Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models

We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider which susceptible and infected populations evolve according different orders. a model based on Caputo derivative, for we establish existence results of solutions. Furthermore, investigate Caputo–Fabrizio operator, provide solutions equilibria. Both can be framed context SIS with time-varying total population, competition between birth death rates macroscopically described by orders derivatives. Numerical simulations both direct numerical comparison are also provided.