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The 2019 coronavirus disease (COVID-19) is now a global pandemic. Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is the causative pathogen of COVID-19. Here, we study an in-host model that highlights the effector T cell response to SARS-CoV-2. The stability of a unique positive equilibrium point, with viral load V * , suggests that the virus may replicate fast enough to overcome T cell response and cause infection. This overcoming is the bifurcation point, near which the orders of magnitude for V * can be sensitive to numerical changes in the parameter values. Our work offers a mathematical insight into how SARS-CoV-2 causes the disease., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (© 2020 Elsevier B.V. All rights reserved.)