Modeling viral dynamics in SARS-CoV-2 infection based on differential equations and numerical analysis

Computational modeling and simulation of viral dynamics would explain the pathogenesis for any virus. Such computational attempts have been successfully made to predict and control HIV-1 or hepatitis B virus. However, the dynamics for SARS-CoV-2 has not been adequately investigated. The purpose of this research is to propose different SARS-CoV-2 dynamics models based on differential equations and numerical analysis towards distilling the models to explain the mechanism of SARS-CoV-2 pathogenesis. The proposed four models formalize the dynamical system of SARS-CoV-2 infection, which consists of host cells and viral particles. These models undergo numerical analysis, including sensitivity analysis and stability analysis. Based on the sensitivity indices of the four models' parameters, the four models are simplified into two models. In advance of the following calibration experiments, the eigenvalues of the Jacobian matrices of these two models are calculated, thereby guaranteeing that any solutions are stable. Then, the calibration experiments fit the simulated data sequences of the two models to two observed data sequences, SARS-CoV-2 viral load in mild cases and that in severe cases. Comparing the estimated parameters in mild cases and severe cases indicates that cell-to-cell transmission would significantly correlate to the COVID-19 severity. These experiments for modeling and simulation provide plausible computational models for the SARS-CoV-2 dynamics, leading to further investigation for identifying the essential factors in severe cases.