Within-host dynamics, stability, and treatment approaches for Dengue-Zika virus co-infection with CTL immunity

Dengue virus (DENV) and Zika virus (ZIKV) are primarily transmitted by Aedes aegypti and Aedes albopictus. Because they share the same mosquito vectors, co-infections with both viruses have been reported worldwide. These pathogens are among the most significant mosquito-borne viruses, responsible for considerable morbidity and mortality. Simultaneous infection may affect viral activity as well as the host immune response, which could influence clinical outcomes. Yet, the within-host mechanisms governing DENV-ZIKV interactions remain poorly understood. In this work, we develop a within-host model of DENV-ZIKV co-infection incorporating cytotoxic T lymphocyte (CTL) immunity, including cross-reactive CTL responses. The system tracks uninfected target cells, infected cells, free viruses and CTLs. All solutions remain non-negative and bounded. The analysis identifies four equilibria: disease-free, DENV mono-infection, ZIKV mono-infection, and viral coexistence. Using the next-generation matrix, we derive the reproduction numbers for the DENV submodel, the ZIKV submodel, and the co-infection system ( \(R_{D}\) , \(R_{Z}\) and \(R_{0} =\max \{R_{D},R_{Z}\}\) ). In addition, we compute the invasion reproduction numbers for the DENV and ZIKV submodels, denoted by \(R_{D}^{inv}\) and \(R_{Z}^{inv}\) , respectively. Global stability is established and verified via Lyapunov functions. Sensitivity analysis of \(R_{D}\) and \(R_{Z}\) highlights parameters most strongly influencing viral clearance. The model further examines three therapeutic strategies: (i) entry-blocking antiviral, (ii) agents reducing viral output, and (iii) interleukin-2 immunotherapy (IL-2) therapy enhancing CTL activity. The influence of CTLs cross-reactivity on co-infection dynamics is also established. Results show that cross-reactive CTLs can reduce \(R_{D}\) and \(R_{Z}\) similarly to treatment interventions. Numerical simulations confirm theoretical predictions, demonstrating that combining antiviral and immune-based strategies enhances viral control by limiting replication and boosting immune-mediated clearance. Moreover, ignoring cross-reactive CTL responses could theoretically lead to an overestimation of the antiviral treatment intensity required for viral elimination. These findings reflect the interactions captured by the model dynamics and are not intended to provide direct clinical predictions.