Mathematical Biosciences and Engineering

2019, Issue 6: 6274-6297. doi: 10.3934/mbe.2019313
Research article Special Issues

Mosquito population control strategies for fighting against arboviruses

• Received: 16 January 2019 Accepted: 24 June 2019 Published: 05 July 2019
• In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called Wolbachia, blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for population replacement and sterile insect technique. Then, we establish some properties of the optimal control and illustrate them with numerical simulations.

Citation: Luis Almeida, Michel Duprez, Yannick Privat, Nicolas Vauchelet. Mosquito population control strategies for fighting against arboviruses[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6274-6297. doi: 10.3934/mbe.2019313

Related Papers:

• In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called Wolbachia, blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for population replacement and sterile insect technique. Then, we establish some properties of the optimal control and illustrate them with numerical simulations.

 [1] A. A. Hoffmann, B. L. Montgomery, J. Popovici, et al., Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission, Nature, 476 (2011), 454–457. [2] B. Stoll, H. Bossin, H. Petit, et al., Suppression of an isolated population of the mosquito vector Aedes polynesiensis on the atoll of Tetiaroa, French Polynesia, by sustained release of Wolbachia-incompatible male mosquitoes, Conference: ICE - XXV International Congress of Entomology, At Orlando, Florida, USA. [3] D. D. Thomas, C. A. Donnelly, R. J. Wood, et al., Insect population control using a dominant, repressible, lethal genetic system. Science, 287 (2000), 2474–2476. [4] J. Heinrich and M. Scott, A repressible female-specific lethal genetic system for making transgenic insect strains suitable for a sterile-release program. Proc. Natl. Acad. Sci. USA, 97 (2000), 8229–8232. [5] G. Fu, R. S. Lees, D. Nimmo, et al., Female-specific flightless phenotype for mosquito control Proc. Natl. Acad. Sci., 107 (2010), 4550–4554. [6] F. Gould, Y. Huang, M. Legros, et al., A Killer–Rescue system for self-limitinggene drive of anti-pathogen constructs, Proc. R. Soc. B, 275 (2008), 2823–2829. [7] J. M. Marshall, G. W. Pittman, A. B. Buchman, et al., Semele: a killer-male, rescue-female system for suppression and replacement of insect disease vector populations, Genetics, 187 (2011), 535–551. [8] C. M. Ward, J. T. Su, Y. Huang, et al., Medea selfish genetic elements as tools for altering traits of wild populations: a theoretical analysis. Evolution, 65 (2011), 1149–1162. [9] M. A. Robert, K. Okamoto, F. Gould, et al., A reduce and replace strategy for suppressing vector-borne diseases: insights from a deterministic model, PLoS ONE, 8 (2012), e73233. [10] H.J. Barclay and M. Mackuer, The sterile insect release method for pest control: a density dependent model, Environ. Entomol., 9 (1980), 810–817. [11] V.A.Dyck, J.HendrichsandA.S.Robinson, TheSterileInsectTechnique, PrinciplesandPractice in Area-Wide Integrated Pest Management, Springer, Dordrecht, 2006 [12] R. Anguelov, Y. Dumont and J. Lubuma, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl., 64 (2012), 374–389. [13] C. Dufourd and Y. Dumont, Impact of environmental factors on mosquito dispersal in th e prospect of sterile insect technique control, Comput. Math. Appl., 66 (2013), 1695–1715. [14] Y. Dumont and J. M. Tchuenche, Mathematical studies on the sterile insect technique for the chikungunya disease and Aedes albopictus, J. Math. Biol., 65 (2012), 809–855. [15] L. Cai, S. Ai and J. Li, Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes, SIAM J. Appl. Math., 74 (2014), 1786–1809. [16] J. Li and Z. Yuan, Modelling releases of sterile mosquitoes with different strategies, J. Biol. Dyn., 9 (2015), 1–14. [17] G. Sallet and M. A. H. B. da Silva, Monotone dynamical systems and some models of Wolbachia in aedes aegypti populations, ARIMA, 20 (2015), 145–176. [18] M. Huang, X. Song and J. Li, Modelling and analysis of impulsive releases of sterile mosquitoes, J. Biol. Dyn., 11 (2017), 147–171. [19] H. Bossin, Y. Dumont and M. Strugarek, Using sterilizing males to reduce or eliminate Aedes populations: insights from a mathematical model, Appl. Math. Model., 68 (2019), 443–470. [20] P.