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Among numerical techniques used to facilitate the analysis of biochemical reactions, we can use the method of moments to directly approximate statistics such as the mean numbers of molecules. The method is computationally viable in time and memory, compared to solving the chemical master equation (CME) which is notoriously expensive. In this study, we apply the method of moments to a chemical system with a constant rate representing a vascular endothelial growth factor (VEGF) model, as well as another system with time-dependent propensities representing the susceptible, infected, and recovered (SIR) model with periodic contact rate. We assess the accuracy of the method using comparisons with approximations obtained by the stochastic simulation algorithm (SSA) and the chemical Langevin equation (CLE). The VEGF model is of interest because of the role of VEGF in the growth of cancer and other inflammatory diseases and the potential use of anti-VEGF therapies in the treatment of cancer. The SIR model is a popular epidemiological model used in studying the spread of various infectious diseases in a population.