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<p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0\)</EquationSource> </InlineEquation>) using the next-generation matrix approach. Stability analysis showed that the disease-free equilibrium is locally asymptotically stable when (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R_0&lt;1\)</EquationSource> </InlineEquation>). Notably, the model exhibits backward bifurcation, indicating that reducing&#xa0;<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R_0\)</EquationSource> </InlineEquation>&#xa0;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.</p>

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Mathematical modeling and analysis of a sex-structured syphilis model with control measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Renfei Luo,
  • Agbata Benedict Celestine,
  • Mehmet Gümüş,
  • Obeng-Denteh William,
  • Homan Emadifar,
  • Aseel Smerat,
  • A.K. Awasthi

摘要

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 ( \(R_0\) ) using the next-generation matrix approach. Stability analysis showed that the disease-free equilibrium is locally asymptotically stable when ( \(R_0<1\) ). Notably, the model exhibits backward bifurcation, indicating that reducing  \(R_0\)  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.