The paper aims to develop a computational method for studying the impact of antiviral drugs on the novel coronavirus. The method utilizes the moving least squares (MLS) approximation functions in the discrete Galerkin method. The MLS is an e ective technique for approximating unknown functions using locally weighted least squares polynomial tting. The proposed algorithm is computationally ecient and easily implementable on computers. The validity and eciency of the method are demonstrated through a numerical example.