Analysis of risk-structured vaccination model for the dynamics of oncogenic and warts-causing HPV types

A new deterministic model is designed and used to assess the community-wide impact of mass vaccination of new sexually active individuals on the dynamics of the oncogenic and warts-causing HPV types. Rigorous qualitative analyses of the model, which incorporates the two currently available anti-HPV vaccines, reveal that it undergoes competitive exclusion when the reproduction of one HPV risk type (low/high) exceeds unity, while that of the other HPV risk type is less than unity. For the case when the reproduction numbers of the two HPV risk types (low/high) exceed unity, the two risk types co-exist. It is shown that the sub-model with the low-risk HPV types only has at least one endemic equilibrium whenever the associated reproduction threshold exceeds unity. Furthermore, this sub-model undergoes a re-infection-induced backward bifurcation under certain conditions. In the absence of the re-infection of recovered individuals and cancer-induced mortality in males, the associated disease-free equilibrium of the full (risk-structured) model is shown to be globally asymptotically stable whenever the reproduction number of the model is less than unity (that is, the full model does not undergo backward bifurcation under this setting). It is shown, via numerical simulations, that the use of the Gardasil vaccine could lead to the effective control of HPV in the community if the coverage rate is in the range of 73-95 % (84 %). If 70 % of the new sexually active susceptible females are vaccinated with the Gardasil vaccine, additionally vaccinating 34-56 % (45 %) of the new sexually active susceptible males can lead to the effective community-wide control (or elimination) of the HPV types.