Immunokinetic Model for COVID-19 Patients

In this paper, we develop a fractional-order differential model for the dynamics of immune responses to SARS-CoV-2 viral load in one host. In the model, a fractional-order derivative is incorporated to represent the effects of temporal long-run memory on immune cells and tissues for any age group of patients. The population of cytotoxic T-cells (CD8+), natural killer (NK) cells and infected viruses are unknown in this model. Some interesting sufficient conditions that ensure the asymptotic stability of the steady states are obtained. This model indicates some complex phenomena in COVID-19 such as "immune exhaustion" and "Long COVID". Sensitivity analysis is also investigated for model parameters to determine the parameters that are effective in determining of the long COVID duration, disease control and future treatment as well as vaccine design. The model is verified with clinical and experimental data of 5 patients with COVID-19.