Mathematical Model of Basal Stem Rot (BSR) Disease Spread in Oil Palm Plants

Teguh Rizali Zahroni; Fahrizal Fahrizal

doi:10.51967/tanesa.v25i1.3003

Authors

Teguh Rizali Zahroni Wood Engineering, State Agricultural Polytechnic of Samarinda Samarinda
Fahrizal Planantation Managent, State Agricultural Polytechnic of Samarinda

DOI:

https://doi.org/10.51967/tanesa.v25i1.3003

Keywords:

Oil palm, Basal Stem Rot, Ganoderma sp., equilibrium point, asymptotic local stability

Abstract

This study discusses the stability analysis of mathematical models for the spread of Basar Stem Rot(BSR) in oil palm plants. In developing this mathematical model, several assumptions are taken to obtain a model that is suitable for the spread of BSR disease. The resulting model is a system of first-order nonlinear differential equations with three variables. This research includes both analytical and numerical analysis. Analytical analysis includes determination of equilibrium points and local stability analysis, while numerical analysis is conducted using Microsoft Excel application. From this study, two equilibrium points were found with stability conditions that depend on the fulfillment of certain conditions. One important result obtained is that the equilibrium point will be locally stable if and only if α > μ and b > √D, where D is the discriminant of a quadratic equation. After analyzing analytically, the study continued with numerical simulations to illustrate and test the analytical results. Numerical results in the form of graphs show that the solution of the system is stable, which indicates that the disease will be endemic under certain conditions and time. This research provides a deeper understanding of the dynamics of the spread of BSR and the conditions that affect the stability of the spread of the disease. With this analysis, it is expected to contribute to efforts to control BSR disease in oil palm plants. In addition, this research also opens opportunities for the development of similar mathematical models for other plant diseases.

References

A. Elkhateeb, W. (2022). The precious Ganoderma mushroom and plant diseases. Pharmacy and Drug Development, 1(1), 01–05. https://doi.org/10.58489/2836-2322/005

Anderson, J. R., Lee, H. S., & Fincham, J. M. (2014). Discovering the structure of mathematical problem solving. NeuroImage, 97, 163–177. https://doi.org/10.1016/j.neuroimage.2014.04.031

Aziz, M. H. A., Khairunniza-Bejo, S., Wayayok, A., Hashim, F., Kondo, N., & Azmi, A. N. N. (2021). Temporal Changes Analysis of Soil Properties Associated with Ganoderma boninense Pat. Infection in Oil Palm Seedlings in a Controlled Environment. Agronomy, 11(11). https://doi.org/10.3390/AGRONOMY11112279

Barcelos, E., De Almeida Rios, S., Cunha, R. N. V., Lopes, R., Motoike, S. Y., Babiychuk, E., Skirycz, A., & Kushnir, S. (2015). Oil palm natural diversity and the potential for yield improvement. Frontiers in Plant Science, 6(MAR), 1–16. https://doi.org/10.3389/fpls.2015.00190

Durand-Gasselin, T., Asmady, H., Flori, A., Jacquemard, J. C., Hayun, Z., Breton, F., & De Franqueville, H. (2005). Possible sources of genetic resistance in oil palm (Elaeis guineensis Jacq.) to basal stem rot caused by Ganoderma boninense - Prospects for future breeding. Mycopathologia, 159(1), 93–100. https://doi.org/10.1007/S11046-004-4429-1/METRICS

Iljin, Y. A. (2015). On the C1-equivalence of essentially nonlinear systems of differential equations near an asymptotically stable equilibrium point. Vestnik St. Petersburg University: Mathematics, 48(1), 9–17. https://doi.org/10.3103/S1063454115010057

Inayah, N., Manaqib, M., Fitriyati, N., & Yupinto, I. (2020). Model Matematika Dari Penyebaran Penyakit Pulmonary Tuberculosis Dengan Penggunaan Masker Medis. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 14(3), 461–472. https://doi.org/10.30598/barekengvol14iss3pp461-472

Li, W., & Szidarovszky, F. (1999). An elementary result in the stability theory of time-invariant nonlinear discrete dynamical systems. Applied Mathematics and Computation, 102(1), 35–49. https://doi.org/10.1016/S0096-3003(98)10013-9

Naher, L., Yusuf, U., Ismail, A., Tan, S., & Mondal, M. M. A. (2013). Ecological status of Ganoderma and basal stem rot disease of oil palms (Elaeis guineensis Jacq.). Australian Journal of Crop Science.

