Modelling the transmission dynamics of banana xanthomonas wilt disease with control measures

A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Master’s in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyBanana Xanthomonas Wilt disease (BXW) is a bacterial disease which highly threaten banana production in East and Central Africa. It is caused by a bacteria known as Xanthomonas campestris pv. musacearum (Xcm). Mathematical modelling gives an insight on how to best understand the transmission dynamics and control of the disease. The existing mathematical models for the dynamics of BXW disease have not included contaminated soil, community farming education programmes and clearance of Xcm bacteria in the soil. This study formulated a model which includes contaminated soil. In analysis of the model, the existence and stability of the equilibrium points was checked, calculated the basic reproduction number and carried out sensitivity analysis of some model parameters. We further conducted numerical simulation to validate the results. The numerical simulations showed that the infection rate by contaminated farming tools (β i and β e ), the infection rate by contaminated soil (ω ), vertical disease transmission rate (θ), and the shedding rate of Xcm bacteria in the soil (φ) are positively sensitive to the basic reproduction number. While, the most negative sensitive parameters are the clearance rate of Xcm bacteria from the soil (µ ), removal of infected plants from the farm (r), harvesting (α p h ), and banana plants disease induced death rate (d). The result also showed that contaminated soil contributes to the transmission and persistence of BXW disease. Furthermore, the basic model was modified to include the control measures. Numerical simulations was conducted to examine the impact of the suggested control measures. It was observed that as Participatory community farming education programmes, timely removal of infected banana plants, clearance of Xcm bacteria in the soil and vertical transmission control measures increases it dramatically reduces the number of secondary infections hence greatly contribute to the control of the BXW disease. Therefore, It is recommend 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, scientist and technologist should carry out studies to find a way to reduce or avoid vertical disease transmission and increase the Xcm clearance rate in the soil. Furthermore, technology for early detection of infected plants should be brought down to the local farmers at affordable costs. This will help stakeholders to detect and remove the infected plants from the farm in time and hence reduce the number of secondary infections. Moreover, Participatory community farming education programmes such as Farmers field schools (FFS) should be emphasized and practised.