Abstract
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 u1 and u2 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.
Highlights
The banana is a fruit of great economic importance and food sovereignty, because it is found in the shopping basket of people across different social strata and because of its nutritional content
R EV IS E D Amendments from Version 1. In this version we include the evaluators’ suggestions; The explanation of the mathematical model that was not clear was included, the sensitivity and stability analysis was organized into independent items and the optimal control problem was included with the new graphs complementing the results
Its production is threatened by re-emerging diseases such as Moko, caused by the bacterium Ralstonia solanacearum race 2 philotype II (Fegan & Prior, 2006), which causes wilting and deterioration of the plant
Summary
Any reports and responses or comments on the article can be found at the end of the article. This article is included in the Agriculture, Food and Nutrition gateway In this version we include the evaluators’ suggestions; The explanation of the mathematical model that was not clear was included, the sensitivity and stability analysis was organized into independent items and the optimal control problem was included with the new graphs complementing the results. This improved version is longer but more complete. Any further responses from the reviewers can be found at the end of the article
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