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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Mathematical Model for emph{Hypothenemus Hampei} and emph{Colletotrichum Kahawae} Co-Dynamics in a Coffee Farm

Journal of Applied Nonlinear Dynamics 15(2) (2026) 387--400 | DOI:10.5890/JAND.2026.06.010

Abdisa Shiferaw Melese, Legesse Lemecha Obsu, Feyissa Kebede Bushu

Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia

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Abstract

Production of \textit{Coffee Arabica} in many African countries is challenged by several pests and diseases. Particularly, quantity and quality of coffee production is reduced by coffee berry borer (CBB) and coffee berry disease (CBD). The CBB is a destructive pest caused by \emph{Hypothenemus hampei}, while CBD is a fungal disease caused by \emph{Colletotrichum kahawae}. In this study, we focused on developing and analyzing a mathematical model to understand the co-dynamics of CBB and CBD in a coffee plantation ecosystem. The CBB and CBD free and endemic equilibrium point of the model were computed. Mathematically, positivity and boundedness of the solutions, existence of CBB and CBD free and endemic equilibria were investigated. The basic reproduction number is derived using the next-generation matrix. The local and global stability of equilibria are established via Routh Hurwitz-criteria and Lyapunov function, respectively. Finally, the numerical simulations are performed using MATLAB ode45 software to visualize the co-dynamics of the system under various scenarios and validate the analytical results.

