A theoretical model for optimal control of banana Moko ( Musa AAB Simmonds)

A population simulation model with non-linear ordinary differential equations is presented, which interprets the dynamics of the banana Moko, with prevention of the disease and population of susceptible and infected plants over time. A crop with a variable population of plants and a logistic growth of replanting is assumed, taking into account the maximum capacity of plants in the delimited study area. Also, with the help of farmers, the costs of implementing prevention strategies and elimination of infected plants were calculated per week in order to determine the optimal conditions that control the disease and reduce production costs. We found that the implementation of prevention strategies (f) plays an important role, but the parameter that most influences the threshold value is the elimination of infected plants g . However, to reduce production costs due to the high implementation of prevention strategies and to maintain the disease in a controlled state, both controls u (1) and u (2) should be implemented between 40% and 60%, obtaining with this percentage an approximate reduction of 51.37% in production costs per week, where in 23 weeks following the same conditions it is expected to have a healthy plantation without infected plants.