Efficient solution of fractional-order SIR epidemic model of childhood diseases with optimal homotopy asymptotic method

Abstract

In providing an accurate approximate analytical solution to the non-linear system of fractional-order susceptible-infected-recovered epidemic model (FOSIREM) of childhood disease has been a challenge, because no norm to guarantees the convergence of the infinite series solution. We compute an accurate approximate analytical solution using the optimal homotopy asymptotic method (OHAM). The fractional differential equations operator (FDEO) is given as conformable derivative operator (CDO). We show the basic idea of the proposed method, the CDO sense, equilibrium points, local asymptotic stability, reproduction number, and the convergence analysis of the proposed method. Numerical results and comparisons with other approximate analytical methods are given to validate the efficiency of the method. The proposed method speedily converges to the exact solution as the fractional-order derivative approaches 1, proved as an excellent tool for solving, and predicting the model.