Purnomo, H., Okarda, B., Dermawan, A., Ilham, Q. P., Pacheco, P., Nurfatriani, F., & Suhendang, E. (2020). Reconciling oil palm economic development and environmental conservation in Indonesia: A value chain dynamic approach. Forest Policy and Economics, 111(January), 102089. https://doi.org/10.1016/j.forpol.2020.102089

Qaim, M., Sibhatu, K. T., Siregar, H., & Grass, I. (2020). Environmental, Economic, and Social Consequences of the Oil Palm Boom. Annual Review of Resource Economics, 12, 321–344. https://doi.org/10.1146/ANNUREV-RESOURCE-110119-024922

Rakib, M. R. M., Bong, C. F. J., Khairulmazmi, A., Idris, A. S., Jalloh, M. B., & Ahmed, O. H. (2017). Association of Copper and Zinc Levels in Oil Palm (Elaeis guineensis) to the Spatial Distribution of Ganoderma Species in the Plantations on Peat. Journal of Phytopathology, 165(4), 276–282. https://doi.org/10.1111/JPH.12559

Salsabila, A., Ramdan, E. P., Asnur, P., & Hidayat, H. (2022). Survei Penyakit Busuk Pangkal Batang Kelapa Sawit Di Kebun Cikasungka, Pt Perkebunan Nusantara Viii, Bogor. Agrosains : Jurnal Penelitian Agronomi, 24(1), 1. https://doi.org/10.20961/agsjpa.v24i1.56720

Soares, A. L. O., & Bassanezi, R. C. (2020). Stability analysis of epidemiological models incorporating heterogeneous infectivity. Computational and Applied Mathematics, 39(3). https://doi.org/10.1007/S40314-020-01293-6

Stephen Wiggins. (1991). Chaotic Transport in Dynamical Systems. Springer. https://books.google.co.id/books?hl=id&lr=&id=KRP5BwAAQBAJ&oi=fnd&pg=PR7&dq=wiggins+introduction+nonlinear+dynamical+systems&ots=uwwLr_09Hw&sig=_C72zIZHHP2-pqbzPK7AhBCNMOs&redir_esc=y#v=onepage&q=wiggins introduction nonlinear dynamical systems&f=false

Sujarit, K., Pathom-aree, W., Mori, M., Dobashi, K., Shiomi, K., & Lumyong, S. (2020). Streptomyces palmae CMU-AB204T, an antifungal producing-actinomycete, as a potential biocontrol agent to protect palm oil producing trees from basal stem rot disease fungus, Ganoderma boninense. Biological Control, 148. https://doi.org/10.1016/J.BIOCONTROL.2020.104307

Szulczewska-Remi, A., Nogala-Kałucka, M., & Nowak, K. W. (2019). Study on the influence of palm oil on blood and liver biochemical parameters, beta-carotene and tocochromanols content as well as antioxidant activity in rats. Journal of Food Biochemistry, 43(2), e12707. https://doi.org/10.1111/JFBC.12707

Wong, W. C., Tung, H. J., Fadhilah, M. N., Midot, F., Lau, S. Y. L., Melling, L., Astari, S., Hadziabdic, Trigiano, R. N., Goh, K. J., & Goh, Y. K. (2021). Genetic diversity and gene flow amongst admixed populations of Ganoderma boninense, causal agent of basal stem rot in African oil palm (Elaeis guineensis Jacq.) in Sarawak (Malaysia), Peninsular Malaysia, and Sumatra (Indonesia). Mycologia, 113(5), 902–917. https://doi.org/10.1080/00275514.2021.1884815

Xu, J., & Jiang, S. (2010). Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation. Ergodic Theory and Dynamical Systems, 31(2), 599–611. https://doi.org/10.1017/S0143385709001114

Zakaria, L. (2022). Basal Stem Rot of Oil Palm - The Pathogen, Disease Incidence, and Control Methods. Plant Disease. https://api.semanticscholar.org/CorpusID:250453414