Coupled Pest–disease dynamics and cacao losses: A mathematical modeling approach

Myriam Djoukwe Tapi; Nico Stollenwerk; Samuel Bowong; Maíra Aguiar; Myriam Djoukwe Tapi; Nico Stollenwerk; Samuel Bowong; Maíra Aguiar

doi:10.3934/mbe.2026096

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 9: 2655-2697. doi: 10.3934/mbe.2026096

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Coupled Pest–disease dynamics and cacao losses: A mathematical modeling approach

1.
Department of Mathematics and Computer Science, Faculty of Science, The University of Douala, PO Box 24157 Douala
2.
IRD, Sorbonne University, UMMISCO, F-93143, Bondy, France
3.
EPITAG project, MACBES, Sophia Antipolis, France
4.
Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
5.
Ikerbasque, Basque Foundation for Science, Bilbao, Spain

Received: 23 February 2026 Revised: 20 July 2026 Accepted: 05 August 2026 Published: 07 September 2026

Black pod disease and mirids attacks cause substantial losses in cacao production. Black pod disease darkens the affected areas of cacao pods, while the cacao mirids (Sahlbergella singularis) is a major pest in West African plantations. Together, these threats significantly reduce crop yield and shorten the lifespan of the plants. This study evaluates production losses caused by the combined effects of Miridae infestation and black pod disease. We formulate and analyze a mathematical model incorporating spores, pods, and Miridae populations, governed by a system of ordinary differential equations. Theoretical analyses include equilibrium computations and threshold conditions for optimal plantation productivity. The analytical findings are validated through numerical simulations. We also examine the effects of three control strategies, Phytosanitary measures, Miridae control, and their combined application on production optimization. These strategies are modeled using impulsive differential equation systems. Our key quantitative findings show that black pod disease alone causes approximately 88.94% production loss, Miridae alone cause 34.21% loss, and co-infection leads to near-total losses exceeding 90%.
- cacao production,
- Miridae pests,
- black pod disease,
- mathematical modeling,
- vector–host dynamics,
- impulsive differential equations,
- pest management
Citation: Myriam Djoukwe Tapi, Nico Stollenwerk, Samuel Bowong, Maíra Aguiar. Coupled Pest–disease dynamics and cacao losses: A mathematical modeling approach[J]. Mathematical Biosciences and Engineering, 2026, 23(9): 2655-2697. doi: 10.3934/mbe.2026096

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Abstract

Black pod disease and mirids attacks cause substantial losses in cacao production. Black pod disease darkens the affected areas of cacao pods, while the cacao mirids (Sahlbergella singularis) is a major pest in West African plantations. Together, these threats significantly reduce crop yield and shorten the lifespan of the plants. This study evaluates production losses caused by the combined effects of Miridae infestation and black pod disease. We formulate and analyze a mathematical model incorporating spores, pods, and Miridae populations, governed by a system of ordinary differential equations. Theoretical analyses include equilibrium computations and threshold conditions for optimal plantation productivity. The analytical findings are validated through numerical simulations. We also examine the effects of three control strategies, Phytosanitary measures, Miridae control, and their combined application on production optimization. These strategies are modeled using impulsive differential equation systems. Our key quantitative findings show that black pod disease alone causes approximately 88.94% production loss, Miridae alone cause 34.21% loss, and co-infection leads to near-total losses exceeding 90%.

References

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