Qualitative analysis of an age- and sex-structured vaccination model for human papillomavirus

Abstract

A new model for the transmission dynamics of human pappilomavirus (HPV) is designed and analysed. The model, which stratifies the total population in terms of age and gender, incorporates an imperfect anti-HPV vaccine with some therapeutic benefits. Rigorous qualitative analysis of the resulting age-structured model, which takes the form of a deterministic system of non-linear partial differential equations with separable transmission coefficients, shows that the disease-free equilibrium of the model is locally-asymptotically stable whenever the effective reproduction number (denoted by $\mathcal{R}_v$) is less than unity. It is shown to be globally-asymptotically stable if certain additional conditions hold. Furthermore, it is shown that the model has at least one endemic equilibrium when $\mathcal{R}_v$ exceeds unity. Hence, the effective control of HPV spread in a community, using a vaccine, is governed by the threshold quantity $\mathcal{R}_v$ (the use of the vaccine will lead to effective disease control or elimination only if it reduces the threshold quantity to a value less than unity; and the use of such vaccine will not lead to effective disease control if it fails to make the threshold quantity to be less than unity).