Stability analysis in COVID-19 within-host model with immune response

Alexis Erich S Almocera; Griselda Quiroz; Esteban A Hernandez-Vargas

doi:10.1016/j.cnsns.2020.105584

Stability analysis in COVID-19 within-host model with immune response

Commun Nonlinear Sci Numer Simul. 2021 Apr:95:105584. doi: 10.1016/j.cnsns.2020.105584. Epub 2020 Nov 3.

Authors

Alexis Erich S Almocera¹, Griselda Quiroz², Esteban A Hernandez-Vargas^{3

4}

Affiliations

¹ Division of Physical Sciences and Mathematics, College of Arts and Sciences, University of the Philippines Visayas, Philippines.
² Universidad Autónoma de Nuevo León, FIME, Av. Universidad S/N, Ciudad Universitaria, C.P. 66455, San Nicolás de los Garza, Nuevo León, Mexico.
³ Instituto de Matemáticas, Universidad Nacional Autonoma de Mexico, Boulevard Juriquilla 3001, Santiago de Querétaro, Qro., 76230, México.
⁴ Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany.

Abstract

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.

Keywords: Bifurcation; COVID-19; Effector T cell response; In-host model; SARS-CoV-2.