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 Technology
Banana 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.
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