Modelling and investigating memory immune responses in infectious disease. Application to influenza a virus and sars-cov-2 reinfections

Understanding effector and memory immune responses against influenza A virus (IAV) and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections and re-infections is extremely important, given that they are now endemic in the community. The goal of this study is to investigate the role of memory cells and antibodies in the immune responses against IAV and SARS-CoV-2 re-infections. To this end, we adapt a previously-published within-host mathematical model (Sadria & Layton, 2021) for the primary immune response against SARS-CoV-2 infections, by including two types of memory immune cells, i.e., memory CD8⁺ T-cells and memory B-cells, and by parametrising the new model with values specific to the two viruses. We first investigate the long-term dynamics of the model by identifying the virus-free steady states and studying the conditions that ensure the stability of these states. Then, we investigate the transient dynamics of this in-host model by simulating different viral reinfection times: 20 days, 60 days and 400 days after the first encounter with the pathogen. This allows us to highlight which memory immune components have the greatest impact on the viral elimination depending on the time of reinfection. Our results suggest that memory immune responses have a greater impact in the case of IAV infections compared to SARS-CoV-2 infections. Moreover, we observe that the immune response after a secondary infection is more efficient when the reinfection occurs at a shorter time.