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

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Abstract
In this investigation, we study for a dynamical system aimed at elucidating a disease model under the influence of environmental stress from a broad perspective. The model is articulated through both standard differential equations and their Caputo fractional form. Our methodology involves a numerical approach using the Adams-Bashforth-Moulton technique to solve the system of differential equations, including the initial conditions. The existence, uniqueness and convergence of the technique are also briefly discussed. This study aims not only to improve the current technique, but also to introduce a novel design for obtaining numerical solutions to issues discussed in the existing literature, thus paving the way for further research. We also perform a stability analysis focusing on the coexistence equilibrium. In addition, we present visualisations of the results to elucidate the behaviour of the system, time evolution and phase plane plots with respect to specific parameters.

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