Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators

In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number $R_0$ of the proposed model is established along with the feasible region and disease-free equilibrium point $E^0$. We prove that $E^0$ is locally asymptotically stable when $R_0$ is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the proposed epidemic model by using a novel numerical scheme, which is generated by Newton polynomials. The given model is numerically solved by considering some other fractional derivatives like Caputo, Caputo-Fabrizio and fractal-fractional with power law, exponential decay and Mittag-Leffler kernels.