Abstract
Black pod disease is caused by fungi of the species Phytophthora palmivora or Phytophthora megakarya. The disease causes darkening of affected areas of cocoa trees and/or fruits and leads to significant reduction in crop yields and decreases lifespan of the plant. This study presents a simple S_1S_2IT-type model with variable population size to assess the impact of fungicide treatment on the dynamics of the black pod disease. We do both theoretical studies and numerical simulations of the model. In particular, we analyze the existence of equilibrium points and their stability, simulate the model using data on reported black pod cases from Ghana. In addition, we perform sensitivity analysis of the basic reproduction number with respect to the model parameters. The results show that the top three parameters that govern the dynamics of the black pod disease are the treatment rate, transmission rate, and planting rate of new trees
Highlights
Cocoa is the most economically important species in the Phytophthora genus [1, 2]
The main focus of this study is to assess the potential impact of fungicide treatment on the black pod disease that has been a burden for cocoa farmers in the west coast of Africa, over the years
Sensitivity index -1.6451 1 1 -0.8523 0.4974. These results suggest that intervention strategies that focus on increasing the fungicide spraying and decreasing the transmission coefficient could be effective in controlling the black pod disease
Summary
Cocoa is the most economically important species in the Phytophthora genus [1, 2]. It can be grown only within the tropical belt [1, 3] with the largest growing region being the west coast of Africa. There are few research studies on modeling of black pod diseases mathematically [21, 22]. None of these published papers is an SIR-type[27, 28, 29, 30]. We develop and analyze a system of differential equations model describing the black pod transmission with variable population size and fungicide spraying of cocoa trees. The main focus of this study is to assess the potential impact of fungicide treatment on the black pod disease that has been a burden for cocoa farmers in the west coast of Africa, over the years. The paper is organized as follows: The model is formulated in Section 2, the existence of equilibria and their stability is presented in Section 3, numerical simulations and sensitivity analyzes of the reproduction number of the model are performed in Section 4, and Section 5 discusses the results from the analysis of the model
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