Dynamical Characteristics and Signal Flow Graph of Nonlinear Fractional Smoking Mathematical Model

Abstract

Abstract In this article, we study approximate analytic solutions for one of the famous models in biomathematics, namely the nonlinear fractional mathematical smoking model. When alpha=1, we deduce the analytical solution using the Reduced differential transforms method (RDTM) for the nonlinear ordinary mathematical smoking model. The disease-free equilibrium point, the stability of the equilibrium point, and the reproduction number are all discussed for the fractional mathematical smoking model. We use mathematical software packages such as Mathematica to find more iteration when calculating the approximate solution. Results are presented graphically to illustrate the behavior of the obtained approximate solutions. The system is presented by a proposed novel signal flow graph and simulated via SIMULINK/MATLAB. The graph of signal flow is used to calculate some of the model invariants such as the adjacency matrix, model energy, and Estrada index. Also, the novelty and significance of the results are clear using a 3D plot.