Dynamics of human papillomavirus (HPV) incorporating homosexual transmission and HPV-induced cancers

Human papillomavirus is a sexually transmitted disease and the major cause of human cancers such as cervical, vulva, rectal, anal, and penile cancer. These cancers lead to the death of many people annually especially cervical cancer in women. This paper presents a deterministic compartmental model for the transmission of human papillomavirus and its progression to cancer. The disease-free equilibrium, reproduction number, and endemic equilibrium are determined. The disease-free equilibrium is both locally and globally asymptotically stable when the vaccination reproduction number (a control parameter) is less than one. The unique endemic equilibrium exists when the vaccination reproduction number exceeds one and the vaccine’s efficacy is negligible. However, the model undergoes a backward bifurcation when the reproduction number approaches one. The bifurcation clears when the vaccine’s efficacy is negligible. With the negligible vaccine efficacy, the endemic equilibrium is locally stable and globally stable. The model is fitted to real cervical cancer data released from Zambia that agreed with the predicted data. The fitted parameters are used for the numerical simulations. The simulation verified the global stability of the disease-free and endemic equilibrium. The numerical simulation results reveal that: different or same-sex contact leads to fewer infections than both contacts, vaccinating girls alone will slightly reduce the susceptibility of adult women but has no effect on the susceptibility of men, vaccinating only girls has an insignificant impact in reducing the number of women with cervical and other HPV-induced cancers, while vaccinating children and adults of both sex show a significant effect in reducing the cervical cancer cases.