A Dissertation Submitted in Partial Fulfillment 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
The Prosopis julifrola plant is a thorny leguminous shrub or small tree, a kind of mesquite in a
family of Fabacea. It is extremely aggressive and invasive. The spreading agents include livestock
dispersal and seeds in their droppings, human activity by vegetation restoration, firewood and
charcoal and soil erosion control. In this study a deterministic model examines the dynamics of
Prosopis juliflora plant by adopting a similar approach of a dynamical system as used in
epidemiological modeling. The local and global stability analyses of the equilibrium points of the
model were conducted by using next generation matrix for the computation of basic reproduction
number R0 and Lypunov function. The study showed that the Prosopis juliflora plant free
equilibrium of the model is both locally and globally asymptotically stable if and only if the
number of secondary infections is less than unity, that is if R0 < 1. Furthermore, the study shows
that there exists Prosopis juliflora endemic equilibrium for the spread of the plant when R0> 1.
The numerical simulation was implemented in MATLAB ODE 45 algorithm for solving linear
ordinary differential equations. The study showed that the plant spread with an increase of animals
that ingested it. Based on the study, recommended is the application of the model on the endemic
area to improve the existing situation through: Enlightening and involving policymakers,
environmentalists, stakeholders and community groups in the preservation framework on the
spread and control strategy of the Prosopis juliflora invasion