Impact of whitefly maturation on mosaic disease dynamics using a stage-structured model

Aeshah A. Raezah; Konstantin B. Blyuss; Selim Reja; Fahad Al Basir; Aeshah A. Raezah; Konstantin B. Blyuss; Selim Reja; Fahad Al Basir

doi:10.3934/math.20251098

AIMS Mathematics

2025, Volume 10, Issue 10: 24779-24803. doi: 10.3934/math.20251098

Previous Article Next Article

Research article Special Issues

Impact of whitefly maturation on mosaic disease dynamics using a stage-structured model

1.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia
2.
Department of Mathematics, University of Sussex Falmer, Brighton BN1 9QH, United Kingdom
3.
Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, India
4.
Department of Mathematics, Asansol Girls' College, Dr. Anjali Roy Sarani, Asansol-4, West Bengal 713304, India

Received: 21 September 2025 Revised: 20 October 2025 Accepted: 24 October 2025 Published: 29 October 2025
MSC : 92-10, 37G15

Plant viral infections are primarily propagated by adult insect vectors, which generally require a maturation period of approximately ten to twelve days. Following ingestion of the virus from an infected host plant, these vectors become capable of transmitting the pathogen to susceptible plants. In this study, a stage-structured mathematical model was formulated and analyzed to characterize the transmission dynamics of plant viral diseases mediated by adult insect vectors. Particular emphasis was placed on assessing how the maturation period of vectors influences the progression of infection transmission. To establish the mathematical validity of the model, it was shown to possess non-negative and bounded solutions, which confirms its well-posedness. We identified all steady states and studied their stability. The results show how infection rate, maturation rate, and maturation time can cause stability changes in steady states. Numerical stability and simulations were presented to analyze the behaviors of the system in different dynamical regimes. The stabilizing effect of the maturation period can help develop control methods for the management of plant viral diseases.
- vector-borne plant disease,
- basic reproduction number,
- stability analysis,
- sensitivity analysis,
- Hopf bifurcation,
- numerical simulation
Citation: Aeshah A. Raezah, Konstantin B. Blyuss, Selim Reja, Fahad Al Basir. Impact of whitefly maturation on mosaic disease dynamics using a stage-structured model[J]. AIMS Mathematics, 2025, 10(10): 24779-24803. doi: 10.3934/math.20251098

Related Papers:

Abstract

Plant viral infections are primarily propagated by adult insect vectors, which generally require a maturation period of approximately ten to twelve days. Following ingestion of the virus from an infected host plant, these vectors become capable of transmitting the pathogen to susceptible plants. In this study, a stage-structured mathematical model was formulated and analyzed to characterize the transmission dynamics of plant viral diseases mediated by adult insect vectors. Particular emphasis was placed on assessing how the maturation period of vectors influences the progression of infection transmission. To establish the mathematical validity of the model, it was shown to possess non-negative and bounded solutions, which confirms its well-posedness. We identified all steady states and studied their stability. The results show how infection rate, maturation rate, and maturation time can cause stability changes in steady states. Numerical stability and simulations were presented to analyze the behaviors of the system in different dynamical regimes. The stabilizing effect of the maturation period can help develop control methods for the management of plant viral diseases.

