Behaviors and numerical simulations of malaria dynamic models with transgenic mosquitoes. (English) Zbl 1406.92596

Summary: The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number \(\mathbf{R}_0\) is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, when \(\mathbf{R}_0 \leq 1\), malaria will disappear; when \(\mathbf{R}_0 > 1\), malaria will become an endemic disease in the target field.


92D30 Epidemiology
Full Text: DOI


[1] Collins, F. A.; James, A. A., Genetic modifications of mosquitoes, Science Medicine, 3, 52-61 (1996)
[2] Christophides, G. K., Transgenic mosquitoes and malaria transmission, Cellular Microbiology, 7, 3, 325-333 (2005) · doi:10.1111/j.1462-5822.2005.00495.x
[3] Gould, F.; Magori, K.; Huang, Y. X., Genetic strategies for controlling mosquito-borne diseases, American Scientist, 94, 3, 238-246 (2006) · doi:10.1511/2006.3.238
[4] Levy, S., Mosquito modifications: new approaches to controlling malaria, BioScience, 57, 10, 816-821 (2007) · doi:10.1641/B571003
[5] Lavery, J. V.; Harrington, L. C.; Scott, T. W., Ethical, social, and cultural considerations for site selection for research with genetically modified mosquitoes, American Journal of Tropical Medicine and Hygiene, 79, 3, 312-318 (2008)
[6] Knols, B. G. J.; Bossin, H. C.; Mukabana, W. R.; Robinson, A. S., Transgenic mosquitoes and the fight against malaria: managing technology push in a turbulent GMO world, The American Journal of Tropical Medicine and Hygiene, 77, 6, 232-242 (2007)
[7] Dai, L. M., The influence of resistant mosquitoes to malaria dynamical system [M.S. thesis] (2009), Chongqing, China
[8] Antia, R.; Yates, A.; de Roode, J. C., The dynamics of acute malaria infections. I. Effect of the parasite’s red blood cell preference, Proceedings of the Royal Society B, 275, 1641, 1449-1458 (2008) · doi:10.1098/rspb.2008.0198
[9] Chitnis, N. R., Using mathematical models in controlling the spread of malaria [Ph.D. thesis] (2005), Tucson, Arizona: the university of Arizona, Tucson, Arizona
[10] Li, J., Simple stage-structured models for wild and transgenic mosquito populations, Journal of Difference Equations and Applications, 15, 4, 327-347 (2009) · Zbl 1159.92033 · doi:10.1080/10236190802566491
[11] Li, J., Simple mathematical models for interacting wild and transgenic mosquito populations, Mathematical Biosciences, 189, 1, 39-59 (2004) · Zbl 1072.92053 · doi:10.1016/j.mbs.2004.01.001
[12] Li, J., Discrete time models with mosquitoes carrying genetically modified bacteria, Mathematical Biosciences, 240, 1, 35-44 (2012) · Zbl 1319.92043
[13] Li, J.; Ai, S. B.; Lu, J. L., Mosquito-stage-structuried Malaria models and their global dynamics, SIAM Journal of Applied Mathematics, 27, 1223-1237 (2012) · Zbl 1267.34076
[14] Li, J., Modelling of transgenic mosquitoes and impact on malaria transmission, Journal of Biological Dynamics, 5, 5, 474-494 (2011) · Zbl 1225.92033 · doi:10.1080/17513758.2010.523122
[15] Kermack, W. O.; Mckendrick, A. G., A contribution to the mathematical theory of epidemics, Proceeding of the Royal Society of London A, 115, 772, 700-721 (1927) · JFM 53.0517.01
[16] Lakshmikantham, V., Nonlinear Systems and Applications (1976), Princeton, NJ, USA: Princeton University Press, Princeton, NJ, USA
[17] Chen, L. S.; Meng, X. Z.; Jiao, J. J., Biodynamics (2009), Beijing, China: Science Press, Beijing, China
[18] Kim, B. H.; Kim, H. K.; Lee, S. J., Experimental analysis of the blood-sucking mechanism of female mosquitoes, The Journal of Experimental Biology, 214, 7, 1163-1169 (2011) · doi:10.1242/jeb.048793
[19] Oduro, F.; Okyere, G. A.; Azu-Tungmah, G. T., Transmission dynamics of Malaria in ghana, Journal of Mathematics Research, 4, 6, 22-33 (2012) · Zbl 1357.92074
[20] Ruan, S.; Xiao, D.; Beier, J. C., On the delayed Ross-Macdonald model for malaria transmission, Bulletin of Mathematical Biology, 70, 4, 1098-1114 (2008) · Zbl 1142.92040 · doi:10.1007/s11538-007-9292-z
[21] Harris, A. F.; Nimmo, D.; McKemey, A. R.; Kelly, N.; Scaife, S.; Donnelly, C. A.; Beech, C.; Petrie, W. D.; Alphey, L., Field performance of engineered male mosquitoes, Nature Biotechnology, 29, 11, 1034-1037 (2011) · doi:10.1038/nbt.2019
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