In this study, we have investigated the asymmetry term effect for the (p, alpha) and (p, np) reaction cross-sections and obtained new coefficients for the (p, alpha) and (p, np) reaction cross-sections at 17.9 and 22.3 MeV energies. We have suggested semi-empirical formulas including the non-elastic effects of optical model found by fitting two parameters for proton-induced reactions. The coefficients were determined by least-square fitting method. The obtained cross-section formulas with new coefficients have been discussed and compared with the available experimental data.