A mathematical Model to assess the Role of Neglected Control Techniques in the Dynamics of Banana Xanthomonas Wilt Disease

Abstract

Banana Xanthomonas Wilt disease (BXW) is a destructive bacterial disease that highly threatens banana production in East and Central Africa. It is caused by a bacteria known as. In this paper, a mathematical model for the dynamics and control of BXW disease is formulated and analyzed. Numerical simulations were performed to examine the impact of participatory community education programmes, clearance of Xcm bacteria in the soil, single diseased stem removal, and vertical transmission control strategies. It was found that participatory community farming education programmes, timely removal of infected banana plants, clearance of Xcm bacteria in the soil dramatically reduce the number of secondary infections hence greatly contributing to the control of the BXW disease. The study recommends that, along with the existing control measures such as sterilization of farming tools, timely removal of the male bud using a forked stick and planting healthy suckers, more emphasis should be invested in educating farmers on disease detection and management strategies and increasing the rate of clearing Xcm bacteria in the soil so as to avoid persistence of the disease in the farms.

A Fractional-Order Mathematical Model of Banana Xanthomonas Wilt Disease Using Caputo Derivatives

“…Here, we define the Caputo-type fractional-order generalization of a BXW disease model, including some control measures, which was given in [14]. We know that fractional derivatives are non-local differential operators that allow memory effects in the system, which is a very important feature for studying disease outbreaks more accurately.…”

“…Kweyunga et al [13] developed a model of BXW considering both horizontal and vertical modes of transmission. In [14], the authors derived a non-linear model to analyze the role of neglected control measures in the BXW transmission.…”

“…To date, the aforementioned studies of mathematical modeling of the BXW disease [9][10][11][12][13][14] have yet to be analyzed using fractional derivatives. In this paper, we generalize the non-linear control-based model of BXW [14] by using Caputo fractional derivatives.…”

“…To date, the aforementioned studies of mathematical modeling of the BXW disease [9][10][11][12][13][14] have yet to be analyzed using fractional derivatives. In this paper, we generalize the non-linear control-based model of BXW [14] by using Caputo fractional derivatives. The motivation behind this generalization is that fractional derivatives are non-local and may be more effective to include memory effects in the model.…”