Modeling The Dynamics Of Banana Xanthomonas Wilt Disease With Mixed-Cropping Control Measure

Abstract

Banana Xanthomonas Wilt (BXW) is a devastating disease of Banana plant caused by a bac- terium called Xanthomonas campestris pv.musacearum (Xcm). This study focuses on modeling the dynamics of BXW with mixed-cropping control measure using a system of non-linear ordi- nary differential equations. Next-generation matrix is used to calculate the basic reproduction number. Then, the stability conditions of both the disease-free and endemic equilibria are studied. The qualitative analysis results shows that disease-free equilibrium is both locally and globally stable if the basic reproduction number is less than unity and endemic equilibrium point is globally stable if the basic reproduction number is greater than unity. Sensitivity analysis is carried out to determine the relative significance of parameters and the impacts of possible control method. It is shown that the parameter representing the rate at which contaminated soil causes infection (ω2 ), total number of non-host plant in banana plant field (N ), rate of Xcm bacteria losses from contaminated soil by planting non-host plant (a 4 ) are highly influential in determining the time evolution of the disease. That is, ω2 increase has a positive role in increasing the number of new infections, where as an increase in a 4 and N show the suppression of a new infection of the disease. Finally, using MATLAB numerical simulations are performed for a brief illustration of the disease’s dynamical behavior. The simulations results supports the analytic findings and suggest that applying the mixed-cropping cultural control method can reduces the occurrence of secondary infections thus it plays a crucial role in controlling BXW disease.