MST-Department of Mathematics

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Browsing MST-Department of Mathematics by Author "Isaac Chepkwony"

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    Analysis of Dynamics of HTLV Type 1 Infection on Cd4+ T-Cells with Cell-to-Cell and Mitotic Transmissions Using Fractional Order Model
    (Kenyatta University, 2024-07) Chepng’eno, Mary; Isaac Chepkwony
    Human T lymphotropic virus-1 which attacks CD4+ T-cells is a serious epidemic throughout the world. Even though research has been done extensively on the virus, it is still a threat in various parts of the world. In this research project, we formulate a fractional order model of Human T lymphotropic virus type 1 infection on CD4 cells. The model is made up of three nonlinear differential equations with fractional derivatives defined using caputo. The main aim is to develop and to explore the dynamics of infection of CD4 cells by the virus using fractional order model. The uniqueness of solution was discussed and positivity of solution provided using generalized fractional mean value theorem. Making use of the next generation matrix mathematical method, the basic reproduction number, Ro, is calculated. Model eqilibria are determined. The Routh Hurwitz stability requirement and the LaSalle’s invariance principle are used to investigate the stability of model equilibria. The global stability of equilibria is determined using the Lyapunov functional method. From the investigation done on stability, both endemic equilibrium point and the equilibrium point free of disease were discovered to be globally and locally asymptotically stable whenever the number of reproductions is more than one and when it is less than one respectively. To acquire numerical results, we used a numerical methodology that involves writing the differential equations with fractional order as an infinite system of ordinary differential equations of the first order. Then by using relatively small number of terms, the solutions are obtained by use of Runge-Kutta method of fourth order applied with the help of python. Finally, we presented the results obtained for various values of alpha graphically. The findings point to the need to control mitotic transmission during therapeutic intervention as well as the benefits of employing fractional order to model viral infection on CD4 cells.