-A. Bliman, D. Cardona-Salgado, Y. Dumont, et al., Implementation of Control Strategies for Sterile Insect Techniques, arXiv:1812.01277. [21] K. Bourtzis, Wolbachia-based technologies for insect pest population control, In: Aksoy S. (eds) Transgenesis and the Management of Vector-Borne Disease. Advances in Experimental Medicine and Biology, 627 (2008), Springer, New York, NY. [22] S. P. Sinkins, Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochem. Mol. Biol., 34 (2004), 723–729. [23] J. H. Werren, L. Baldo and M. E. Clark, Wolbachia: master manipulators of invertebrate biology, Nature Rev. Microbiol., 8 (2008), 741–751. [24] T. Walker, P. H. Johnson, L. A. Moreira, et al., The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature, 476 (2011), 450–453. [25] J. Z. Farkas and P. Hinow, Structured and unstructured continuous models for wolbachia infections, B. Math. Biol., 72 (2010), 2067–2088. [26] A. Fenton, K. N. Johnson, J. C. Brownlie, et al., Solving the Wolbachia paradox: modeling the tripartite interaction between host, Wolbachia, and a natural enemy, The American Naturalist, 178 (2011), 333–342. [27] G. Schraiber, A. N. Kaczmarczyk, R. Kwok, et al., Constraints on the use of lifespan-shortening wolbachia to control dengue fever, J. Theor. Bio., 297 (2012), 26–32. [28] H. Hughes and N. F. Britton, Modeling the Use of Wolbachia to Control Dengue Fever Transmission, Bull. Math. Biol., 75 (2013), 796–818. [29] P.-A. Bliman, M. S. Aronna, F. C. Coelho, et al., Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control, J. Math. Biol., 76 (2018), 1269–1300. [30] M. Strugarek, Modélisation mathématique de dynamiques de populations, applications à la lutte anti-vectorielle contre Aedes spp. (Diptera:Culicidae), Ph.D thesis, Sorbonne Université, 2018. [31] R. C. A. Thome, H. M. Yang and L. Esteva, Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide, Math. Biosci., 223 (2010), 12–23. [32] D. E. Campo-Duarte, O. Vasilieva, D. Cardona-Salgado, et al., Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations, J. Math. Biol., 76 (2018), 1907–1950. [33] P.-A. Bliman, Feedback Control Principles for Biological Control of Dengue Vectors, preprint. [34] H. Yang, M. Macoris, K. Galvani, et al., Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue, Epidemiol. Infect., 137 (2009), 1188–1202. [35] A. A. Hoffmann and M. Turelli, Cytoplasmic incompatibility in insects, pp 42-80 in S. L. O'Neil, J. H. Werren, and A. A. Hoffmann, eds, Influential passengers: inherited microorganisms and arthropod reproduction. Oxford University Press, Oxford. [36] M. Strugarek and N. Vauchelet, Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type, SIAM J. Appl. Math., 76 (2016), 2068–2080. [37] L. Almeida, Y. Privat, M. Strugarek, et al., Optimal releases for population replacement strategies, application to Wolbachia, to appear in SIAM J. Math. Anal., preprint, Hal-01807624 (2018). [38] L. Beal, D. Hill, R. Martin, et al., GEKKO Optimization Suite, Processes, Multidisciplinary Digital Publishing Institute, 6 (2018), 106. [39] A. Wächter and L. T. Biegler. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program., 106 (2006), 25–57. [40] H. Dutra, L. dos Santos, E. Caragata, et al., From lab to field: the influence of urban landscapes on the invasive potential of Wolbachia in Brazilian Aedes aegypti mosquitoes, PLoS Neglect. Rrop. D., 9 (2015), e0003689. [41] L. Almeida, M. Duprez, Y. Privat, et al., Optimal release strategy for the sterile mosquitoes technique, work in progress. [42] E. B. Lee and L. Markus, Foundations of optimal control theory, SIAM Series Appl. Math., Wiley, 1967.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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