Syphilis, an infection transmitted through sexual contact and attributed to the bacterium Treponema pallidum, remains a great public health challenge worldwide. We present a syphilis model with multi-phase treatments to study their impacts on the syphilis infection spread and control. The threshold which determines the spread and eradication of the syphilis is calculated. It is established that the syphilis-free equilibrium and endemic state for a special case are globally asymptotically stable when the reproduction numbers \(R_{o} < 1\) and \(\overline{R}_{o} > 1\) respectively. Furthermore, the sensitivity analysis conducted highlights the significance of the contact rate and rates of treating people with primary and secondary syphilis, indicating their pivotal role in influencing the transmission and management of the disease. The simulations are carried out using the ODE45 solver in MATLAB and results demonstrate that with the non-existence of treatment in the primary phase of the infection, treating those with secondary syphilis effectively reduces the disease burden. However, simultaneous treatment of people with secondary and primary syphilis and increasing the rates of treating them proves to be highly effective in diminishing the overall syphilis-infected population. Conclusively, the best strategy for alleviating the disease burden entails reducing contact rates and augmenting the rates of treating people with secondary and primary syphilis.
