Analytical solution of a non-linear fractional order SIS epidemic model utilizing a new technique

Abstract

The solution of fractional order epidemic models is an emerging area of research due to its wide applications in various fields of applied sciences. In this study, we investigate the non-linear fractional order SIS epidemic model. Specifically, we use the Laplace redisual power series (LRPS) method to analytically solve the non-linear fractional order coupled initial value problems. The LRPS method combines the RPS approach with the Laplace transform operator to obtain a rapid convergent series approximation with less time and resources. Our results are compared with the exact solution of the SIS epidemic model to validate the accuracy of our method. The proposed LRPS method is a useful, time-saving analytical technique for developing approximations of solutions for non-linear fractional order SIS epidemic models. Numerical and graphical analysis of the outcomes demonstrate the efficacy of the LRPS method and suggest its potential as a new approach for solving a variety of real-world problems involving differential equations of any order. Future work can explore the application of this method to other non-linear fractional order epidemic models to further validate its effectiveness.