Global Stability of a MERS-CoV Infection Model with CTL Immune Response and Intracellular Delay

Tuersunjiang Keyoumu, Wanbiao Ma () and Ke Guo
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Tuersunjiang Keyoumu: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Wanbiao Ma: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Ke Guo: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Mathematics, 2023, vol. 11, issue 4, 1-26

Abstract: In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number R 0 and an immunity-activated reproduction number R 1 . By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle’s invariance principle and Barbalat’s lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 ; the immunity-inactivated equilibrium is locally asymptotically stable if R 0 > 1 > R 1 and globally asymptotically stable if R 0 > 1 > R 1 and condition (H1) holds, but unstable if R 1 > 1 ; and the immunity-activated equilibrium is locally asymptotically stable if R 1 > 1 and is globally asymptotically stable if R 1 > 1 and condition (H1) holds.

Keywords: MERS-CoV infection; CTL immune response; global stability; Lyapunov functionals; intracellular delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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