In this study, we formulated and analyzed a within-host co-infection model of Dengue virus (DENV) and Zika virus (ZIKV) that incorporated CTL-mediated immunity, and four types of distributed time delays. The model described the dynamics of uninfected cells, latently, and productively infected cells for each virus, along with free DENV and ZIKV particles and virus-targeted CTL responses. We first proved that all model solutions remained nonnegative and bounded. We computed the basic reproduction numbers $ R_{D}^{L} $ for DENV and $ R_{Z}^{L} $ for ZIKV, together with the invasion reproduction numbers $ R_{D}^{L, inv} $ and $ R_{Z}^{L, inv} $, which determined invasion capability under pre-existing infection. These numbers governed the existence and the global asymptotic stability of model equilibria. Global stability was established using the Lyapunov method, and numerical simulations were performed to validate the analytical results. In addition, sensitivity analysis identified the most influential parameters affecting viral clearance. The effects of antiviral therapy, time delays, and latent infection stages on the DENV–ZIKV co-dynamics were investigated. The results showed that treatment intervention, prolonged delays, and the inclusion of latent infection stages led to a reduction in $ R_{D}^{L} $ and $ R_{Z}^{L} $. Furthermore, neglecting intracellular delays or latent infection stages leads to an overestimation of $ R_{D}^{L} $ and $ R_{Z}^{L} $ and the antiviral efficacy required for infection control. This suggests that therapeutic strategies aimed at prolonging intracellular delay phases and accounting for latent-stage dynamics may decrease these reproduction numbers below unity, thereby promoting viral elimination within the host.
Citation: Ahmed Elaiw, Zainab Alkhudhari, Ebtehal Almohaimeed. Mathematical analysis of DENV–ZIKV co-infection with CTL-mediated immune response and time delays[J]. Networks and Heterogeneous Media, 2026, 21(4): 1262-1333. doi: 10.3934/nhm.2026050
In this study, we formulated and analyzed a within-host co-infection model of Dengue virus (DENV) and Zika virus (ZIKV) that incorporated CTL-mediated immunity, and four types of distributed time delays. The model described the dynamics of uninfected cells, latently, and productively infected cells for each virus, along with free DENV and ZIKV particles and virus-targeted CTL responses. We first proved that all model solutions remained nonnegative and bounded. We computed the basic reproduction numbers $ R_{D}^{L} $ for DENV and $ R_{Z}^{L} $ for ZIKV, together with the invasion reproduction numbers $ R_{D}^{L, inv} $ and $ R_{Z}^{L, inv} $, which determined invasion capability under pre-existing infection. These numbers governed the existence and the global asymptotic stability of model equilibria. Global stability was established using the Lyapunov method, and numerical simulations were performed to validate the analytical results. In addition, sensitivity analysis identified the most influential parameters affecting viral clearance. The effects of antiviral therapy, time delays, and latent infection stages on the DENV–ZIKV co-dynamics were investigated. The results showed that treatment intervention, prolonged delays, and the inclusion of latent infection stages led to a reduction in $ R_{D}^{L} $ and $ R_{Z}^{L} $. Furthermore, neglecting intracellular delays or latent infection stages leads to an overestimation of $ R_{D}^{L} $ and $ R_{Z}^{L} $ and the antiviral efficacy required for infection control. This suggests that therapeutic strategies aimed at prolonging intracellular delay phases and accounting for latent-stage dynamics may decrease these reproduction numbers below unity, thereby promoting viral elimination within the host.
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Ahmed Elaiw, Zainab Alkhudhari, Ebtehal Almohaimeed. Mathematical analysis of DENV–ZIKV co-infection with CTL-mediated immune response and time delays[J]. Networks and Heterogeneous Media, 2026, 21(4): 1262-1333. doi: 10.3934/nhm.2026050
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