The global pandemic caused by the outbreak of Covid-19 (SARS-CoV-2) remains to be an unsolved issue worldwide and has caused major uncertainties in our lives. This work models the viral kinetics of Covid-19, where the replication and elimination of the virus can be modelled using a system of ordinary differential equations (ODE). The unknown parameters will be determined using two different computational means; Nonlinear mixed effects (NLME) and Genetic Algorithm (GA). The data has been gathered from sixty patients in five published studies in several countries. The data includes the viral load record by day after the patient has been tested positive for Covid-19, as well as the indication of each patient’s severity. We adopted an Immune-Viral Dynamics model developed by a research group of Merck & Co to describe the viral dynamics and disease progression of Covid-19. The model consists of the relationship between rates of change in target cells (lung epithelial cells), productively infected cells, and the viral load. Built-in functions in Matlab, such as the Nonlinear mixed-effects estimation and the Genetic algorithm, has been used to calibrate the model to the data, and hence to determine the values of the unknown parameters.