Analysis of a reaction-diffusion oncolytic SARS-CoV-2 model

The association between cancer and SARS-CoV-2 infection is a subject of debate. While the infection can potentially exacerbate the condition of a cancer patient, there are documented cases of remission following SARS-CoV-2 infection. The notion that SARS-CoV-2 may possess oncolytic properties has been proposed, warranting further investigation. Mathematical modeling stands as a potent tool capable of greatly supporting experimental and medical studies. In this study, we introduce and analyze a reaction-diffusion oncolytic SARS-CoV-2 model incorporating immune responses. The model explores the interactions among six components: nutrient, epithelial cells, cancer cells, SARS-CoV-2, Cytotoxic T Lymphocytes (CTLs), and antibodies. We establish the fundamental properties of the model, compute the equilibrium points, and determine their stability conditions. Using Lyapunov theory, we demonstrate the global stability of key equilibria. Numerical simulations are conducted to validate the theoretical findings. In our model, SARS-CoV-2 is shown to potentially reduce the concentration of cancer cells either by infecting them or eliciting an anti-cancer immune response. These theoretical findings correspond with various studies underscoring the oncolytic function of SARS-CoV-2. This suggests that the results can be tested against real data, and that the model can be employed in studies exploring the potential oncolytic role of SARS-CoV-2.