On the Solution of the Fractional-Order PneumoniaModel Using Numerical Computational Methods

Abstract

This paper deals with the solution and the dynamics of the pneumonia fractional-order mathematical model using numerical computational methods. We study positivity, boundedness, equilibria, local and global stability, and the basic reproductive number R0 of the proposed model, which is the one most significant parameter in epidemiological modeling. It estimates the average number of additional infections induced by a sole infectious individual within a fully susceptible group during the mean period of infection. To verify the theoretical analysis of the proposed model, we use numerical techniques including the Adams-Bashforth-Moulton method, the generalized Euler method, the generalized Runge-Kutta method, and the multistep generalized differential transform method. The numerical results and simulations confirm the convergence between the presented fractional-order model and its integer-order form. The proposed model proves to be a valuable tool for investigating dynamical and numerical analysis for a variety of disease models in epidemiology.