Mathematical modeling of dengue virus transmission: exploring vector, vertical, and sexual pathways with sensitivity and bifurcation analysis

Dengue virus (DENV) remains a critical global health threat, particularly in tropical and subtropical regions. Traditional models primarily focus on mosquito-borne transmission, overlooking alternative pathways such as vertical and sexual transmission. This study develops a comprehensive mathematical model that integrates multiple transmission routes to improve understanding of dengue dynamics and inform effective control strategies. We develop a compartmental SEIR-based model that captures dengue virus transmission through mosquito vectors, vertical (transovarial), and sexual routes. The model undergoes rigorous mathematical analysis to derive equilibrium points and assess their stability. Both local and global sensitivity analyses are performed to identify key drivers of disease dynamics. Additionally, the model is calibrated using weekly dengue incidence data from Delhi, India, to validate its predictive capacity. The sensitivity analysis identifies the most influential parameters driving transmission. Although the human-to-human contact rate (sexual transmission) has a high sensitivity index, the actual contribution of sexual transmission to the basic reproduction number ( $$R_d$$ ) is biologically negligible—approximately 0.01704 out of a total $$R_d$$ of 0.02, i.e., less than 1%. In contrast, mosquito-borne transmission remains the dominant route. The vaccination rate exhibits a negative sensitivity index, indicating its suppressive impact on disease spread. Numerical simulations reveal that dengue can persist even when $$R_d < 1$$ , indicating backward bifurcation, which necessitates enhanced intervention strategies beyond just reducing $$R_d$$ . The model reveals that dengue can persist even when $$R_d < 1$$ , due to backward bifurcation. Although sexual transmission contributes less than 1% to $$R_d$$ under current estimates, vector control and vaccination remain the most critical strategies. Incorporating climate and mobility dynamics in future studies can further enhance model accuracy and policy relevance.