Global stability of antibody–based and CTL–based PDE models for secondary dengue infection

  • Ebtehal Almohaimeed orcid

    Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
  • Ahmed Elaiw orcid

    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • Reem Aldubiban orcid

    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • Aatef Hobiny orcid

    Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Article ID: 3720
DOI: https://doi.org/10.59400/adecp3720
Keywords: DENV infection; antibody immunity; CTL immunity; global stability; Lyapunov function; diffusion; latency; sensitivity analysis

Abstract

Infections caused by Flavivirus species, such as dengue virus (DENV), remain a significant public health concern. Because DENV has four antigenically distinct serotypes, a person can be reinfected after a first exposure. Existing within–host models, mostly based on ODEs, describe viral behavior during primary and secondary DENV infection but generally assume uniform mixing and ignore the spatial motion of cells and virions. The present work introduces two PDE models for secondary DENV infection. One captures antibody action against free virus, while the other represents cytotoxic T lymphocyte (CTL) destruction of infected cells. Immune cell production combines an intrinsic source term with a predator–prey–type activation mechanism. The study begins by verifying well-posedness through proofs of global existence and uniform bounds on all solutions. Equilibria are then determined, and the basic reproduction number is calculated to characterize the threshold separating clearance from persistence of infection. Lyapunov techniques, together with LaSalle’s invariance principle, show that the infection–free equilibrium is globally asymptotically stable for R0 ≤ 1, while the endemic state attracts all trajectories for R0 >1.Numerical tests confirm the analytical results. A sensitivity investigation highlights the parameters with the greatest impact on secondary DENV dynamics.

Published
2025-11-24
How to Cite
Almohaimeed, E., Elaiw, A., Aldubiban, R., & Hobiny, A. (2025). Global stability of antibody–based and CTL–based PDE models for secondary dengue infection. Advances in Differential Equations and Control Processes, 32(4). https://doi.org/10.59400/adecp3720
Issue
Vol. 32 No. 4 (2025)
Section
Articles

Copyright (c) 2025 Ebtehal Almohaimeed, Ahmed Elaiw, Reem Aldubiban, Aatef Hobiny

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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