A Mathematical Model for the Vector Transmission and Control of Banana Xanthomonas Wilt

Abstract

Banana Xanthomonas wilt is currently wrecking havoc in East and Central Africa. In this paper, a novel theoretical model for the transmission of banana Xanthomonas wilt by insect vectors is formulated and analyzed. The model incorporates roguing of infected plants and replanting using healthy suckers. The model is analyzed for the existence and stability of the equilibrium points. The global stability of the disease-free equilibrium point was determined by using a Lyapunov function and LaSalle's invariance principle. For the global stability of the endemic equilibrium point, the theory of competitive systems, compound matrices and stability of periodic orbits were used. It was established that if the basic reproduction number satisfies R 0 ≤ 1, the disease-free equilibrium point is globally stable and the disease will be wiped out and if R 0 > 1, the endemic equilibrium is stable and the disease persists. A numerical simulation of the model was also carried out. It was found out that at appropriate roguing and replanting, the disease can be contained.

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

“…Several mathematical models have been derived by researchers to understand the transmission dynamics of BXW disease and provide possible control techniques. In [9], the authors derived a model to understand the transmission structure of the BXW epidemic by vectors with control measures. In [10], the authors proposed a non-linear model to analyze the role of contaminated measures in the reiteration of BXW.…”

“…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.…”

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

“…In order to understand the dynamics of BXW disease, several scholars have developed mathematical models to study the transmission dynamics of BXW and its controls. Horub et al [24] developed a mathematical model to study the transmission dynamics of BXW disease by vectors and its controls. The study showed that timely removing the male bud using a forked stick, increasing rougeing and planting health suckers helps to reduce transmission of the disease.…”

Eco-epidemiological model and analysis of potato leaf roll virus using fractional differential equation

“…In their studies, whitefly vector is considered to be the cause. Banana Xanthomonas wilt deterministic model also proposed by Horub and Julius (2017). This model was formulated and analyzed with system of ordinary differential equation.…”