Computation and analysis of stationary and periodic solutions of the COVID-19 infection dynamics model

In this work, we search for the conditions for the occurrence of long COVID using the recently developed COVID-19 disease dynamics model which is a system of delay differential equations. To do so, we search for stable stationary or periodic solutions of this model with low viral load that can be interpreted as long COVID using our recently developed technology for analysing time-delay systems. The results of the bifurcation and sensitivity analysis of the mathematical model of SARS-CoV-2 infection suggest the following biological conclusions concerning the mechanisms of pathogenesis of long COVID-19. First, the possibility of SARS-CoV-2 persistence requires a 3-time reduction of the virus production rate per infected cell, or 18-times increase of the antibody-mediated elimination rate of free viruses as compared to an acute infection baseline estimates. Second, the loss of kinetic coordination between virus-induced type I IFN, antibody, and cytotoxic T lymphocyte (CTL) responses can result in the development of mild severity long-lasting infection. Third, the low-level persistent SARS-CoV-2 infection is robust to up to 100-fold perturbations (increase) in viral load and most sensitive to parameters of the humoral immune response.