A co-infection model for HPV and syphilis with optimal control and cost-effectiveness analysis

In this work, we develop and present a co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown not to exist, when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of both the syphilis-only sub-model and HPV-only sub-model were established. The global asymptotic stability of disease-free equilibrium of the HPV-only sub-model is also proven. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.