Shu H, Jin HY, Wang XS, Wu J. Viral infection dynamics with immune chemokines and CTL mobility modulated by the infected cell density.
J Math Biol 2024;
88:43. [PMID:
38491217 DOI:
10.1007/s00285-024-02065-0]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 12/05/2023] [Accepted: 02/09/2024] [Indexed: 03/18/2024]
Abstract
We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a standing assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. We then define the basic reproduction number of viral infection R 0 and prove (by the uniform persistence theory, Lyapunov function technique and LaSalle invariance principle) that the infection-free steady state E 0 is globally asymptotically stable ifR 0 < 1 . WhenR 0 > 1 , then E 0 becomes unstable, and another basic reproduction number of CTL response R 1 becomes the dynamic threshold in the sense that ifR 1 < 1 , then the CTL-inactivated steady state E 1 is globally asymptotically stable; and ifR 1 > 1 , then the immune response is uniform persistent and, under an additional technical condition the CTL-activated steady state E 2 is globally asymptotically stable. To establish the global stability results, we need to prove point dissipativity, obtain uniform persistence, construct suitable Lyapunov functions, and apply the LaSalle invariance principle.
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