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

• Published in: Mathematical biosciences Vol. 333; p. 108530
• Main Authors: Marcano, Mariano, Bose, Amitabha, Bayman, Paul
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.03.2021; Elsevier Science Ltd
• Subjects: Biological control; Borers; Coffee; coffee beans; Dynamic stability; females; Fixed points (mathematics); Fruits; Hypothenemus hampei; Infestation; insect pests; Insects; Mathematical modeling; Mathematical models; One-dimensional map; Pest control; Pest management; Pests; Population dynamics; reproduction; Seasons; Stability analysis; Mathematical modeling; One-dimensional map; Pest management; Biological control; Hypothenemus hampei
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2020.108530

The coffee berry borer (CBB, Hypothenemus hampei) is the most serious insect pest of coffee worldwide; understanding the dynamics of its reproduction is essential for pest management. The female CBB penetrates the coffee berry, eats the seed, and reproduces inside it. A mathematical model of the infestation progress of the coffee berry by the CBB during several coffee seasons is formulated. The model represents the interaction among five populations: uninfested, slightly infested, and severely infested coffee berries, and free and encapsulated CBBs. Coffee harvesting is also included in the model. A one-dimensional map is derived for tracking the population dynamics subject to certain coffee harvesting percentages over several seasons. Stability analysis of the map’s fixed points shows that CBB infestation could be eliminated or controlled to a specific level over multiple seasons of coffee harvesting. However, the percent of coffee harvesting required is determined by the level of CBB infestation at the beginning of the first season and in some cases it is impossible to achieve that percentage. •We pose a multi-season population model of coffee and the coffee berry borer (CBB)•We derive a novel 1-dimensional map of CBB population dynamics•Stability analysis of the map’s fixed points reveals infestation type thresholds•CBB infestation can be controlled with appropriate harvesting strategies