Dynamics of sexually transmitted diseases with multi-pathway transmission and sex-based contact patterns

Sexually transmitted diseases (STDs) are a significant public health concern. Although their propagation has garnered extensive scientific attention, previous research rarely considers the multiple transmission pathways of STDs within sexual contact networks featuring different group interaction patterns. In this paper, we introduce a generalized SEIR model on a double-layer interconnected network to represent the diverse transmission pathways of STDs, including vertical and sexual contact routes, as well as the complexities of sex- and status-based contact patterns, such as same-sex contact, opposite-sex contact, and latent period transmission. We present rigorous results on the basic reproduction number R0 and the global stability of equilibria, specifically showing that the system cannot undergo a Hopf bifurcation. Our theoretical and sensitivity analysis of R0 quantifies the impact of related parameters on STD dynamics. This analysis reveals a strong dependence of R0 on the internal structure of the female and male layers, as well as the connections between these layers. Both same-sex and opposite-sex transmission rates affect R0, but due to mutual reactions within a layer, changes in same-sex transmission parameters can have a more pronounced effect when contact patterns are equivalent. Our results even extend beyond STDs to address how sex-specific influences on individual behaviors contribute to differences in risk of other types of transmissions. We also propose and evaluate epidemic control strategies, discovering that isolation tracking and targeted immunization are particularly effective in controlling disease spread. Numerical simulations on both empirical and synthetic complex networks support and enhance our theoretical findings. Finally, we apply our framework to HIV transmission, highlighting the critical role of condom use in combating the virus.