Exploring of Homotopy Perturbation Method (HPM) for Solving Spread of COVID-19

Abstract

This article discusses the solution to the non-linear differential equation system for the spread of COVID19 with SEIR (Susceptible, Exposed, Infected, Recovered) model using the Homotopy Perturbation Method. Specifically, this article examines the impact of moving the recovered subpopulation back to the susceptible subpopulation on the spread of COVID-19 in the city of Medan. The data used is real data for the city of Medan in 2021. The results of constructing a model for the spread of COVID-19 were analyzed to obtain a disease-free critical point. By using the Next Generation Matrix method, the Basic Reproduction number R0 = 4.61 is obtained, this indicates that COVID-19 is still possible to spread in Medan City. Simulations using the Homotopy Perturbation Method numerical approach and the results compared with the Runge Kutte Order 4 method show results that accurately describe the dynamics of the spread of COVID-19 in Medan City. The very small error indicates that the Homotopy Perturbation Method is very suitable for use in solving non-linear differential equation systems, especially in the SEIRS model of the spread of COVID-19. The simulation results show that the impact of the movement of recovered sub-populations to susceptible sub-populations results in accelerated transmission of COVID-19. The greater the number of movements higher the rate of spread of COVID-19.