A SIS model for Human Papillomavirus transmission

Laureen Ribassin-Majed (1) , Rachid Lounes (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Human Papillomavirus (HPV) infections are the primary cause of cervical cancer and its precursor lesions. Two prophylactic vaccines against HPV infections are available. Mathematical models can be used to compare several vaccine strategies. A Susceptible-Infected-Susceptible model of heterosexual transmission of Human Papillomavirus infections is developed. Immunity obtained from vaccination is taken into account. The basic and vaccinated reproduction number are derived using the Next Generation Matrice. We find that if the vaccinated reproduction number is greater than unity, the disease free equilibrium (DFE) is unstable and we prove the existence and uniqueness of endemic equilibrium. If the vaccinated reproduction number is less than unity, there is a locally stable DFE and HPV will be eliminated.

Keywords: reproduction number; HPV; SIS model; equilibrium; stability; reproduction number.

Domains: Infectious diseases; Santé publique et épidémiologie

Laureen Ribassin-Majed, Rachid Lounes. A SIS model for Human Papillomavirus transmission. 2010. ⟨hal-00555733v2⟩