Mathematical modeling of begomovirus dynamics in tomato fields using whitefly and fungal biocontrol

Volume 39, Issue 4, pp 474--499 https://dx.doi.org/10.22436/jmcs.039.04.05

Publication Date: May 21, 2025 Submission Date: November 27, 2024 Revision Date: February 09, 2025 Accteptance Date: March 11, 2025

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Authors

M. Ido - Department of Mathematics, University of Nazi BONI, Burkina Faso. M. Barro - Department of Mathematics, University of Nazi BONI, Burkina Faso. Y. Savadogo - Department of Mathematics, University of Nazi BONI, Burkina Faso. B. Traoré - Department of Mathematics, University of Nazi BONI, Burkina Faso. - Center of Banfora, University of Nazi BONI, Burkina Faso.

Abstract

Tomato cultivation in Burkina Faso and elsewhere constitutes a source of income for farmers. Tomato is a very important fruit for a good complete diet, unfortunately low productivity is caused by various factors including climate change, fungal plant diseases linked to pathogens and spread by insect pests. Every year farmers suffer huge losses due to the tomato yellow virus (begomovirus), which is transmitted by insect vectors Bemisia Tabaci. However, we analyze these insect management problems using mathematical models. In this paper we developed a mathematical model of tomato yellow leaf curve virus (TYLCV) disease in the tomato plantation with the growth rate of insects vectors following the logistic function, taking into account the two latent stages of the vegetative phase and the generative phase of tomato plants. We determined the value of the basic reproduction number \(\mathcal{R}_0\) of the model from the dominant eigenvalue of the next generation matrix. In practice the basic reproduction number represent the number of new cases generated by an infectious individual during its infection phase . But in theory we use the basic reproduction number to analyze the stability of the equilibrium states of the model. This parameter is used to evaluated the speed of spread of the virus in the population. The results illustrates that when \(\mathcal{R}_0 < 1\), the disease-free equilibrium point is asymptotically globally stable and the model has an endemic equilibrium point which is asymptotically globally stable when \(\mathcal{R}_0 >1\). We have also provided numerical simulation examples describing the population of the model that was developed. The numerical simulation results illustrate that for a use of Verticillium lecanii at a dose greater than \(10\%\) the population of tomato plants latent, infected in the vegetative and in the generative phase will experience extinction, just like the susceptible and infected population of Bemisia Tabaci. In the last part of our work, we also calculated the sensitivity indices of certain parameters that are very sensitive to the variation in the value of the basic reproduction number. These findings provide a scientific basis for optimizing biocontrol strategies in tomato farming.

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Keywords

• Latent stage
• logistic function
• Verticillium lecanii
• basic reproduction number
• differential equations
• numerical simulations
• sensitivity index

MSC

•  34B18
•  34D23
•  34E05

References

• [1] F. Akad, A. Eybishtz, D. Edelbaum, R. Gorovits, O. Dar-Issa, N. Iraki, H. Czosnek, Making a friend form a foe: Expressing a GroEl gene from the whitefly Bemisia tabaci in the pholem of tomato plants confers resistance to tomato yellow leaf curl virus, Arch. Virol., 152 (2007), 1323–1339
  • View Article
  • Google Scholar


• [2] A. AL-MUSA, Incidence, economic importance and control of tomato yellow leaf curl in Jourdan, Plant Dis., 66 (1982), 561–563
  • View Article
  • Google Scholar


• [3] R. Amelia, N. Anggriani, N. Istifadah, A. K. Supriatna, Dynamic analysis of mathematical model of the spread of yellow virus in red chilli plants through insect vectors with logiscal function, AIP Conf. Proc., 2264 (2024), 1–10
  • View Article
  • Google Scholar


• [4] B. Anderson, J. Jackson, M. Sitharam, Descartes’ rule of signs revisited, Amer. Math. Monthly, 105 (1998), 447–451
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] N. Atifah, D. Murni, R. S. Winanda, Mathematical Model of Effect of Yellow Virus on Tomato Plants Through Bemisia tabaci Insects Using Verticillium lecanii Fungus, Rangkiang Math. J., 1 (2022), 72–80
  • View Article
  • Google Scholar


• [6] N. Barboza, E. Hernández, A. K. Inoue-Nagata, E. Moriones, L. Hilje, Achievements in the epidemiology of begomovirus and their vector bemisia tabaci in Costa Rica, Rev. Biol. Trop, 67 (2019), 46 pages
  • View Article
  • Google Scholar


• [7] S. Busenberg, K. Cooke, Vertically transmitted diseases: models and dynamics, Springer-Verlag, Berlin (1993)
  • View Article
  • Google Scholar
  • MATH