References

[1]	P. A. Link, M. Fuchs, Transmission specificity of plant viruses by vectors, J. Plant Pathol., 87 (2005), 153–165. Available from: https://www.jstor.org/stable/41998234.
[2]	V. Z. Graff, V. Brault, Role of vector-transmission proteins, In: Plant Virology Protocols, Methods in Molecular Biology, Humana Press, 451 (2008), 81–96. https://doi.org/10.1007/978-1-59745-102-4_6
[3]	A. E. Whitfield, B. W. Falk, D. Rotenberg, Insect vector-mediated transmission of plant viruses, Virology, 479 (2015), 278–289. https://doi.org/10.1016/j.virol.2015.03.026 doi: 10.1016/j.virol.2015.03.026
[4]	H. Naveed, W. Islam, M. Jafir, V. Andoh, L. Chen, K. Chen, A review of interactions between plants and whitefly-transmitted begomoviruses, Plants, 12 (2023), 3677. https://doi.org/10.3390/plants12213677 doi: 10.3390/plants12213677
[5]	F. A. Basir, K. B. Blyuss, S. Ray, Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas, Ecol. Complex., 36 (2018), 92–100. https://doi.org/10.1016/j.ecocom.2018.07.004 doi: 10.1016/j.ecocom.2018.07.004
[6]	H. Czosnek, A. H. Shalev, I. Sobol, R. Gorovits, M. Ghanim, The incredible journey of begomoviruses in their whitefly vector, Viruses, 9 (2017), 273. https://doi.org/10.3390/v9100273 doi: 10.3390/v9100273
[7]	D. R. Jones, Plant viruses transmitted by whiteflies, Eur. J. Plant Pathol., 109 (2003), 195–219. https://doi.org/10.1023/A:1022846630513 doi: 10.1023/A:1022846630513
[8]	M. J. Jeger, J. Holt, F. V. D. Bosch, L. V. Madden, Epidemiology of insect-transmitted plant viruses: Modelling disease dynamics and control interventions, Physiol. Entomol., 29 (2004), 291–304. https://doi.org/10.1111/j.0307-6962.2004.00394.x doi: 10.1111/j.0307-6962.2004.00394.x
[9]	D. Gerling, A. R. Horowitz, J. Baumgaertner, Autecology of Bemisia tabaci, Agr. Ecosyst. Environ., 17 (1986), 5–19. https://doi.org/10.1016/0167-8809(86)90022-8
[10]	J. Salas, O. Mendoza, Biology of the sweetpotato whitefly (Homoptera: Aleyrodidae) on tomato, Fla. Entomol., 78 (1995), 154–160. https://doi.org/10.2307/3495680 doi: 10.2307/3495680
[11]	N. S. Butter, Insect vectors and plant pathogens, CRC Press, 2018. https://doi.org/10.1201/9780429503641
[12]	M. Jackson, B. M. C. Charpentier, Modeling plant virus propagation with delays, J. Comput. Appl. Math., 309 (2017), 611–621. https://doi.org/10.1016/j.cam.2016.04.024 doi: 10.1016/j.cam.2016.04.024
[13]	Q. Li, Y. Dai, X. Guo, X. Zhang, Hopf bifurcation analysis for a model of plant virus propagation with two delays, Adv. Differ. Equ., 2018 (2018), 259. https://doi.org/10.1186/s13662-018-1714-8 doi: 10.1186/s13662-018-1714-8
[14]	F. A. Basir, K. B. Blyuss, E. Venturino, Stability and bifurcation analysis of a multi-delay model for mosaic disease transmission, AIMS Math., 8 (2023), 24545–24567. https://doi.org/10.3934/math.20231252 doi: 10.3934/math.20231252
[15]	F. A. Basir, Y. N. Kyrychko, K. B. Blyuss, S. Ray, Effects of vector maturation time on the dynamics of cassava mosaic disease, B. Math. Biol., 83 (2021), 87. https://doi.org/10.1007/s11538-021-00921-4 doi: 10.1007/s11538-021-00921-4
[16]	A. Uke, H. Tokunaga, Y. Utsumi, N. A. Vu, P. T. Nhan, P. Srean, et al., Cassava mosaic disease and its management in Southeast Asia, Plant Mol. Biol., 109 (2022), 301–311. https://doi.org/10.1007/s11103-021-01168-2 doi: 10.1007/s11103-021-01168-2
[17]	J. P. Legg, African cassava mosaic disease, In: Encyclopedia of Virology, 3 Eds., Academic Press, 2008, 30–36. https://doi.org/10.1016/B978-012374410-4.00693-2
[18]	B. Erick, M. Mayengo, Modelling the dynamics of cassava mosaic disease with non-cassava host plants, Inform. Med. Unlocked, 33 (2022), 101086. https://doi.org/10.1016/j.imu.2022.101086 doi: 10.1016/j.imu.2022.101086
[19]	M. Banerjee, Y. Takeuchi, Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, J. Theor. Biol., 412 (2017), 154–171. https://doi.org/10.1016/j.jtbi.2016.10.016 doi: 10.1016/j.jtbi.2016.10.016
