Optimal control strategies to curtail cacao swollen-shoot virus infection and maximize net economic benefit

Abstract

Cacao production in West Africa is being endangered by the cacao swollen shoot disease. The virus that causes the disease is spread by mealybugs. A mild strain of the virus can be used to inoculate susceptible (healthy) seedlings, thus reducing impacts of the closely related severe virus on such trees, which may also reduce spread of the disease. In the present study, we developed a mathematical model based on ordinary differential equations with an age structure that models the temporal dynamics of susceptible, inoculated, and severely infected trees and their interaction with mealybugs. Optimal control approaches integrated with this model were employed to identify the most effective strategy for maximizing the economic net benefit for farmers by adjusting the ratio of susceptible to inoculated seedlings utilized to replace severely infected trees. Two scenarios that reflected different strategies for cutting and replacing infected trees were considered. Numerical simulations using real data were performed. Based on model assumptions and control strategies studied, the optimal strategy was to establish a farm with some inoculated seedlings, remove only severely infected trees from the field, and replace them with inoculated seedlings for approximately 10 years and then with the susceptible seedlings. Further study employing models that incorporate additional processes and extended data sets is essential to assess the effectiveness of this strategy.