Li, X. Liu, A sex-structured model with birth pulse and release strategy for the spread of Wolbachia in mosquito population, J. Theor. Biol., 448 (2018), 53–65. https://doi.org/10.1016/j.jtbi.2018.04.001 doi: 10.1016/j.jtbi.2018.04.001
[33]	H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems (Mathematical Surveys And Monographs), American Mathematical Society, 1995. https://doi.org/10.1090/surv/041

This article has been cited by:

1.	Yangjin Kim, Hyunji Kang, Gibin Powathil, Hyeongi Kim, Dumitru Trucu, Wanho Lee, Sean Lawler, Mark Chaplain, Dominik Wodarz, Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma, 2018, 13, 1932-6203, e0204865, 10.1371/journal.pone.0204865
2.	Yangjin Kim, Junho Lee, Donggu Lee, Hans Othmer, Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model, 2019, 11, 2072-6694, 215, 10.3390/cancers11020215
3.	Christian Engwer, Christian Stinner, Christina Surulescu, On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation, 2017, 27, 0218-2025, 1355, 10.1142/S0218202517400188
4.	Markos Antonopoulos, Dimitra Dionysiou, Georgios Stamatakos, Nikolaos Uzunoglu, Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study, 2019, 20, 1471-2105, 10.1186/s12859-019-2997-9
5.	Junho Lee, Donggu Lee, Sean Lawler, Yangjin Kim, Stacey Finley, Role of neutrophil extracellular traps in regulation of lung cancer invasion and metastasis: Structural insights from a computational model, 2021, 17, 1553-7358, e1008257, 10.1371/journal.pcbi.1008257
6.	Stefaan W. Verbruggen, Laoise M. McNamara, 2018, 9780128129524, 157, 10.1016/B978-0-12-812952-4.00006-4
7.	Thomas Hillen, Kevin J. Painter, Magdalena A. Stolarska, Chuan Xue, Multiscale phenomena and patterns in biological systems: special issue in honour of Hans Othmer, 2020, 80, 0303-6812, 275, 10.1007/s00285-020-01473-2
8.	Min-Jhe Lu, Chun Liu, John Lowengrub, Shuwang Li, Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis, 2020, 82, 0092-8240, 10.1007/s11538-020-00716-z
9.	Yangjin Kim, Donggu Lee, Junho Lee, Seongwon Lee, Sean Lawler, Eugene Demidenko, Role of tumor-associated neutrophils in regulation of tumor growth in lung cancer development: A mathematical model, 2019, 14, 1932-6203, e0211041, 10.1371/journal.pone.0211041
10.	Raluca Eftimie, Joseph J. Gillard, Doreen A. Cantrell, Mathematical Models for Immunology: Current State of the Art and Future Research Directions, 2016, 78, 0092-8240, 2091, 10.1007/s11538-016-0214-9
11.	S. L. Waters, L. J. Schumacher, A. J. El Haj, Regenerative medicine meets mathematical modelling: developing symbiotic relationships, 2021, 6, 2057-3995, 10.1038/s41536-021-00134-2
12.	Vladimir Simic, Miljan Milosevic, Vladimir Milicevic, Nenad Filipovic, Milos Kojic, A novel composite smeared finite element for mechanics (CSFEM): Some applications, 2022, 09287329, 1, 10.3233/THC-220414
13.	Miloš Kojić, Miljan Milošević, Arturas Ziemys, 2023, 9780323884723, 65, 10.1016/B978-0-323-88472-3.00002-5
14.	Gabriella Bretti, Adele De Ninno, Roberto Natalini, Daniele Peri, Nicole Roselli, Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment, 2021, 10, 2075-1680, 243, 10.3390/axioms10040243
15.	Dimitrios G. Patsatzis, Algorithmic asymptotic analysis: Extending the arsenal of cancer immunology modeling, 2022, 534, 00225193, 110975, 10.1016/j.jtbi.2021.110975
16.	Joseph D. Butner, Prashant Dogra, Vittorio Cristini, Thomas S. Deisboeck, Zhihui Wang, 2023, 9780128216248, 251, 10.1016/B978-0-12-821618-7.00244-3
17.	Jonggul Lee, Donggu Lee, Yangjin Kim, Mathematical model of STAT signalling pathways in cancer development and optimal control approaches, 2021, 8, 2054-5703, 10.1098/rsos.210594
18.	Junho Lee, Jin Su Kim, Yangjin Kim, Stacey Finley, Atorvastatin-mediated rescue of cancer-related cognitive changes in combined anticancer therapies, 2021, 17, 1553-7358, e1009457, 10.1371/journal.pcbi.1009457
19.	Aurelio A. de los Reyes, Yangjin Kim, Optimal regulation of tumour-associated neutrophils in cancer progression, 2022, 9, 2054-5703, 10.1098/rsos.210705
20.	Min-Jhe Lu, Wenrui Hao, Chun Liu, John Lowengrub, Shuwang Li, Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis, 2022, 459, 00219991, 111153, 10.1016/j.jcp.2022.111153
21.	Tingzhe Sun, Multi-scale modeling of hippo signaling identifies homeostatic control by YAP-LATS negative feedback, 2021, 208, 03032647, 104475, 10.1016/j.biosystems.2021.104475
22.	Yangjin Kim, Junho Lee, Chaeyoung Lee, Sean Lawler, Role of senescent tumor cells in building a cytokine shield in the tumor microenvironment: mathematical modeling, 2023, 86, 0303-6812, 10.1007/s00285-022-01850-z
23.	Rebecca M. Crossley, Philip K. Maini, Tommaso Lorenzi, Ruth E. Baker, Traveling waves in a coarse‐grained model of volume‐filling cell invasion: Simulations and comparisons, 2023, 0022-2526, 10.1111/sapm.12635
24.	Anneke S.K. Verbruggen, Elan C. McCarthy, Roisin M. Dwyer, Laoise M. McNamara, Mechanobiological cues to bone cells during early metastasis drive later osteolysis: a computational mechanoregulation framework prediction, 2024, 29499070, 100100, 10.1016/j.mbm.2024.100100

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)