Global Stability Analysis of Secondary DENV Infection Models with Antibody-Mediated Immunity and Distributed Time Delays (Contemporary Mathematics, 2025)
This study develops and analyzes mathematical models describing secondary infection with the Dengue Virus (DENV), explicitly incorporating the effects of both non-specific and strain-specific antibodies. The first model introduces two distributed time delays corresponding to monocyte infection and virion maturation. An extended model further differentiates between latent and actively infected monocytes and includes two additional delays that represent the latency and activation phases of monocyte infection. Analytical investigations focus on the non-negativity and boundedness of model solutions, and the basic reproduction number (R0) is derived to examine the existence and stability of equilibrium points. Global stability of equilibria is established using Lyapunov technique. To validate the theoretical findings, numerical simulations and sensitivity analyses are performed. Results demonstrate that incorporating latent infection and time delays can reduce the value of R0, suggesting that their omission may lead to overestimation of antiviral treatment requirements. Moreover, prolonged delays can mimic the effects of antiviral interventions by slowing viral propagation, indicating potential therapeutic strategies that target viral replication and maturation timing.
Keywords: dengue fever model; Global asymptotic stability; Time delay; Lyapunov function