A co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis is developed and presented. 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 the syphilis-only sub-model was established, for a special case. Sensitivity analysis is also carried out on the parameters of the model. Using the syphilis associated reproduction number, $ℛ_{0 s}$ , as the response function, it is observed that the five-ranked parameters that drive the dynamics of the co-infection model are the demographic parameter $μ$ , the effective contact rate for syphilis transmission, $β_{s}$ , the progression rate to late stage of syphilis $σ_{2}$ , and syphilis treatment rates: $τ_{1}$ and $τ_{2}$ for co-infected individuals in compartments $H_{i}$ and $H_{l}$ , respectively. Moreover, when the HPV associated reproduction number, $ℛ_{0 h}$ , is used as the response function, the five most dominant parameters that drive the dynamics of the model are the demographic parameter $μ$ , the effective contact rate for HPV transmission, $β_{h}$ , the fraction of HPV infected who develop persistent HPV $ρ_{1}$ , the fraction of individuals vaccinated against incident HPV infection $ϕ$ and the HPV vaccine efficacy $π_{h}$ . 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.

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AMSC: 92B05

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