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 wouldlead to major health problems. Syphilis can easily be contracted by direct contact withSyphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on froman infected mother to her unborn child. In this paper, a nonlinear deterministic modelof Syphilis disease was constructed to determine the dynamics of Syphilis infections.The study deduced model’s equilibria and analyzed the local and global stability ofthese equilibria. The model was extended to optimal control problem by adding timedependent controls that helped characterize a range of possible controls that minimizedthe disease. The control system was solved qualitatively and numerically to evaluatethe effectiveness of the considered controls using Pontryagin’s Maximum Principle.The analysis indicated that strategies B and C are considered most effective as theysubstantially minimized the exposed, asymptomatic and symptomatic infectious. Werecommend that stakeholders should consider strategy B and C in their effort to mitigate the disease from the population as they all have the same effect of substantiallyminimizing the exposed, symptomatic and asymptomatic populations.