Fractional Multi-Step Differential Transformed Method for Approximating a Fractional Stochastic SIS Epidemic Model with Imperfect Vaccination.

Salah Abuasad,Ahmet Yildirim,J.F. Gómez-Aguilar,Ishak Hashim,Samsul Abdul Karim

doi:10.3390/ijerph16060973

Abstract

In this paper, we applied a fractional multi-step differential transformed method, which is a generalization of the multi-step differential transformed method, to find approximate solutions to one of the most important epidemiology and mathematical ecology, fractional stochastic SIS epidemic model with imperfect vaccination, subject to appropriate initial conditions. The fractional derivatives are described in the Caputo sense. Numerical results coupled with graphical representations indicate that the proposed method is robust and precise which can give new interpretations for various types of dynamical systems.

Highlights

Mathematical modeling of nonlinear systems is a key challenge for contemporary scientists; it is a basic description of physical reality expressed in mathematical terms
The aim of this paper is to apply the fractional multi-step differential transform method (FMsDTM) to find an accurate approximation for a fractional stochastic SIS epidemic model with imperfect vaccination
The fractional derivatives are described in the Caputo sense

Summary

Introduction

Mathematical modeling of nonlinear systems is a key challenge for contemporary scientists; it is a basic description of physical reality expressed in mathematical terms. The study of the exact or approximate solution benefits us to understand the means of these mathematical models. Fractional order derivatives provide researchers new fields for modeling numerous types of phenomena in sciences. Numerous kinds of fractional derivatives and their properties were considered (see [1,2,3,4,5,6]). The main reason for using fractional derivatives instead of integer derivatives is that fractional order model considered the memory effect, while integer order does not give us any information about the effect of the memory of human population which influences disease transmission [7]

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Conclusion