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Movement is an important part of life. For example, in a central and fundamental process known as gene expression, there is a movement of biological particles called RNA polymerases on the DNA strand to produce messenger RNA (mRNA). Understanding these complex transport phenomena has been a significant area of research in mathematics, biology, and physics. Over the years, the Ribosome Flow Model (RFM), obtained via a mean-field approximation of a stochastic model called the Totally Asymmetric Simple Exclusion Process (TASEP), has provided a rigorous mathematical framework for the analysis. It is a deterministic, continuous-time model for analyzing the flow of interacting particles, and its dynamics are described by ordinary differential equations (ODEs). The results of the RFM analysis can be used to model and engineer gene expression. In this talk, I rely on the framework of RFM to model and analyze the dynamical flow of particles along an ordered chain of sites encapsulating various biologically observed features. The presentation will focus on formulating a system of non-linear ordinary differential equations, where the densities of each site on a lattice serve as the state variables and understand their asymptotic behavior. Exploring cooperative irreducible systems of ODEs with a first integral exhibiting positive gradient, results are leveraged on the global phase portrait of such systems in the proposed models. These frameworks yield deeper insights into how parameters influence system dynamics, enhancing our comprehension of the underlying processes.