A numerical approach for a dynamical system of fractional infectious disease problem

Abstract

In this study, a dynamical system to explain a disease model with environmental stress in a general aspect is considered. The model is expressed by the standard differential equations and its Caputo fractional form. We describe a numerical approach based on the numerical technique of Adams-Bashforth-Moulton for the solution of the system of differential equations including the initial conditions. Besides, we indicate briefly the existence, uniqueness, and convergence of the technique. One of the subjects of the study is to contribute with a new design of the present technique to obtain numerical solutions to such problems in the literature which can be investigated for further approximations. Further, we provide the stability analysis around the coexistence equilibrium. Additionally, we illustrate the findings to show the behaviour of the system, time evolution, and the phase plane plots for the specific parameters.