The paper discusses the application of the R package FME for inverse modeling, sensitivity analysis, and Monte Carlo (MCMC) analysis in mathematical modeling. FME is designed to fit mathematical models to data, estimate parameter uncertainties, and perform sensitivity analysis. The authors demonstrate the use of FME through a case study on a dynamic model of HIV virus dynamics. They apply FME to estimate parameters, assess parameter identifiability, and quantify the impact of parameter uncertainties on model predictions. The paper also covers local and global sensitivity analysis, MCMC methods for parameter uncertainty estimation, and the visualization of these uncertainties. The results highlight the importance of considering parameter correlations and measurement errors in model fitting and uncertainty quantification. The authors conclude by discussing the practical implications of their findings and the broader applicability of FME in various modeling contexts.The paper discusses the application of the R package FME for inverse modeling, sensitivity analysis, and Monte Carlo (MCMC) analysis in mathematical modeling. FME is designed to fit mathematical models to data, estimate parameter uncertainties, and perform sensitivity analysis. The authors demonstrate the use of FME through a case study on a dynamic model of HIV virus dynamics. They apply FME to estimate parameters, assess parameter identifiability, and quantify the impact of parameter uncertainties on model predictions. The paper also covers local and global sensitivity analysis, MCMC methods for parameter uncertainty estimation, and the visualization of these uncertainties. The results highlight the importance of considering parameter correlations and measurement errors in model fitting and uncertainty quantification. The authors conclude by discussing the practical implications of their findings and the broader applicability of FME in various modeling contexts.