Mathematical Modeling of Fruit Flies Infestation in Mangoes and Its Management

The fruit production sector is rapidly expanding within African horticulture business, playing a vital role in enhancing food security, increasing export revenues, and alleviating poverty across the continent. Despite its importance, the industry faces significant challenges from fruit fly infestations, which threaten the success of horticultural production in many African nations. This study develops and analyzes a mathematical model to explore the dynamics of fruit flies in the presence of susceptible fruits, aiming to identify key factors that drive fruits infestation and inform effective control strategies. We utilize the next generation method to calculate the basic reproduction number R0, which indicates whether the fruit fly population will decline or persist. Results demonstrate the existence of both fruit fly infestation-free and fruit fly infestation equilibrium points. The fruit fly infestation-free equilibrium point is globally asymptotically stable (GAS) when R0 1. Sensitivity analysis indicate that the maturation rate of fruit fly population, the egg-laying rate, the transfer rate from unfertilized to fertilized females, and the natural death rate of adult fruit flies drive the growth of fruit flies. This suggests that interventions aimed at reducing adult fruit flies are crucial for managing fruit fly infestation. To address fruit fly infestation, we developed and analyzed a mathematical model incorporating environmentally friendly control measures namely pheromone traps, field sanitation, food attractants, and parasitoids. These control measures were evaluated both individually and in various combinations to assess their effectiveness in reducing fruit fly infestation in mangoes. The results indicate that, in the absence of control measures, the fruit fly population grows rapidly, resulting in substantial losses of susceptible fruits. In contrast, the control combinations involving food attractants, egg and larval parasitoids, and food attractants, pheromone traps, egg and larval parasitoids have the greatest impact in reducing fruit fly infestation in mangoes. The control combination effectively suppresses the fruit fly population, thereby reducing fruit infestation and promoting sustainable fruit production.