• [8] N. S. Butter, H. S. Rataul, The virus vector relationship of the tomato leaf curl virus (TLCV) and its vector Bemisia tabaci (Hemiptera: aleyrodidae), Phytoparasitica, 5 (1977), 173–186
  • View Article
  • Google Scholar


• [9] C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A.-A. Yakubu, Mathematical approaches for emerging and reemerging infectious diseases: models, methods and theory, Springer-Verlag, New York (2002)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] C. Castillo-Chavez, Z. Feng, W. Huang, On the Computation of R0 and its role on global stability. Mathematical Approaches for Emerging and Reemerging Infectious Disease, IMA Vol. Math. Appl., 125 (2002), 229–250
  • View Article


• [11] S. Cohen, F. E. Nitzany, Transmission and host range of tomato yellow leaf curl virus, Phytopathology, 56 (1966), 1127–1131
  • View Article
  • Google Scholar


• [12] N. J. Cunniffe, C. A. Giligan, A theoretical framework for biological control of soil-borne plant pathogens: identifying effective strategies, J. Theoret. Biol., 278 (2011), 32–43
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] H. Czosnek, H. Laterrot, worldwide survey of tomato yellow leaf curl viruses, Arch. Virol., 142 (1997), 1391–1406
  • View Article
  • Google Scholar


• [14] O. Diekman, J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model bulding,analysis and interpretation Wiley, John Wiley & Sons, Chichester (2000)
  • View Article
  • Google Scholar
  • MATH


• [15] G. A. A. Gabaze, D. Mohamed, M. KOUAKOU, C. N. Diakaria, F. Lassina, K. Abo, Efficacy of a biopesticide based on Cymbopogon winteranus (lemon grass) extract in tomato (Solanum lycopersicum L.) cultivation in central Côte d’Ivoire, Int. J. Innov. Appl. Stud., 36 (2022), 832–841
  • View Article
  • Google Scholar


• [16] E. Glick, Y. Levy, Y. Gafni, The Viral Etiology of Tomato Yellow Leaf Curl Disease – A Review, Plant Protect. Sci., 45 (2009), 81–97
  • View Article
  • Google Scholar


• [17] O. Gnakine, L. Mouton, A. Avado, T. Martin, A. Sanon, R. K. Dabire, F. Fleury, Biotype statuts and resistance to neonicotinoids and carbosulfan in Bemisia tabaci (Hemiptera: Aleyrodidae) in Burkina Faso, west africa, Int. J. Pest Manag., 59 (2013), 95–102
  • View Article
  • Google Scholar


• [18] H. Guo, M. Y. Li, Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q., 14 (2006), 259–284
  • View Article
  • Google Scholar
  • MATH


• [19] H. Guo, M. Y. Li, Z. Shuai, A graph-theoretic approach to the method of global Lyapunov functions, Proc. Amer. Math. Soc., 136 (2008), 2793–2802
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] J. H. Heffernan, R. J. Smith, L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface., 2 (2005), 281–293
  • View Article
  • Google Scholar


• [21] M. Jabło ´ nska-Sabuka, R. Kalaria, T. Kauranne, A dynamical model for epidemic outbursts by begomovirus population, Ecol. Model., 297 (2015), 60–68
  • View Article
  • Google Scholar


• [22] M. J. Jeger, F. Van den Bosch, L. V. Madden, Modelling virus-and host-limitation in vectored plant disease epidemics, Virus Res., 159 (2011), 215–222
  • View Article
  • Google Scholar


• [23] M. J. Jeger, Z. Chen, G. Powell, S. Hodge, F. Van den Bosch, Interactions in a host plant-virus–vector–parasitoid system: Modelling the consequences for virus transmission and disease dynamics, Virus Res., 159 (2011), 183–193
  • View Article
  • Google Scholar


• [24] P. Jittamai, N. Chanlawong, W. Atisattapong, W. Anlamlert, N. Buensanteai, Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design, Math. Biosci. Eng., 18 (2021), 5069–5093
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] C. M. Jones, K. Gorman, I. Denholm, M. S. Williamson, High-throughput allelic discrimination of B and Q biotypes of the whitefly, Bemisia tabaci, using TaqMan allele-selective PCR, Pest Manag. Sci., 64 (2008), 12–15
  • View Article
  • Google Scholar


• [26] B. D. Kashima, R. B. Mabagala, A. Mpunami, Tomato yellow leaf curl begomovirus disease in Tanzania: Status and strategies for sustainable management, J. Sustain. Agric., 22 (2023), 23–41
  • View Article
  • Google Scholar


• [27] T. Kinene, L. S. Luboobi, B. Nannyonga, G. G. Mwanga, A mathematical model for the dynamics and cost effectiveness of the current controls of cassava brown streak disease in Uganda, J. Math. Comput. Sci., 5 (2015), 567–600
  • View Article
  • Google Scholar


