The effect of public health awareness and behaviors on the transmission dynamics of syphilis in Northwest China, 2006–2018, based on a multiple-stages mathematical model

Syphilis, a sexually transmitted infectious disease caused by the bacterium treponema pallidum, has re-emerged as a global public health issue with an estimated 12 million people infected each year. Understanding the impacts of health awareness and behaviors on transmission dynamics of syphilis can help to establish optimal control strategy in different regions. In this paper, we develop a multiple-stage SIRS epidemic model taking into account the public health awareness and behaviors of syphilis. First, the basic reproduction number [Formula: see text] is obtained, which determines the global dynamics behaviors of the model. We derive the necessary conditions for implementing optimal control and the corresponding optimal solution for mitigation syphilis by using Pontryagin's Maximum Principle. Based on the data of syphilis in Ningxia from 2006 to 2018, the parameterizations and model calibration are carried out. The fitting results are in good agreement with the data. Moreover, sensitivity analysis shows that the public awareness induced protective behaviors C(e), compliance of condom-induced preventability ε and treatment for the primary syphilis m(1) play an important role in mitigating the risk of syphilis outbreaks. These results can help us gain insights into the epidemiology of syphilis and provide guidance for the public health authorities to implement health education programs.