An Observation on the Use of Integral Transform to Solve Fractional SIR and SIS Epidemic Models

This study shows the effective approximate solutions of a particular case of fractional SIR and SIS epidemic models (FSIR and FSIS EMs) for constant population, characterized by connected nonlinear differential equations. The Elzaki transform (ET), an integral transform, is utilized in this process. Fractional derivatives (FDs) are by definition characterized by the Caputo sense. The solutions to the FSIR and FSIS EMs were found in an understandable, sequential fashion using ET. This work also discusses the convergence of the ET approach to the solutions of the FSIR and FSIS EMs. Two examples of nonlinear FSIR and FSIS EM are presented to demonstrate the suggested approach. The results of this novel approach show that it is an effective way to solve FSIR and FSIS EMs and that it speeds up the procedure. One observation regarding the use of integral transforms to solve fractional SIR and SIS epidemic models is that integral transforms, such as the ET, can greatly simplify the process of finding analytical solutions. By transforming the fractional differential equations that govern these models into algebraic equations, researchers can more easily study and interpret the dynamics of disease spread within communities.