<![CDATA[Coinfection of SARS-CoV-2 and Influenza A virus within a host poses a unique challenge in understanding immunological dynamics, especially the role of cytotoxic T lymphocytes (CTL) in mediating the immune response. This work present a mathematical model to examine the dynamics of coinfection within a host, highlighting CTL-mediated immunity. Generally, this model encompasses several compartments, including epithelial cells, free viruses, and CTLs specific of both SARS-CoV-2 and Influenza A. The basic properties of the model, equilibrum state analysis, stability using the Lyapunov function, and numerical simulations are examined to investigate the dynamics behavior of the model. Eight equilibrium states are identified: the virus-free equilibrium (E0), single SARS-CoV-2 infection without CTLs (E1), single Influenza A virus infection without CTLs (E2), single SARS-CoV-2 infection with SARS-CoV-2-specific CTLs (E3), single Influenza A virus infection with Influenza A virus-specific CTLs (E4), SARS-CoV-2 and Influenza A virus coinfection with SARS-CoV-2-specific CTLs (E5), SARS-CoV-2 and Influenza A virus coinfection with Influenza A virus-specific CTLs (E6), and SARS-CoV-2 and Influenza A virus coinfection with both SARS-CoV-2-specific and Influenza A virus-specific CTLs (E7). The existence and stability regions for each equilibrium state are determined and represented in the R1-R2 plane as threshold functions within the model. Numerical simulations confirm the results of the qualitative analysis, demonstrating that CTLs specific to SARS-CoV-2 and Influenza A virus can be activated, reducing the number of infected epithelial cells as well as inhibiting virus transmission within epithelial cells. Furthermore, analysis of parameter changes shows that increasing the proliferation rate of epithelial cells and CTLs, while lowering the virus formation rate, can shift the system's stability threshold and stabilize it at the virus-free equilibrium.]]>
