Epidemic model analyzed via particle swarm optimization based homotopy perturbation method

Abstract

Abstract In this paper, the problem of the spread of a non-fatal disease in a population known as a nonlinear epidemic model is solved using an Optimized Homotopy Perturbation Method (OHPM). In order to discretize the governing nonlinear differential equations, the Finite Difference Method (FDM) is applied to approximate the derivatives of the problem and the penalty method is employed to satisfy the initial conditions. The unknown nodal values of the discretized objective function are regarded as the design variables and would be found by the Particle Swarm Optimization (PSO) algorithm. In order to find more accurate results, the solution proposed by the Homotopy Perturbation Method (HPM) is considered as the global best particle of PSO at the first iteration of the optimization process, and this idea is named the Optimized Homotopy Perturbation Method (OHPM). The results obtained by the introduced methodology are associated with those of the HPM, PSO, and a numerical method to assess the performance of the OHPM.