Mathematical Modelling of Sterile Insect Technology for Mosquito Control

Abstract

Reduction of mosquito populations will, at least, reduce substantially the transmission of malaria disease. One potential method of achieving this reduction is the environmentally-friendly population control method known as the Sterile Insect Control (SIT) method. The SIT method has so far not been widely used against insect disease vectors, such as mosquitoes, because of various practical difficulties in rearing, sterilization and distribution of the parasite population. For mosquitoes, male-only release is considered essential since sterile females will bite and so may transmit disease, whereas male mosquitoes do not bite. This work concerns the mathematical modelling of the effectiveness of Sterile Insect Technique for Aedes aegypti mosquitoes, when the female sexual preference is incorporated. We found that for a released value of the sterile male mosquito below 40,000, the wild mosquito population decreases over time while the sterile male mosquito population increases. Therefore, the transmission of malaria and dengue infection declines because the sterile male mosquitoes dominated the environment. We also found that for a released value of the sterile male mosquito above 40,000, the wild mosquito population decreases and the sterile male mosquito population decreases as well. Therefore, if the injection of sterile male mosquitoes is large enough, the environment will be rid of mosquitoes over time. The result also shows that if sexual selection is incorporated into a reaction diffusion system, modelling the spread of Aedes aegypti mosquitoes, the Sterile Insect Technique (SIT) will still be a successful control measure.

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Patinvoh, R. and Susu, A. (2014) Mathematical Modelling of Sterile Insect Technology for Mosquito Control. Advances in Entomology, 2, 180-193. doi: 10.4236/ae.2014.24027.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Roll Back Malaria (2001) Country Strategies and Resource Requirements. WHO/CDS/RBM/2001.34
[2] Ribeiro, J.M.C. (1987) Role of Saliva in Blood-Feeding by Arthropods. Annual Review of Entomology, 32, 463-478. http://dx.doi.org/10.1146/annurev.en.32.010187.002335
[3] Cator, L.J, Arthur, B.J., Harrington, L.C. and Hoy, R.R. (2009) Harmonic Convergence in the Love Songs of the Dengue Vector. Mosquito. Science, 323, 1077-1079.
[4] Crow, J.F. (1986) Basic Concepts in Population, Quantitative, and Evolutionary Genetics. W.H. Freeman, New York, 273.
[5] Lee, N., Elias, D.O. and Mason, A.C. (2009) A Precedence Effect Resolves Phantom Sound Source Illusions in the Parasitoid Fly Ormia ochracea. Proceedings of the National Academy of Sciences of the United States of America, 106, 6357-6362. http://dx.doi.org/10.1073/pnas.0809886106
[6] Cator, L.J., NgHabi, K.R., Hoy, R.R. and Harrington, L.C. (2010) Sizing up a Mate: Variation in Production and Response to Acoustic Signals in Anopheles gambiae. Behavioral Ecology, 21, 1033-1039.
http://dx.doi.org/10.1093/beheco/arq087
[7] Belton, P, (1994) Attraction of Male Mosquitoes to Sound. Journal of the American Mosquito Control Association, 10, 297-301.
[8] Clements, A.N. (1999) The Biology of Mosquitoes. Sensory Reception and Behavior. CABI Publishing Inc., New York.
[9] Yuval, B. and Bouskila, A. (1993) Temporal Dynamics of Mating and Predation in Mosquito Swarms. Oecologia, 85, 65-69.
[10] Yuval, B., Wekesa, J.W. and Washino, R.K. (1993) Effects of Body Size on Swarming Behavior and Mating Success of Male Anopheles Freeborni (Diptera: Culicidae). Journal of Insect Behavior, 6, 333-342.
http://dx.doi.org/10.1007/BF01048114
[11] Engelstädter, J. (2010) The Effective Size of Populations Infected with Cytoplasmic Sex-Ratio Distorters. Genetics, 186, 309-320. http://dx.doi.org/10.1534/genetics.110.120014
[12] Anguelov, R., Dumont, Y. and Lubuma, J. (2012) Mathematical Modelling of Sterile Insect Technology for Control of Anopheles Mosquito. Computers and Mathematics with Applications, 64, 374-389.
http://dx.doi.org/10.1016/j.camwa.2012.02.068
[13] Parshad, R.D. and Agusto, F.B. (2011) Global Dynamics of a PDE Model for Aedes aegypti Mosquitoe Incorporating Female Sexual Preference. Dynamics of Partial Differential Equations, 8, 311-343.
[14] Thomé, R.C.A, Yang, H.M. and Esteva, L. (2010) Optimal Control of Aedes aegypti Mosquitoes by the Sterile Insect Technique and Insecticide. Mathematical Biosciences, 223, 12-23.
http://dx.doi.org/10.1016/j.mbs.2009.08.009
[15] Bartlett, A.C. (1990) Insect, Sterility, Insect Genetics, and Insect Control. In: Pimentel, D., Ed., Handbook of Pest Management in Agriculture, CRC Press, Boca Raton, 279-287.
[16] Esteva, L. and Yang, H.M. (2005) Mathematical Model to Assess the Control of Aedes aegypti Mosquitoes by the Sterile Insect Technique. Mathematical Biosciences, 198, 132-147.
http://dx.doi.org/10.1016/j.mbs.2005.06.004
[17] Gubler, D.J. (1986) Dengue, the Arboviruses, Epidemiology and Ecology. Vol. 11, Monath, T.P., Ed., p. 213.
[18] Rafikov, M., Bevilacqua, L. and Wyse, A.P.P. (2009) Optimal Control Strategy of Malaria Vector Using Genetically Modified Mosquitoes. Journal of Theoretical Biology, 258, 418-429.
http://dx.doi.org/10.1016/j.jtbi.2008.08.006
[19] Takahashi, L.T., Maidana, N.A., Ferreira Jr., W.C., Pulino, P. and Yang, H.M. (2005) Mathematical Models for the Aedes aegypti Dispersal Dynamics: Travelling Waves by Wing and Wind. Bulletin of mathematical Biology, 67, 509-528. http://dx.doi.org/10.1016/j.bulm.2004.08.005
[20] Jacob-Lorena, M. Genetic Approaches for Malaria Control. Johns Hopkins School of Public Health, Malaria Research Institute, Dept. Molecular Microbiology and Immunology, Baltimore.

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