Fuzzy Dynamic Model of Tungro Virus in Rice Plant Related to Pruning and Insecticide
Abstract
Rice Tungro Disease (RTD) is a significant threat to global rice production, with planthoppers acting as the principal transmission vectors. While insecticide application is a common vector control method, many agricultural practices also incorporate pruning interventions to mitigate the spread of the Tungro virus within rice crops. This study develops a fuzzy dynamical model to capture the uncertainties associated with two key parameters: the mortality of rice plants induced by pruning and the mortality of planthoppers due to insecticide treatment. Specifically, the fuzzy membership function for pruning-induced mortality is formulated as a function of the Tungro virus load. In contrast, the insecticide-related planthopper mortality is defined as a function of insecticide dosage, accounting for the varying levels of resistance observed in planthopper populations. The resulting fuzzy dynamical system is numerically solved using the Non-Standard Finite Difference (NSFD) scheme, which preserves the qualitative properties of the underlying mode. Numerical simulations are conducted to analyze the effects of fuzzy parameter variations on the disease dynamics. Numerical results indicate that the integrated application of pruning and insecticide strategies significantly reduces infected populations compared to single-control strategies. This modeling framework provides a more realistic and flexible tool for analyzing plant disease control strategies under parameter uncertainty.
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References
S. Dey, R. Das, and M. De, “A brief review on present status of rice tungro disease: Types of viruses, vectors, occurrence, symptoms, control and resistant rice varieties,” International Journal of Advancement in Life Sciences Research, vol. 7, pp. 15–23, Jul. 2024. https://doi.org/10.31632/ijalsr.2024.v07i03.002.
I. N. Widiarta, F. Firmansyah, M. Yunus, A. Apriana, A. Sisharmini, T. Santoso, R. Terryana, R. Rahmini, I. Rumanti, T. Sitaresmi, S. Margaret, C. Chaerani, A. Widarti, Y. Nugraha, and A. Hairmansis, “Rice virus disease in indonesia: epidemiology and varietal resistance,” Phytopathology Research, vol. 7, 02 2025. https://doi.org/10.1186/s42483-024-00302-4.
H. Hamdayanty, F. T. Ladja, and Mansur, “Molecular detection of tungro virus on mekongga and inpari 4 rice varieties in west papua,” IOP Conference Series: Earth and Environmental Science, vol. 807, p. 022088, jul 2021. https://dx.doi.org/10.1088/1755-1315/807/2/022088.
K. S. Patel, B. Rajeswari, and D. Krishnaveni, “Efficacy of insecticides against rice tungro disease and its vector (nephotettix virescens) under glasshouse conditions,” Agricultural Science Digest, vol. 38, no. 3, pp. 225–227, 2018. https://arccjournals.com/journal/agricultural-science-digest/D-4728
M. W. Gulzar, R. Maqsood, H. Abbas, M. Manzoor, M. Suleman, H. Bajwa, A. Hamza, S. Yar, M. Zain, A. Wadood, and N. Aslam, “Use of insecticides and their impact on viral diseases in humans, animals and environment,” Hosts and Viruses, vol. 11, 06 2024. https://dx.doi.org/10.17582/journal.hv/2024/11.64.77.
H. van den Berg, H. Bezerra, S. Al-Eryani, E. Chanda, B. Nagpal, T. Knox, R. Velayudhan, and R. S. Yadav, “Recent trends in global insecticide use for disease vector control and potential implications for resistance management,” Scientific Reports, vol. 11, 12 2021. https://doi.org/10.1038/s41598-021-03367-9.
S. Barathi, N. Sabapathi, S. Kandasamy, and J. Lee, “Present status of insecticide impacts and eco-friendly approaches for remediation-a review,” Environmental Research, vol. 240, p. 117432, 2024. https://doi.org/10.1016/j.envres.2023.117432.
R. Amelia, N. Anggriani, A. K. Supriatna, and N. Istifadah, “Mathematical model for analyzing the dynamics of tungro virus disease in rice: A systematic literature review,” Mathematics, vol. 10, no. 16, 2022. https://doi.org/10.3390/math10162944.
H. Ali, S. Alkhalaf, and N. Arafa, “The influence of quarantine and uprooting control measures in reducing rice tungro disease through a mathematical model,” International Journal of Analysis and Applications, vol. 23, p. 40, 02 2025. https://doi.org/10.28924/2291-8639-23-2025-40.
R. Amelia, N. Anggriani, A. K. Supriatna, and N. Istifadah, “Optimal control model for the spread of tungro disease in rice plants by controlling using pesticides,” Engineering Letters, vol. 32, pp. 1097–1106, 06 2024. https://www.engineeringletters.com/issues_v32/issue_6/EL_32_6_04.pdf.
