Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses

Ahmed. M. Elaiw (), Abdullah J. Alsaedi, Aatef. D. Hobiny and Shaban. A. Aly
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Ahmed. M. Elaiw: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abdullah J. Alsaedi: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Aatef. D. Hobiny: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Shaban. A. Aly: Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71516, Egypt

Mathematics, 2022, vol. 11, issue 1, 1-32

Abstract: A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system’s response plays a significant role in viral progression. This article develops and analyzes a system of partial differential equations (PDEs), which describe the in-host dynamics of SARS-CoV-2 under the effect of cytotoxic T-lymphocyte (CTL) and antibody immune responses. The model characterizes the interplay between six compartments, healthy epithelial cells (ECs), latent infected ECs, active infected ECs, free SARS-CoV-2 particles, CTLs, and antibodies. We consider the logistic growth of healthy ECs. We first investigate the properties of the model’s solutions, then, we calculate all steady states and determine the conditions of their existence and global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulations.

Keywords: SARS-CoV-2; COVID-19; immune response; reaction–diffusion virus infection model; global asymptotic stability; Lyapunov functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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