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The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model's solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient. [ABSTRACT FROM AUTHOR]