A new approach to the life cycle of Mediterranean fruit fly with a view to estimating some parameters

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran.

2 Afzalipour Research Institute- Mahani Math Center, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran

3 ‎Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran.

4 Research and Technology Institute of Plant Production, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran.

Abstract

‎Ceratitis capitate, commonly known as the Mediterranean fruit fly, is one of the most destructive fruit pests in the world. The Mediterranean fruit fly is the most economically important fruit fly species because it causes severe destruction. In this paper, a dynamical model based on a delay differential equation is introduced that is described the life cycle of the insect. As follows, Hopf bifurcation is checked by changing the time delays. In the next issue is estimated unknown parameters. It is proposed a method, based on the least square approach and a finite set of observation, to estimate the parameters which are identifiable. Finally, using numerical simulation, the stability at endemic equilibrium point is investigated.

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References

[1] Brauer, F. (2008). Mathematical epidemiology. Springer
[2] Canto, B., Carmen, C.,& Sanchez, E. (2017). Estimation of parameters in a structured SIR model. Advances in Di erence Equations, 2017, 1-13. https://doi.org/10.1186/s13662-017-1078-5
[3] Carey, J. R., & Liedo, P. (1995) Sex-speci c life table aging rates in large med y cohorts. Experimental Gerontology, 30, 315-325. doi: 10.1016/0531-5565(94)00041-z
[4] Carey, J. R., Liedo, P. Harshman, L. G., Zhang, Y., Muller, H. G., (2002) Life History Response of Mediterranean Fruit Flies to Dietary Restriction. Aging Cell 1, 1-15.
[5] Carey, J. R., Papadopoulos, N. T., Muller, H. G., Katsoyannos, B. I., Kouloussis, N. A., Wang, J. L., Wachter, K., Yu, W., & Liedo, P. (2008) Age structure changes and extraordinary lifespan in wild med y populations. Aging Cell, 7(3), 426-437. doi:
10.1111/j.1474-9726.2008.00390.x
[6] Carey, J. R., Papadopoulos, N. T., Papanastasiou, S., Diamantidis, A., & Nakas, C. T. (2012) Estimating changes in mean population age using the death distributions of live-captured medies. Ecological Entomology, 37(5), 359-369. https://doi.org/10.1111/j.1365-2311.2012.01372.x
[7] Carey, R., Silverman, S., & Rao, A. S. S. (2018) The life table population identity: discovery, formulations, proof, extensions, and applications. In Handbook of statistics, 39, 155-186.
[8] Chiou, J. M., Muller, H. G., Wang, J. L., & Carey, J. R. (2003) A functional multiplicative e ects model ¨ for longitudinal data, with application to reproductive histories of female med ies. Statistica Sinica, 13(4), 11-19.
[9] Cohen, Y., Cohen, A., Hetzroni, A., Alchanatis, V., Broday, D., Gazit, Y., & Timar, D. (2008) Spatial decision support system for med y control in citrus. Computers and Electronics in Agriculture, 62(2), 107-117. https://doi.org/10.1016/j.compag.2007.12.005
[10] Flores, J., (2020) Game theory approach to sterile release populations and replicator dynamics: Niche fragmentation and resilience. Physica A: Statistical Mechanics and its Applications, 551, 124-212. https://doi.org/ 10.1016/j.physa.2020.124212
[11] Gerofotis, C. D., NikosA. Kouloussis, N. A., Koukougiannidou, C., Papadopoulos, N. T., Damos, P., Koveos, D. S.,& Carey, J. R., (2019) Age, sex, adult and larval diet shape starvation resistance in the Mediterranean fruit fy: an ecological and gerontological perspective. Scienti c reports, 9(10704), 1-12.
[12] Izadi, M., & Waezizadeh, T., (2024) Stability analysis and numerical evaluations of a COVID-19 model with vaccination. BMC Medical Research Methodology, 24(97), 1-19. https://doi.org/10.1186/s12874-024-02209-2
[13] Liedo, P., Orozco, D., Vaupel, J., & et al. (1992) Slowing of mortality rates at older ages in large med y cohorts. Science, 258(5081), 457-461. doi: 10.1126/science.1411540
[14] Meats, A., & Smallridge, C., (2007) Short-and long-range dispersal of med y, ceratitis capitata (dipt., tephritidae), and its invasive potential.Journal of Applied Entomology, 131(8), 518-523. doi:10.1111/j.1439-0418.2007.01168.x
[15] Novoseltsev, V. N., Arking, R., Carey, J. R., Novoseltseva, J. A., & Yashin, A. I., (2005) Individual fecundity and senescence in drosophila and med y. The journals of gerontology. Series A, Biological sciences and medical sciences, 60(8), 953-962. doi:10.1093/gerona/60.8.953
[16] Novoseltsev, V., Carey, J., Liedo, P., Novoseltseva, J., & Yashin, A., (2000) Anticipation of oxidative damage decelerates aging in virgin female med ies: hypothesis tested by statistical modeling. Experimental Gerontology, 35(8), 971- 987. doi: 10.1016/s0531-5565(00)00165-0
[17] Novoseltsev, V. N., (2006) Mathematical modeling in biology: Systems capable to live and die. Automation and Remote Control, 67(6), 835-855. https://doi.org/10.1134/s0005117906060014
[18] Rahman, B., Blyuss, K. B., & Kyrychko, Y. N., (2015) dynamics of neural systems with discreate and distributed time delays. SIAM Journal on Applied Dynamical Systems, 14(4), 2069-2095. https://doi.org/10.1137/15M1006398
[19] Skiadas, C. H., (2010). Advances in data analysis. Springer
[20] Thomas, M. C., Heppner, J. B., Woodru , R. E., Weems, H. V., Steck, G. J., & Fasulo, T. R., (2001) Mediterranean fruit 
y, ceratitis capitata (wiedemann). IFAS extension university of Florida.
[21] Toorani, A. M., & Abbasipour, H., (2017) E ect of geographical directions, height and the color of yellow trapes in capture of Mediterranean fruit y, ceratitis capitata in citrus orchards. Acta agriculturae Slovenica, 109(3), 561- 575. doi:10.14720/aas.2017.109.3.08
[22] Waezizadeh, T., Mehrpooya, A., Rezaeizadeh, M., & Yarahmadian, S., (2018) Mathematical models for the e ects of hypertension and stress on kidney and their uncertainty. Mathematical Biosciences, 305, 77-95. https://doi.org/10.1016/j.mbs.2018.08.013
[23] Zhao, Z., Hui, C., Plant, R. E., Su, M., Carpenter, T., Papadopoulos, N., Li, Z., & Carey, J. R., (2019) Life table invasion models: spatial progression and species-speci c partitioning. Ecology, 100(5), 1-11. https://doi.org/10.1002/ecy.2682
Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 199-226

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History

  • Receive Date: 28 December 2024
  • Revise Date: 17 June 2025
  • Accept Date: 10 August 2025

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