Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies

Syphilis is a sexually transmitted infection which when left untreated would lead to major health problems. Syphilis can easily be contracted by direct contact with Syphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on from an infected mother to her unborn child. In this paper, a nonlinear deterministic model of Syphilis disease was constructed to determine the dynamics of Syphilis infections. The study deduced model’s equilibria and analyzed the local and global stability of these equilibria. The model was extended to optimal control problem by adding time-dependent controls that helped characterize a range of possible controls that minimized the disease. The control system was solved qualitatively and numerically to evaluate the effectiveness of the considered controls using Pontryagin’s Maximum Principle. The analysis indicated that strategies B and C are considered most effective as they substantially minimized the exposed, asymptomatic and symptomatic infectious. We recommend that stakeholders should consider strategy B and C in their effort to miti-gate the disease from the population as they all have the same effect of substantially minimizing the exposed, symptomatic and asymptomatic populations.