Unusual infection outcomes and establishment of desirable immunity in COVID-19 patients: a mathematical modeling study

Currently, the pathogenesis of long COVID and viral reactivation remains unclear. The study proposes a dynamic model of SARS-CoV-2 transmission from the vascular to the tissue. The stability of the equilibrium points is discussed in the model. Clinical pulmonary viral data from eight patients are used to fit parameters, and parameter robustness is validated through practical identifiability. For most patients, pulmonary viral loads exhibit periodic oscillations, whereas vascular viruses decay asymptotically. Curiously, numerical simulation shows multistability phenomena, such as coexisting periodic and chaotic attractors or multiple periodic attractors under potent drug administration. The periodic orbits explain virus persistence and reactivation in tissues. Coexisting attractors, particularly chaotic attractors, indicate the complexity of SARS-CoV-2 infection and reveal the pathogenesis of long COVID and viral reactivation. Therefore, this study applies classic chaos control methods to reduce the probability of chaos occurring. The controlled results are a disease-free state and a desirable immune status with clinical significance (protective immunity). Notably, this desirable state is not the equilibrium point of the model. By comparing different control methods, some recommendations are provided on therapeutic aspects. In summary, this study establishes a novel mathematical model that provides strong numerical support for medical hypotheses about long COVID and viral reactivation, as well as practical guidance for clinicians.