Abstract

An optimal control framework is designed in which the use of clean planting materials, debudding, disinfection of tools, and roguing are considered as control measures of Banana Xanthomonas Wilt (BXW) within a plantation of multiple cultivars. A model for a special case of two cultivars (AAA- and ABB-genome cultivars) was analyzed. By Pontryagin’s Maximum Principle, we characterized and discussed possible control strategies that substantially reduce the infection levels of BXW within a plantation of ABB- and AAA-genome cultivars. A combination of both prevention and containment controls yielded the greatest decline in the infection levels in both cultivars. Additionally, for effective BXW management, it is important to assess the endemic level of the plantation before application of controls, and once implemented, this should be maintained even when the disease is undetectable to eliminate possible resurgence.

Highlights

  • Banana is a major crop grown in the East and Central African region

  • The pathogen caused by Xanthomonas campestris pv. musacearum (Xcm) was first reported in Ethiopia on Ensete, a related crop to banana in 1964 [3]

  • ABB-genome cultivars are more susceptible to insect infection due to the greater production of sweet nectar that attracts the insects as compared to AAA-genome cultivars

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Summary

Introduction

Banana is a major crop grown in the East and Central African region. It provides food security and income to over 20 million people in the region [1]. ABB-genome cultivars are more susceptible to insect infection due to the greater production of sweet nectar that attracts the insects as compared to AAA-genome cultivars These features influence BXW management and control adoption by farmers in these respective regions. Our model focuses on determining the optimal control combination within smallholder plantations with mixed cultivars given that in banana cropping system different cultivars are managed differently and the risk of infection is different. We formulate an optimal control model with debudding, use of clean planting material (reducing the proportion of infected suckers), roguing/SSDR, and disinfection of tools used for cultivating between and within cultivars as our control options.

Model Formulation
Optimal Control Model
Quadratic Control Terms for Debudding and Use of
Findings
Conclusions
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