Mathematics and Computer Science: Contemporary Developments Vol. 5

Abstract

The dynamics of Mathematical model of Human Immunodeficiency Virus with three non overlapping classes has been taken into consideration in this chapter. A mathematical model that calculates susceptible CD4⁺T cells, infected CD4⁺T cells and virus particles has been examined here using the fractional differential transform method(FDTM) with stability analysis. A stability of the fractional nonlinear model with Hurwitz state matrix is examined using the Lyapunov direct method. A brief review of literature for integer order as well as fractional order on mathematical biological modeling has been collected to solidify our mathematical approach to solve the proposed HIV model. A nonlinear mathematical model of differential equations has been put forward and analyzed by applying FDTM. The proposed technique gives a solution in the form convergent series as a linear combination in the form of polynomial. An infinite series solution of the system of differential equation is computed by defining fixed components with different time intervals. Furthermore, the solution calculated through FDTM ( integer order) is correlated with the solution calculated using DTM and Laplace Adomain Decomposition Method. Additionally, the graphical representation of the model is given using the fourth order Runge Kutta Method. The solution is analyzed numerically and graphically by using the software Python.