This research article published by Journal of Mathematics and Informatics Vol. 19, 2020Prosopis 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.