具有早期筛查的梅毒传染病模型的动力学分析

Dynamic Analysis of a Syphilis Infectious Disease Model with Early Screening

摘要: 本文根据梅毒传播机制，构建了一类具有早期筛查的梅毒传播模型。我们计算了模型的控制再生数，证明了无病平衡点和地方病平衡点的存在性和稳定性。通过数值模拟，分析了早期筛查和避孕套的使用对梅毒传播的影响，结果表明两种控制措施均会降低梅毒各个阶段的患病人数，且患病人数的峰值会随着筛查频率和避孕套使用依从性的增加而降低，从而有效控制疾病的传播。

Abstract: According to the transmission mechanism of syphilis, a kind of syphilis transmission model with early screening is constructed. The control reproduction number is calculated, and then we prove the existence and stability of both the disease-free equilibrium and the endemic equilibrium. Through numerical simulations, the effects of early screening and condom use on the transmission of syphilis are analyzed. The results show that both control measures can reduce the number of patients at all stages of syphilis, and the peak value of the infectious will decrease with the increase of screening frequency and condom use compliance, so as to effectively control the propagation of syphilis.