Okuonghae D, Gumel A B, Ikhimwin B O, Iboi E
Department of Mathematics, University of Benin, Benin City, Nigeria.
School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA.
Acta Biotheor. 2019 Mar;67(1):47-84. doi: 10.1007/s10441-018-9336-9. Epub 2018 Jul 3.
A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by [Formula: see text]) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by [Formula: see text]) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to [Formula: see text]) are the disease transmission rate ([Formula: see text]), compliance in condom use (c) and efficacy of condom ([Formula: see text]). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.
建立并严格分析了一种新的梅毒传播动力学多阶段确定性模型，该模型纳入了梅毒感染早期潜伏阶段个体的疾病传播以及早期潜伏梅毒向一期和二期的逆转情况。该模型用于评估预防措施（使用避孕套）和治疗措施（使用抗生素治疗）对社区中疾病传播的人群水平影响。结果表明，只要相关控制繁殖数（用[公式：见原文]表示）小于1，模型的无病平衡点就是全局渐近稳定的。当相关繁殖数（用[公式：见原文]表示）超过1时，该模型的一个特殊情况具有唯一且全局渐近稳定的地方病平衡点。使用与尼日利亚梅毒传播动力学相关的参数值和范围对该模型进行不确定性和敏感性分析，结果表明，驱动梅毒感染（相对于[公式：见原文]）的前三个参数是疾病传播率（[公式：见原文]）、避孕套使用依从性（c）和避孕套功效（[公式：见原文]）。该模型的数值模拟表明，对二期梅毒病例进行靶向治疗比针对梅毒感染一期或早期潜伏阶段个体进行靶向治疗更有效。
