Global Properties of Secondary DENV Infection Models with Pre-Existing CTL Immunity and Discrete/Distributed Delays

Dengue, caused by the dengue virus (DENV), is a serious vector-borne disease mainly prevalent in tropical areas. In certain cases, it can lead to death, especially when a person is infected a second time, resulting in a secondary infection. This research begins by presenting an in-host model for secondary DENV infection under the effect of two types of cytotoxic T lymphocytes (CTLs), non-specific and strain-specific CTLs. The first model is incorporating two distinct discrete-time delays. Additionally, the model is refined by integrating two forms of distributed time delays to provide a more realistic representation of secondary DENV infection dynamics. The main objective is to examine the dynamic behavior of both models, including the non-negativity and boundedness of solutions. A qualitative stability analysis is conducted for their steady states, revealing that the uninfected steady state in both models remains globally asymptotically stable when the basic reproduction number (R0) is below one but becomes unstable when R0 exceeds this threshold. Additionally, an infected steady state emerges and is globally asymptotically stable when R0 is greater than one. The stability conditions for the two steady states are determined using the Lyapunov method. To confirm the qualitative results, comprehensive numerical simulations are conducted, offering valuable biological insights. To assess the influence of specific parameters, we conduct a sensitivity analysis on the model. The results indicate that the infection rate and viral production rate significantly impact the sensitivity of R0, ultimately affecting the dynamics of DENV. These insights could contribute to the development of antiviral treatments aimed at inhibiting viral entry and replication. Furthermore, the study explores the impact of time delays on DENV infection dynamics, highlighting that prolonged delays can mimic the effects of antiviral treatments. A sufficiently long delay slows down the virus’s progression, aiding in its control and eventual eradication. These findings suggest potential strategies for developing new treatments that could extend the viral replication or maturation.