R. Amelia, N. Anggriani, A. K. Supriatna, and N. Istifadah, “Dynamic analysis and optimal control of the spread of tungro virus disease in rice plants considering refugia planting and pesticide application,” Mathematics, vol. 12, no. 24, 2024. https://doi.org/10.3390/math12243979.
D. Suandi, M. F. Ansori, D. Aldila, V. Noviantri, E. Sobari, and N. B. M. Nasir, “Investigating the efficacy of insecticides in controlling the spread of tungro virus in rice plants: a mathematical modeling approach,” Communications in Mathematical Biology and Neuro-science, vol. 2025, no. 59, 2025. https://scik.org/index.php/cmbn/article/view/9225.
V. Noviantri, K. Alexander, D. Suandi, S. Achmad, and A. M. B. Sipahutar, “Nonlinear model for aphid and ladybugs interaction with pesticides as fuzzy parameters.,” IAENG International Journal of Applied Mathematics, vol. 54, no. 06, pp. 1182–1197, 2024. https://www.iaeng.org/IJAM/issues_v54/issue_6/IJAM_54_6_21.pdf.
M. Abdy, S. Side, S. Annas, et al., “An sir epidemic model for covid-19 spread with fuzzy parameter: the case of indonesia,” Advances in Difference Equations, vol. 2021, p. 105, 2021. https://link.springer.com/article/10.1186/s13662-021-03263-6
O. Topan, Y. Yazlik, and S. Atpinar, “Dynamics of fuzzy difference equations system with higher-order,” Journal of Applied Mathematics and Computing, vol. 71, pp. 5505–5530, 2025. https://link.springer.com/article/10.1007/s12190-025-02440-0
K. H. Gazi, A. Biswas, P. Singh, M. Rahaman, S. Maity, A. Mahata, and S. P. Mondal, “A comprehensive literature review of fuzzy differential equations with applications,” Journal of Fuzzy Extension and Applications, vol. 6, no. 1, pp. 134–161, 2025. https://doi.org/10.22105/jfea.2024.449970.1426
C. Kraus, C. Rauch, E. M. Kalvelage, F. H. Behrens, D. d’Aguiar, C. Dubois, and M. Fischer, “Minimal versus intensive: How the pruning intensity affects occurrence of grapevine leaf stripe disease, wood integrity, and the mycobiome in grapevine trunks,” Journal of Fungi, vol. 8, no. 3, 2022. https://doi.org/10.3390/jof8030247.
F. G. Horgan and A. Pe˜nalver-Cruz, “Compatibility of insecticides with rice resistance to planthoppers as influenced by the timing and frequency of applications,” Insects, vol. 13, no. 2, 2022. https://doi.org/10.3390/insects13020106.
S.-F. Wu, B. Zeng, C. Zheng, X.-C. Mu, Y. Zhang, J. Hu, S. Zhang, C. Gao, and J.-L. Shen, “The evolution of insecticide resistance in the brown planthopper (nilaparvata lugens st˚al) of china in the period 2012–2016,” Scientific Reports, vol. 8, 03 2018. https://doi.org/10.1038/s41598-018-22906-5.
J. Cresson and F. Pierret, “Non standard finite difference scheme preserving dynamical properties,” Journal of Computational and Applied Mathematics, vol. 303, pp. 15–30, 2016. https://doi.org/10.1016/j.cam.2016.02.007.
A. Yaghoubi and H. saberi najafi, “Comparison between standard and non-standard finite difference methods for solving first and second order ordinary differential equations,” International Journal of Applied Mathematical Research, vol. 4, p. 316, 03 2015. https://doi.org/10.14419/ijamr.v4i2.4331.
G. Gabbriellini, “Aphids, ants and ladybirds: a mathematical model predicting their population dynamics,” Open Journal of Mathematical Sciences, vol. 3(2019), p. 139–151, May 2019. https://doi.org/10.30538/oms2019.0057
W. Suryaningrat, N. Anggriani, A. Supriatna, and N. Istifadah, “The optimal control of rice tungro disease with insecticide and biological agent,” in AIP Conference Proceedings, vol. 2264, p. 040002, 09 2020. https://doi.org/10.1063/5.0023569
M. J. Jeger, J. Holt, F. Van Den Bosch, and L. V. Madden, “Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions,” Physiological Entomology, vol. 29, no. 3, pp. 291–304, 2004. https://doi.org/10.1111/j.0307-6962.2004.00394.x.
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