On modelling the in-host dynamics of HIV/HPV co-infection in the human population

Mathematical modelling of in-host dynamics has proven to be useful in the control of infectious diseases. An in-host model for the transmission dynamics of the human papillomavirus (HPV) among women living with the human immunodeficiency virus (HIV), incorporating HIV treatment and HPV vaccination is presented. The developed model considers latency and adaptive immune response through cytotoxic T-lymphocytes (CTLs) on the co-infection dynamics. The positivity and boundedness of solutions is proven and the disease-free equilibrium as well as the endemic equilibrium points are computed. The stability of equilibrium points is also proven. The model exhibits three significant reproduction numbers, that is, the basic reproduction number, R₀, the effective reproduction number, R_c and the immune response reproduction number, R_K. The conditions for stability based on the reproduction numbers are stated and numerical simulations performed. The simulations established that although the adaptive immune response is effective in the reduction of HPV, it is not adequate, especially among HIV-positive women. Therefore, HPV vaccination before the onset of sexual activity or among HIV-infected women in addition to proper adherence to HIV treatment is beneficial in reducing HPV in-host.