• [28] J. P. Lasalle, The stability of dynamical systems, Society for Industrial and Applied Mathematics, Philadelphia, PA (1976)
  • View Article
  • Google Scholar


• [29] S. Lenhart, J. T. Workman, Optimal control applied to biological models, Chapman & Hall/CRC, Boca Raton, FL (2007)
  • View Article
  • Google Scholar


• [30] L. V. Madden, G. Hughes, F. Van Den Bosch, The Study of Plant Disease Epidemics, APS Press, St. Paul, Minnesota U.S.A. (2007)
  • View Article
  • Google Scholar


• [31] M. N. Maruthi, H. Czosnek, F. Vidavski, S.-Y. Tarba, J. Milo, S. Leviatov, H. M. Venkatesh, A. S. Padmaja, R. S. Kulkarni, V. Muniyappa, Comparison of Resistance to Tomato Leaf Curl Virus (India) and Tomato Yellow Leaf Curl Virus (Israel) among Lycopersicon Wild Species, Breeding Lines and Hybrids, Eur. J. Plant Pathol., 109 (2003), 1–11
  • View Article
  • Google Scholar


• [32] P. Mehta, J. A. Wyman, M. K. Nakhla, D. P. Maxwell, Transmission of Tomato Yellow Leaf Curl Geminivirns by Bemisia tabaci (Homoptera: Aleyrodidae), J. Econ. Entomol., 87 (1994), 1291–1297
  • View Article
  • Google Scholar


• [33] S. M. Moore, E. T. Borer, P. R. Hosseini, Predators indirectly control vector-borne disease: linking predator–prey and host–pathogen models, J. R. Soc. Interface., 7 (2010), 161–176
  • View Article
  • Google Scholar


• [34] A. L. M. Murwayi, T. Onyango, B. Owour, Mathematical Analysis of Plant Disease Dispersion Model that incorporates wind Strength and Insect Vector at Equilibrium, Br. J. Math. Comput. Sci., 22 (2017), 1–17
  • View Article
  • Google Scholar


• [35] A. L. M. Murwayi, T. Onyango, B. Owour, Estimated Numerical Results and Simulation of the Plant Disease Model Incorporating Wind Strength and Insect Vector at Equilibrium, J. Adv. Math. Comput. Sci., 25 (2017), 1–17
  • View Article
  • Google Scholar


• [36] T. Nakazawa, T. Yamanaka, S. Urano, Model Analysis for Plant Disease Dynamics Co-medilated by Herbivory and Herbivore-Borne Phytopathogens, Biol. Lett., 8 (2012), 685–688
  • View Article
  • Google Scholar


• [37] L. V. Nedorezov, Paramecium aurelia dynamics: Non-traditional approach to estimation of model parameter (on an example of Verhulst ang Gompertz models), Ecol. Model., 317 (2015), 1–5
  • View Article
  • Google Scholar


• [38] S. Z. Rida, M. Khalil, H. A. Hosham, S. Gadellah, Mathematical Model of Vector-Borne Plant Disease with Memoire on the Host and the Vector, Progr. Fract. Differ. Appl., 2 (2016), 227–285
  • View Article
  • Google Scholar


• [39] M. G. Roberts, B. T. Grenfell, The Population Dynamics of Nematode Infections of Ruminants: Periodic Perturbations as a Model for Management, IMA J. Math. Appl. Med. Biol., 8 (1991), 83–93
  • View Article
  • Google Scholar
  • MATH


• [40] S. E. Seal, F. VandenBosch, M. J. Jeger, Factors influencing begomovirus evolution and their increasing global significance: implications for sustainable control, Crit. Rev. Plant Sci., 25 (2006), 23–46
  • View Article
  • Google Scholar


• [41] Z. Shuai, P. van den Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math., 73 (2013), 1513–1532
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [42] D. Son, I. Somda, A. Legreve, B. Schiffers, Phytosanitary practices of tomato growers in Burkina Faso and risks for health and the environment, Cah. Agric., 26 (2017),
  • View Article
  • Google Scholar


• [43] P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [44] C. Vargas-De-León, J. A. Castro-Hernández, Local and global stability of host-vector desease models, Revi. Elec. Cont. Mat., 25 (2008), 1–9
  • View Article
  • Google Scholar


• [45] R. S. Varga, Matrix iterative analysis, Springer-Verlag, Berlin (2000)
  • View Article
  • MathSciNet
  • Google Scholar


• [46] X.-S. Zhang, J. Holt, J. Colvin, Mathematical Models of Host Plant Infection by Helper-Dependent Virus Complexes: Why are Helper Virus Always Avirulent, Anal. Theor. Plant Pathol., 90 (2010), 85–93
  • View Article
  • Google Scholar


• [47] F. Zhou, H. Yao, Global dynamics of a host-vector-predator mathematical model, J. Appl. Math., 2014 (2014), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH