Spatio-Temporal Modeling of Immune Response to SARS-CoV-2 Infection

COVID-19 is a disease occurring as a result of infection by a novel coronavirus called SARS-CoV-2. Since the WHO announced COVID-19 as a global pandemic, mathematical works have taken place to simulate infection scenarios at different scales even though the majority of these models only consider the temporal dynamics of SARS-COV-2. In this paper, we present a new spatio-temporal within-host mathematical model of COVID-19, accounting for the coupled dynamics of healthy cells, infected cells, SARS-CoV-2 molecules, chemokine concentration, effector T cells, regulatory T cells, B-lymphocytes cells and antibodies. We develop a computational framework involving discretisation schemes for diffusion and chemotaxis terms using central differences and midpoint approximations within two dimensional space combined with a predict–evaluate–correct mode for time marching. Then, we numerically investigate the model performance using a list of values simulating the baseline scenario for viral infection at a cellular scale. Moreover, we explore the model sensitivity via applying certain conditions to observe the model validity in a comparison with clinical outcomes collected from recent studies. In this computational investigation, we have a numerical range of 10 4 to 10 8 for the viral load peak, which is equivalent to what has been obtained from throat swab samples for many patients.