Abstract
A Stage-Structured Model has been proposed to study the effect of discharge of irradiated male insects and the immigration of wild insects using the Sterile Insect Technique (SIT). The release of sterile male insects will replace natural insects from the environment. The Logistic Growth Rate has been considered for the Larvae population. We have studied the dynamics of the model in three cases. In the first case, the model has been considered without the discharge of sterile male and immigration has not been taken into account. In the second case, the release of sterile male insect has been considered but immigration has not been taken into consideration. Lastly, in the third model, both immigration and discharge of sterile male have been taken into account. In all three cases, equilibrium points have been evaluated and stability analysis has been done. Thresholds for the sterile male population have been obtained which can be helpful in understanding and implementing the SIT.
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References
E.F. Knipling, Sterile-male method of population control. Science 130(3380), 902–904 (1959)
E.F. Knipling, Sterile insect technique as a screwworm control measure: the concept and its development, in Symposium on Eradication of the Screwworm from the United States and Mexico, Misc. Publ. Entomol. Soc. America vol. 62, ed. by O.H. Graham (College Park, MD, 1985), pp. 4–7
W. Costello, H. Taylor, Mathematical Models of the Sterile Male Technique of Insect Control. Lecture Notes in Biomath, vol. 35, (Springer, New York, 1975), pp. 318–359
K. Dietz, The effect of immigration on genetic control. Theor. Popul. Biol. 9, 58–67 (1976)
H.J. Barclay, Combining methods of insect pest control: modelling selection for resistance to control methos in combination, Reserv. Pop. Ecol. 34, 97–107 (1996)
R.E. Plant, M. Mangel, Modeling and simulation in agricultural pest management. SIAM Rev. 29, 235–261 (1987)
A.C. Bartlett, Insect sterility, insect genetics, and insect control, in Handbook of Pest Management in Agriculture, vol. II, ed. by D. Pimentel (CRC Press, Boca Raton, FL, 1990), pp. 279–287
T. Prout, The joint effect of release of sterile males and immigration of fertilized females on a density regulated population. J. Popul. Biol. 13, 40–71 (1978)
L. Esteva, H.M. Yang, Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique. Math. Biosc. 198, 132–147 (2005)
L. Esteva, H.M. Yang, Control of dengue vector by the sterile insect technique considering logistic recruitmen. TEMA Tend. Mat. Apl. Comput. 7(2), 259–268 (2006)
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Bhatia, S.K., Chauhan, S., Arora, P. (2020). Effect of Sterile Insect Technique on Dynamics of Stage-Structured Model Under Immigration. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_7
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