[20]	B. Buonomo, M. Cerasuolo, The effect of time delay in plant–pathogen interactions with host demography, Math. Biosci. Eng., 12 (2015), 473–490. https://doi.org/10.3934/mbe.2015.12.473 doi: 10.3934/mbe.2015.12.473
[21]	J. E. V. D. Plank, Plant diseases: Epidemics and control, Academic Press, 1963.
[22]	K. L. Cooke, Stability analysis for a vector disease model, Rocky Mt. J. Math., 9 (1979), 31–42. Available from: https://www.jstor.org/stable/44238836.
[23]	F. A. Basir, P. K. Roy, Dynamics of mosaic disease with roguing and delay in Jatropha curcas plantations, J. Appl. Math. Comput., 58 (2018), 1–31. https://doi.org/10.1007/s12190-017-1131-2 doi: 10.1007/s12190-017-1131-2
[24]	Z. Wang, B. Hu, L. Zhu, J. Lin, M. Xu, D. Wang, Hopf bifurcation analysis for Parkinson oscillation with heterogeneous delays: A theoretical derivation and simulation analysis, Commun. Nonlinear Sci., 114 (2022), 106614. https://doi.org/10.1016/j.cnsns.2022.106614 doi: 10.1016/j.cnsns.2022.106614
[25]	E. Venturino, P. K. Roy, F. A. Basir, A. Datta, A model for the control of the mosaic virus disease in Jatropha curcas plantations, Energy Ecol. Environ., 1 (2016), 360–369. https://doi.org/10.1007/s40974-016-0033-8 doi: 10.1007/s40974-016-0033-8
[26]	F. A. Basir, Role of whitefly maturation period on mosaic disease propagation in Jatropha curcas plant, Front. Appl. Math. Stat., 9 (2023), 1238497. https://doi.org/10.3389/fams.2023.1238497 doi: 10.3389/fams.2023.1238497
[27]	S. Adhurya, F. A. Basir, S. Ray, Stage-structure model for the dynamics of whitefly transmitted plant viral disease: An optimal control approach, Comput. Appl. Math., 41 (2022), 154. https://doi.org/10.1007/s40314-022-01864-9 doi: 10.1007/s40314-022-01864-9
[28]	J. Holt, M. J. Jeger, J. M. Thresh, G. W. O. Nape, An epidemiological model incorporating vector population dynamics applied to African cassava mosaic virus disease, J. Appl. Ecol., 34 (1997), 793–806. https://doi.org/10.2307/2404924 doi: 10.2307/2404924
[29]	P. V. D. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic steady states for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/s0025-5564(02)00108-6 doi: 10.1016/s0025-5564(02)00108-6
[30]	C. Douskos, P. Markellos, Complete coefficient criteria for five-dimensional Hopf bifurcations, with an application to economic dynamics, J. Nonlinear Dyn., 2015 (2015), 278234. https://doi.org/10.1155/2015/278234 doi: 10.1155/2015/278234
[31]	J. Hale, Theory of functional differential equations, New York: Springer, 1977. Available from: https://link.springer.com/book/10.1007/978-1-4612-9892-2.
[32]	B. D. Hassard, N. D. Kazarinoff, Y. H. Wan, Theory and applications of Hopf bifurcation, London Mathematical Society Lecture Note Series, UK, Cambridge: Cambridge University Press, 41 (1981). https://doi.org/10.1002/zamm.19820621221
[33]	A. Saltelli, M. Scott, The role of sensitivity analysis in the corroboration of models and its link to model structural and parametric uncertainty, Reliab. Eng. Syst. Safe., 57 (1997), 1–4. Available from: https://publications.jrc.ec.europa.eu/repository/handle/JRC14027.
[34]	A. Saltelli, S. Tarantola, K. S. Chan, A quantitative model-independent method for global sensitivity analysis of model output, Technometrics, 41 (1999), 39–56. https://doi.org/10.1080/00401706.1999.10485594 doi: 10.1080/00401706.1999.10485594
[35]	A. C. Ukubuiwe, I. K. Olayemi, F. O. Arimoro, I. C. J. Omalu, B. M. Baba, C. C. Ukubuiwe, et al., Influence of rearing-water temperature on life stages' vector attributes, distribution and utilisation of metabolic reserves in Culex quinquefasciatus (Diptera: Culicidae): Implications for disease transmission and vector control, J. Basic Appl. Zool., 79 (2018), 32. https://doi.org/10.1186/s41936-018-0045-3 doi: 10.1186/s41936-018-0045-3
[36]	C. C. Heu, F. M. McCullough, J. Luan, J. L. Rasgon, CRISPR-Cas9-based genome editing in the silverleaf whitefly (Bemisia tabaci), CRISPR J., 3 (2020), 89–96. https://doi.org/10.1089/crispr.2019.0067 doi: 10.1089/crispr.2019.0067

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)