
Mathematical Biosciences and Engineering, 2019, 16(6): 73627374. doi: 10.3934/mbe.2019367
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Oscillation threshold for a mosquito population suppression model with time delay
1 Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, PRC
2 School of Mathematics and Statistics, Pu’er University, Pu’er, 665000, PRC
Received: , Accepted: , Published:
Special Issues: Inverse problems in the natural and social sciences
References
1. L. Alphey, M. Benedict, R. Bellini, et al., Sterileinsect methods for control of mosquitoborne disease: An analysis, Vector Borne Zoonotic Dis., 10 (2010), 295–311.
2. R. S. Patterson, D. E. Weidhaass, H. R. Ford, et al., Suppression and elimination of an island population of Culex pipiens quinquefasciatus with sterile males, Science, 168 (1970), 1368–1369.
3. S. Ai, J. Li and J. Lu, Mosquitostagestructured malaria models and their global dynamics, SIAM J. Appl. Math., 72 (2012), 1213–1237.
4. L. Cai, S. Ai and J. Li, Dynamics of mosquitoes populations with differential strategies for releasing sterile mosquitoes, SIAM J. Appl. Math., 74 (2014), 1786–1809.
5. K. R. Fister, M. L. Mccarthy, S. F. Oppenheimer, et al., Optimal control of insects through sterile insect release and habitat modification, Math. Biosci., 244 (2013), 201–212.
6. J. Li, L. Cai and Y. Li, Stagestructured wild and sterile mosquito population models and their dynamics, J. Biol. Dynam., 11 (2017), 79–101.
7. J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dynam., 11 (2017), 316–333.
8. X. Zhang, S. Tang and Q. Liu, Models to assess the effects of nonidentical sex ratio augmentations of Wolbachiacarrying mosquitoes on the control of dengue disease, Math. Biosci., 299 (2018), 58–72.
9. B. Zheng, M. Tang, J. Yu, et al., Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol., 76 (2018), 235–263.
10. L. Cai, S. Ai and G. Fan, Dynamics of delayed mosquitoes populations with two different strategies of releasing sterile mosquitoes, Math. Biosci. Eng., 15 (2018), 1181–1202.
11. M. Huang, J. Luo, L. Hu, et al., Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations, J. Theor. Biol., 440 (2018), 1–11.
12. J. Yu, Modelling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math., 78 (2018), 3168–3187.
13. B. Zheng, M. Tang and J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equations, SIAM J. Appl. Math., 74 (2014), 743–770.
14. M. Huang, M. Tang, J. Yu, et al., The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachiadriven mosquito population suppression, Math. Biosci. Eng., 16 (2019), 4741–4757.
15. H. Diaz, A. A. Ramirez, A. Olarte, et al., A model for the control of malaria using genetically modified vectors, J. Theor. Biol., 276 (2011), 57–66.
16. K. R. Fister, M. L. Mccarthy and S. F. Oppenheimer, Diffusing wild type and sterile mosquitoes in an optimal control setting. Optimal control of insects through sterile insect release and habitat modification, Math. Biosci., 302 (2018), 100–115.
17. M. Huang, M. Tang and J. Yu, Wolbachiainfection dynamics by reactiondiffusion equations, Sci. China Math., 58 (2015), 77–96.
18. M. Huang, J. Yu, L. Hu, et al., Qualitative analysis for a Wolbachia infection model with diffusion, Sci. China Math., 59 (2016), 1249–1266.
19. J. C. Floresa, A mathematical model for wild and sterile species in competition: Immigration, Phys. A., 328 (2003), 214–224.
20. L. Hu, M. Tang, Z. Wu, et al., The threshold infection level for Wolbachia invasion in random environment, J. Differ. Equations, 266 (2019), 4377–4393.
21. H. L. Smith, An introduction to delay differential equations with applications to the life sciences, Springer, 2011.
22. I. Györi and G. Ladas, Oscillation theory of delay differential equations: with application, Oxford University Press, 1991.
23. R. Anguelova, Y. Dumontb and J. Lubuma, Mathematical modeling of sterile insect technology for control of Anopheles mosquito, Comput. Math. Appl., 64 (2012), 374–389.
24. N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272–1296.
25. A. A. Hoffmann, M. Turelli and L. G. Harshman, Factors affecting the distribution of cytoplasmic incompatibility in Drosophia simulans, Genetics, 126 (1990), 933–948.
26. Y. Li, F. Kamara, G. Zhou, et al., Urbanization increases Aedes albopictus larval habitats and accelerates mosquito development and survivorship, PLoS Negl. Trop. Dis., 8 (2014), e3301.
27. F. Liu, C. Yao, P. Lin, et al., Studies on life table of the nature population of Aedes albopictus, Acta Sci. Natur. Univ. Sunyatseni, 31 (1992), 84–93.
28. Z. Liu, Y. Zhang and Y. Yang, Population dynamics of Aedes (stegomyia) albopictus (Skuse) under laboratory conditions, Acta Entomol. Sin., 28 (1985), 274–280.
29. D. Zhang, X. Zheng, Z. Xi, et al., Combining the sterile insect technique with the incompatible insect technique: Iimpact of Wolbachia infection on the fitness of triple and doubleinfected strains of Aedes albopictus, PLoS One, 10 (2015), 1–13.
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