Immune response in SARS-CoV-2 epidemics: A fractional-order model

Carvalho, Joao Paulo Simoes Maur'icio de

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a highly contagious virus responsible for coronavirus disease 2019 (CoViD-19). The symptoms of CoViD-19 are essentially reflected in the respiratory system, although other organs are also affected. More than 2.4 million people have died worldwide due to this disease. Despite CoViD-19 vaccines are already being administered, alternative treatments that address the immunopathology of the infection are still needed. For this end, a deeper knowledge on how our immune system responds to SARS-CoV-2 is required. In this study, we propose a non-integer order model to understand the dynamics of cytotoxic T lymphocytes in the presence of SARS-CoV-2. We calculated the basic reproduction number and analysed the values of the model parameters in order to understand which ones inhibit or enhance the progression of the infection. Numerical simulations were performed for different values of the order of the fractional derivative and for different proliferation functions of cytotoxic T lymphocytes.