Dynamical analysis of discrete models for mosquito population suppression

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Abstract

Amid the global challenge of mosquito-borne disease transmission, sterile insect technology (SIT) has emerged as a promising biological control strategy. Based on the classical Beverton–Holt model and the assumption of complete cytoplasmic incompatibility (CI), we develop a discrete-time model with overlapping generations and a corresponding integro-difference equation (IDE) to investigate the population dynamics under different release strategies for infected male mosquitoes. For the discrete-time model, we apply stability and bifurcation theory to determine the existence and stability of equilibria and derive the release threshold r^* above which the wild mosquito population is successfully suppressed. Analysis of the IDE model yields a lower release threshold r^** and a critical patch-size L^*. Comparison of the two models demonstrates that spatial diffusion reduces the required release threshold for achieving population suppression.

Keywords

stability / bifurcation / integro-difference equation / traveling wave / critical patch-size

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References

[1] J. C. Semenza, J. E. Suk, Vector-borne diseases and climate change: a European perspective, FEMS Microbiol. Lett., 365 (2018), fnx244. https://doi.org/10.1093/femsle/fnx244

[2] P. E. Simonsen, M. E. Mwakitalu, Urban lymphatic filariasis, Parasitol. Res., 112 (2013), 35-44. https://doi.org/10.1007/s00436-012-3226-x

[3] F. G. Sauer, E. Kiel, R. Lühken, Effects of mosquito resting site temperatures on the estimation of pathogen development rates in near-natural habitats in Germany, Parasites Vectors, 15 (2022), 390. https://doi.org/10.1186/s13071-022-05505-2

[4] J. Kronen, M. Leuchner, T. Küpper, Zika and chikungunya in Europe 2100-a GIS based model for risk estimation, Travel Med. Infect. Dis., 60 (2024), 102737. https://doi.org/10.1016/j.tmaid.2024.102737

[5] M. B. Thomas, Biological control of human disease vectors: a perspective on challenges and opportunities, BioControl, 63 (2018), 61-69. https://doi.org/10.1007/s10526-017-9815-y

[6] H. A. Flores, S. L. O’Neill, Controlling vector-borne diseases by releasing modified mosquitoes, Nat. Rev. Microbiol., 16 (2018), 508-518. https://doi.org/10.1038/s41579-018-0025-0

[7] 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:10.1038/embor.2011.84

[8] J. H. Yen, A. R. Barr, New hypothesis of the cause of cytoplasmic incompatibility in culex pipiens L., Nature, 232 (1971), 657-658. https://doi.org/10.1038/232657a0

[9] X. Zheng, D. Zhang, Y. Li, C. Yang, Y. Wu, X. Liang, et al., Incompatible and sterile insect techniques combined eliminate mosquitoes, Nature, 572 (2019), 56-61. https://doi.org/10.1038/s41586-019-1407-9

[10] Y. Li, L. A. Baton, D. Zhang, J. Bouyer, A. G. Parker, A. A. Hoffmann, et al., Reply to: Issues with combining incompatible and sterile insect techniques, Nature, 590 (2021), E3-E5. https://doi.org/10.1038/s41586-020-03165-9

[11] Z. Zhang, L. Chang, Q. Huang, R. Yan, B. Zheng, A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession, J. Math. Biol., 86 (2023), 51. https://doi.org/10.1007/s00285-023-01888-7

[12] B. Zheng, J. Yu, At most two periodic solutions for a switching mosquito population suppression model, J. Dyn. Differ. Equations, 35 (2023), 2997-3009. https://doi.org/10.1007/s10884-021-10125-y

[13] 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

[14] R. Jiang, Z. Guo, Dynamics of discrete Ricker models on mosquito population suppression, Math. Methods Appl. Sci., 47 (2024), 4821-4839. https://doi.org/10.1002/mma.9840

[15] B. Zheng, J. Yu, Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency, Adv. Nonlinear Anal., 11 (2022), 212-224. https://doi.org/10.1515/anona-2020-0194

[16] J. Yu, J. Li, Discrete-time models for interactive wild and sterile mosquitoes with general time steps, Math. Biosci., 346 (2022), 108797. https://doi.org/10.1016/j.mbs.2022.108797

[17] Y. Li, J. Li, Discrete-time models for releases of sterile mosquitoes with Beverton-Holt-type of survivability, Ric. Mat., 67 (2018), 141-162. https://doi.org/10.1007/s11587-018-0361-4

[18] Q. Chen, Z. Teng, F. Wang, Fold-flip and strong resonance bifurcations of a discrete-time mosquito model, Chaos Solitons Fractals, 144 (2021), 110704. https://doi.org/10.1016/j.chaos.2021.110704

[19] Y. Liu, Z. Guo, M. S. El, L. Wang, A Wolbachia infection model with free boundary, J. Biol. Dyn., 14 (2020), 515-542. https://doi.org/10.1080/17513758.2020.1784474

[20] K. Wang, H. Wang, H. Zhao, On the role of advection in a spatial epidemic model with general boundary conditions, J. Differ. Equations, 386 (2024), 45-79. https://doi.org/10.1016/j.jde.2023.12.016

[21] K. Wang, H. Wang, H. Zhao, Global threshold dynamics of a spatial chemotactic mosquito-borne disease model, IMA J. Appl. Math., 88 (2023), 354-377. https://doi.org/10.1093/imamat/hxad009

[22] J. Yu, J. Li, Discrete-time models for interactive wild and transgenic sterile mosquitoes, J. Differ. Equations Appl., 30 (2024), 1590-1609. https://doi.org/10.1080/10236198.2024.2325485

[23] R. J. H. Beverton, S. J. Holt, On the Dynamics of Exploited Fish Populations , 1^st edition, Springer Netherlands, London, 2012. https://doi.org/10.1007/978-94-011-2106-4

[24] D. Zhang, R. S. Lees, Z. Xi, J. R. L. Gilles, K. Bourtzis, Combining the sterile insect technique with Wolbachia-based approaches: II-a safer approach to Aedes albopictus population suppression programmes, designed to minimize the consequences of inadvertent female release , PLoS One, 10 (2015), e0135194. https://doi.org/10.1371/journal.pone.0135194

[25] F. Lutscher, Integrodifference Equations in Spatial Ecology , 1^st edition, Springer, Cham, 2019. https://doi.org/10.1007/978-3-030-29294-2

[26] R. Lui, Existence and stability of travelling wave solutions of a nonlinear integral operator, J. Math. Biol., 16 (1983), 199-220. https://doi.org/10.1007/BF00276502

[27] M. H. Wang, M. Kot, M. G. Neubert, Integrodifference equations, Allee effects, and invasions, J. Math. Biol., 44 (2002), 150-168. https://doi.org/10.1007/s002850100116

[28] B. Li, G. Otto, Wave speed and critical patch size for integro-difference equations with a strong Allee effect, J. Math. Biol., 85 (2022), 59. https://doi.org/10.1007/s00285-022-01814-3