A one-dimensional map to study multi-seasonal coffee infestation by the coffee berry borer

Marcano, Mariano; Bose, Amitabha; Bayman, Paul

doi:10.1016/j.mbs.2020.108530

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…In [30], a mathematical model based on nonlinear ordinary differential equations describing the interaction between coffee beans and CBBs was analyzed. The population dynamics of the pest were partially governed by logistic growth, and the carrying capacity, defined as the number of CBBs per tree, was assumed to be 20,000 individuals.…”

Section: Numerical Resultsmentioning

confidence: 99%

Bifurcation Analysis in a Coffee Berry-Borer-and-Ants Prey–Predator Model

Trujillo-Salazar,

Olivar-Tost,

Sotelo-Castelblanco

2024

Mathematics

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One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by penetrating them to feed on the endosperm and deposit its eggs, continuing its life cycle. One strategy to combat CBBs is using biological control agents, such as certain species of ants. Here, a mathematical model (consisting of a system of nonlinear ordinary differential equations) is formulated to describe the prey–predator interaction between CBBs and an unspecified species of ants. From this mathematical perspective, the model allows us to determine conditions for the existence and stability of extinction, persistence or co-existence equilibria. Transitions among those equilibrium states are investigated through the maximum per capita consumption rate of the predator as a bifurcation parameter, allowing us to determine the existence of transcritical and saddle-node bifurcations. Phase portraits of the system are presented for different values of bifurcation parameter, to illustrate stability outcomes and the occurrence of bifurcations. It is concluded that an increase in bifurcation parameters significantly reduces the CBB population, suggesting that ant predation is an effective control strategy, at least theoretically.

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Section: Numerical Resultsmentioning

confidence: 99%

Bifurcation Analysis in a Coffee Berry-Borer-and-Ants Prey–Predator Model

Trujillo-Salazar,

Olivar-Tost,

Sotelo-Castelblanco

2024

Mathematics

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“…Total number of infested averted is computed for each strategy by subtracting total infested with control from without any control implementation throughout the simulation. Each control strategy is compared with the next less effective options as applied in [23]. The numerical output for the control strategies are ranked in increasing order of effectiveness in form of infection averted as shown in Table 3.…”

Section: Cost-effective Analysismentioning

confidence: 99%

Modelling and analysis of temperature and rainfall variability impact on the coffee berry borer infestation with optimal control

Melese

2022

Preprint

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This study focuses on a nonlinear deterministic mathematical model for the impact of temperature and rainfall variability on coffee berry borer \emph{(Hypothenemus hampei)}. In the model analysis, CBB free and coexistence equilibria are computed. The basic reproduction numbers at a minimum and maximum temperature and rainfall are derived. The qualitative analysis of the model revealed the scenario for equilibria together with basic reproduction numbers. The local stability of equilibria is established through the Jacobian matrix and the Routh Hurwitz-criteria, while the global stability of equilibria is demonstrated using an appropriate Lyapunov function. The normalized sensitivity analysis has also been performed to observe the impact of different parameters on basic reproduction numbers. The proposed model is extended into an optimal control problem by incorporating two control variables, namely, the preventive measure variable based on the separation of susceptible coffee berries from contacting the pests based on biological control and an increase in the death rate of colonising females of CBB based on chemical control. Optimal disease control analysis is examined using Pontryagin’s minimum principle. Finally, the numerical simulations are performed based on analytical results and are discussed quantitatively. Furthermore, the cost-effectiveness of control strategies to determine the best approach to minimize the CBB burden was studied. The finding of this study shows that the use of chemical pesticides is very effective to combat pests with minimum costs.

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