A Sex-Structured Mathematical Epidemiology of Syphilis: With Control Measures and Public Health Applications

Syphilis remains a significant global public health challenge, with over seven million new adult infections each year despite the availability of effective treatment. Its continued persistence, particularly among high-risk and underserved populations, highlights the need for robust analytical models to understand transmission dynamics and inform targeted control strategies. This study presents a novel sex-structured compartmental model that captures the biological and behavioral complexity of syphilis transmission, incorporating multiple infection stages (primary, secondary, and latent), gender-specific progression, treatment, natural recovery, and reinfection. The population is stratified by sex and disease stage, allowing detailed analysis of transmission pathways between males and females. We established the positivity and boundedness of model solutions and derived the basic reproduction number (R0) using the next-generation matrix approach. Stability analysis showed that the disease-free equilibrium is locally asymptotically stable when (R0< 1). Notably, the model exhibits backward bifurcation, indicating that reducing R0 below unity may not guarantee disease elimination. Sensitivity analysis using Latin Hypercube Sampling and Partial Rank Correlation Coefficients identified transmission probabilities as the most influential parameters sustaining infection, while treatment and recovery rates substantially reduced transmission. Numerical simulations demonstrated that integrated control strategies combining early diagnosis, treatment coverage above 85%, partner notification, and behavioral interventions can reduce syphilis prevalence by up to 80%. The study presents a comprehensive and biologically realistic modeling framework that enhances understanding of syphilis dynamics. The findings provide actionable insights for public health policy, emphasizing that multifaceted, gender-inclusive interventions are essential for achieving sustained control and eventual elimination of syphilis.