Mathematical modelling and analysis of coffee berry disease dynamics on a coffee farm

Abdisa Shiferaw Melese; Oluwole Daniel Makinde; Legesse Lemecha Obsu; Abdisa Shiferaw Melese; Oluwole Daniel Makinde; Legesse Lemecha Obsu

doi:10.3934/mbe.2022347

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 7349-7373. doi: 10.3934/mbe.2022347

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Research article

Mathematical modelling and analysis of coffee berry disease dynamics on a coffee farm

1.
Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia
2.
Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa

Academic Editor: Hao Wang

Received: 18 January 2022 Revised: 28 February 2022 Accepted: 19 April 2022 Published: 18 May 2022

This paper focuses on a mathematical model for coffee berry disease infestation dynamics. This model considers coffee berry and vector populations with the interaction of fungal pathogens. In order to gain an insight into the global dynamics of coffee berry disease transmission and eradication on any given coffee farm, the assumption of logistic growth with a carrying capacity reflects the fact that the amount of coffee plants depends on the limited size of the coffee farm. First, we show that all solutions of the chosen model are bounded and non-negative with positive initial data in a feasible region. Subsequently, endemic and disease-free equilibrium points are calculated. The basic reproduction number with respect to the coffee berry disease-free equilibrium point is derived using a next generation matrix approach. Furthermore, the local stability of the equilibria is established based on the Jacobian matrix and Routh Hurwitz criteria. The global stability of the equilibria is also proved by using the Lyapunov function. Moreover, bifurcation analysis is proved by the center manifold theory. The sensitivity indices for the basic reproduction number with respect to the main parameters are determined. Finally, the numerical simulations show the agreement with the analytical results of the model analysis.
- mathematical model,
- coffee berry,
- colletotrichum kahawae,
- bifurcation analysis,
- numerical simulations
Citation: Abdisa Shiferaw Melese, Oluwole Daniel Makinde, Legesse Lemecha Obsu. Mathematical modelling and analysis of coffee berry disease dynamics on a coffee farm[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 7349-7373. doi: 10.3934/mbe.2022347

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Abstract

This paper focuses on a mathematical model for coffee berry disease infestation dynamics. This model considers coffee berry and vector populations with the interaction of fungal pathogens. In order to gain an insight into the global dynamics of coffee berry disease transmission and eradication on any given coffee farm, the assumption of logistic growth with a carrying capacity reflects the fact that the amount of coffee plants depends on the limited size of the coffee farm. First, we show that all solutions of the chosen model are bounded and non-negative with positive initial data in a feasible region. Subsequently, endemic and disease-free equilibrium points are calculated. The basic reproduction number with respect to the coffee berry disease-free equilibrium point is derived using a next generation matrix approach. Furthermore, the local stability of the equilibria is established based on the Jacobian matrix and Routh Hurwitz criteria. The global stability of the equilibria is also proved by using the Lyapunov function. Moreover, bifurcation analysis is proved by the center manifold theory. The sensitivity indices for the basic reproduction number with respect to the main parameters are determined. Finally, the numerical simulations show the agreement with the analytical results of the model analysis.

References

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