Browsing by Author "Simon, Joel"

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    A Deterministic Mathematical Model for the Control of Spread of Prosopis Juliflora Plants
    (Journal of Mathematics and Informatics, 2020-09-25) Simon, Joel; Mirau, Silas; Luboobi, Livingstone
    Prosopis juliflora plants are the most aggressive invasive species in the world. They spread by animal movement crossing from one place land to another. In this paper a deterministic model to examine the dynamics of Prosopis julifrola plants is formulated and presented 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 performed by using next-generation for the basic reproduction number R0 computation and Lypunov function method. The finding from the study showed that the Prosopis free equilibrium of the model is both locally and globally asymptotically stable if and only if the number of secondary infections, is less than unit, that is R0 < 1. Furthermore, the study showed that there exist Prosopis endemic equilibrium for the spread when 0 R >1. The numerical simulation implemented in MATLAB ODE45 algorithm for solving linear ordinary differential equations. The study findings showed that as the number of ingested animals increase, the plant spread increases on land. Based on the findings, the study recommend the application of the model on endemic areas to improve through: Awareness on animal feeding the plant, provision of insight on plant invasion to policy makers and environmental stakeholders to include in environment framework, seminars and environment clubs by visiting community groups an educating them on plant invasion, through this the plant eradication could be achieved.
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    Modelling the spread and control of prosopis juliflora plants
    (NM-AIST, 2021-07) Simon, Joel
    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