References

  1. [1]  Sujaritpong, O., Yoo-Kong, S., and Bhadola, P. (2021), Analysis and dynamics of the international coffee trade network, Journal of Physics: Conference Series, 1719, 012106.
  2. [2]  Murphy, S.T. and Moore, D. (1990), Biological control of the coffee berry borer, Hypothenemus hampei, (Ferrari) (Coleoptera: Scolytida): previous programmes and possibilities for the future, Biocontrol News and Information, 11, 107--117.
  3. [3]  Damon, A. (2000), A review of the biology and control of the coffee berry borer, Hypothenemus hampei (Coleoptera: Scolytidae), Bulletin of Entomological Research, 90, 453--465.
  4. [4]  Fuad, A. (2010), Studies on the diversity of insect pests in wild and cultivated coffee plantations in and around Jimma, southwest Ethiopia, International Journal of Biodiversity and Conservation, 8(10), 233--243.
  5. [5]  Vega, F.E., Mercadier, G., Dowd, P.F., and others (1999), Fungi associated with the coffee berry borer Hypothenemus hampei (Ferrari) (Coleoptera: Scolytidae), Colloque Scientifique International sur le Café, 18, 229--238.
  6. [6]  Marino, Y.Y., Vega, V.J., Garcia, J.M., Verle Rodrigues, J.C., Garcia, N.M., and Bayman, P. (2017), The coffee berry borer (Coleoptera: Curculionidae) in Puerto Rico: distribution, infestation, and population per fruit, Journal of Insect Science, 17(2), 58.
  7. [7]  Fotso Fotso, Y., Grognard, F., Tsanou, B., and Touzeau, S. (2018), Modelling and control of coffee berry borer infestation, HAL Id: hal-01871508.
  8. [8]  Melese, A.S. (2024), Mathematical model and optimal control analysis of coffee berry borer with temperature and rainfall variability, International Journal of Biomathematics, 17(5).
  9. [9]  Silva, V.V., Guerra-Guimaraes, L., Azinheira, H.G., Fernandez, D., Petitot, A.S., Bertrand, B., Lashermes, P., and Nicole, M. (2006), Coffee resistance to the main diseases: leaf rust and coffee berry disease, Brazilian Journal of Plant Physiology, 18(1), 119--147.
  10. [10]  Waller, J.M., Bridge, P.D., Black, R., and Hakiza, G. (1993), Characterization of the coffee berry disease pathogen, Colletotrichum kahawae sp. nov., Mycological Research, 97(8), 989--994.
  11. [11]  Vega, M.G., Dowd, P.F., and others (1999), Fungi associated with the coffee berry borer Hypothenemus hampei (Ferrari) (Coleoptera: Scolytidae), Colloque Scientifique International sur le Café, 18, 229--238.
  12. [12]  Griffiths, E., Gibbs, J.N., and Waller, J.M. (1971), Control of coffee berry disease, Annals of Applied Biology, 67(1), 45--74.
  13. [13]  Gaitan, A.L., Cristancho, M.A., Caicedo, B.C., Rivillas, C.A., and Gomez, G.C. (2015), Part I. Infectious diseases, Fitopatologia Brasileira, 32, S135.
  14. [14]  Waller, J.M., Bigger, M., and Hillocks, R.J. (2007), Coffee pests, diseases and their management, CABI.
  15. [15]  Adugna, G. and Jefuka, C. (2006), Resistance levels of Arabica coffee cultivars to coffee berry disease, coffee wilt and leaf rust diseases in Ethiopia, Proceedings of the 12th Crop Science Society of Ethiopia (CSSE), 22--24.
  16. [16]  Artistizabal, L.F., Bustillo, A.E., and Arthurs, S.P. (2016), Integration pest management of coffee berry borer: strategies from Latin America that could be useful for coffee farmers in Hawaii, Insects, 7(1), 6.
  17. [17]  Damon, A. (2000), A review of the biology and control of the coffee berry borer, Hypothenemus hampei (Coleoptera: Scolytidae), Bulletin of Entomological Research, 90(6), 453--465.
  18. [18]  Dufour, B.P. and Frerot, B. (2008), Optimization of coffee berry borer, Hypothenemus hampei Ferrari (Col., Scolytidae), mass trapping with an attractant mixture, Journal of Applied Entomology, 132(7), 591--600.
  19. [19]  Abraha, T., Basir, F.A., Obsu, L.L., and Delfim, F.M. (2021), Pest control using farming awareness: impact of time delays and optimal use of biopesticides, Chaos, Solitons and Fractals, 146, 110869.
  20. [20]  Vega, F. (2004), Coffee berry borer Hypothenemus hampei (Ferrari) (Coleoptera: Scolytidae), Encyclopedia of Entomology, 1, 575--576.
  21. [21]  Change, I.C. (2007), The physical science basis, IPCC Fourth Assessment Report.
  22. [22]  Muhumuza, C. (2018), A mathematical model for the transmission dynamics and optimal control strategy of coffee wilt disease, Makerere University Institutional Repository.
  23. [23]  Maayah, B., Moussaoui, A., Bushnaq, S., and Abu Arqub, O. (2022), The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach, Demonstratio Mathematica, 55(1), 963--977.
  24. [24]  Arqub, O.A. and Maayah, B. (2023), Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a time-fractional sense with the reproducing kernel computational approach: formulations and approximations, International Journal of Modern Physics B, 37(18), 2350179.
  25. [25]  Maayah, B., Arqub, O.A., Alnabulsi, S., and Alsulami, H. (2022), Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme, Chinese Journal of Physics, 80, 463--483.
  26. [26]  Maayah, B. and Arqub, O.A. (2023), Hilbert approximate solutions and fractional geometric behaviors of a dynamical fractional model of social media addiction affirmed by the fractional Caputo differential operator, Chaos, Solitons and Fractals: X, 10, 100092.
  27. [27]  Bedimo, J.A.M., Bieysse, D., Njiayouom, I., Deumeni, J.P., Cilas, C., and Notteghem, J.L. (2007), Effect of cultural practices on the development of Arabica coffee berry disease, caused by Colletotrichum kahawae, European Journal of Plant Pathology, 119(4), 391--400.
  28. [28]  Workafes, W. and Kassu, K. (2000), Coffee production systems in Ethiopia, Proceedings of the Workshop on Control of Coffee Berry Disease in Ethiopia.
  29. [29]  Bedimo, J.A.M., Bieysse, D., Njiayouom, I., Deumeni, J.P., Cilas, C., and Notteghem, J.L. (2007), Effect of cultural practices on the development of Arabica coffee berry disease, caused by Colletotrichum kahawae, European Journal of Plant Pathology, 119(4), 391--400.
  30. [30]  Fotso Fotso, Y., Touzeau, S., Tsanou, B., Bowong, S., and Grognard, F. (2021), Modelling and optimal strategy to control coffee berry borer, Mathematical Methods in the Applied Sciences, 44, 14569--14592.
  31. [31]  Abawari, M.A., Obsu, L.L., and Melese, A.S. (2023), Optimal control analysis of coffee berry borer infestation in the presence of farmer's awareness, Applied Mathematics in Science and Engineering, 31(1), 2169684.
  32. [32]  Melese, A.S., Makinde, O.D., and Obsu, L.L. (2002), Mathematical modelling and analysis of coffee berry disease dynamics on a coffee farm, Mathematical Biosciences and Engineering, 19(7), 7349--7373.
  33. [33]  Fleming, W.H. and Rishel, R.W. (2012), Deterministic and stochastic optimal control, volume 1, Springer Science $\&$ Business Media.
  34. [34]  Mbogne, D.J.F. and Thron, C. (2015), Optimal control of anthracnose using mixed strategies, Mathematical Biosciences, 269, 186--198.
  35. [35]  Cunniffe, N.J. and Gilligan, C.A. (2010), Invasion, persistence and control in epidemic models for plant pathogens: the effect of host demography, Journal of the Royal Society Interface, 7(44), 439--451.
  36. [36]  Diekmann, O., Heesterbeek, J.A.P., and Metz, J.A. (1990), On the definition and the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28(4), 365--382.
  37. [37]  Fotso, Y.F., Grognard, F., Tsanou, B., and Touzeau, S. (2018), Modelling and control of coffee berry borer infestation, CARI'2018, 14\textsuperscript{th Colloque Africain sur la Recherche en Informatique et en Mathématiques Appliquées}.
  38. [38]  Driessche, P. and Watmough, J. (2002), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29--48.
  39. [39]  Martcheva, M. (2015), An introduction to mathematical epidemiology, Springer, 61.
  40. [40]  Lenhart, S. and Workman, J.T. (2007), Optimal control applied to biological models, CRC Press, New York.

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