In-Host Dynamics of the Human Papillomavirus (HPV) in the Presence of Immune Response

High-risk human papillomaviruses (HPV) are one of the major causative agents of cervical cancer in women globally, and it is estimated that about 80% of women are infected by HPV mainly due to sexual activities within their lifetime. Out of these infections and reinfections, some develop into persistent infections that lead to cancer lesions, while some can be cleared provided they are detected by the immune system. Immune response within the body plays a pivotal role in clearing most infections that constantly affect us. Interestingly, viruses such as HPV are seemingly very “clever” in concealing their presence within cells as they devise many ways of avoiding detection by the immune system and therefore manage to create an anti-inflammatory micro environment. This leads us to interesting mathematical modelling research of a little “clever immune evading virus.” We create an in host mathematical model for the dynamics of HPV in the presence of immune response, and rigorous mathematical calculations show that there exist equilibrium points ℰ 0 $$\mathcal {E}_0$$ and ℰ 1 e $$\mathcal {E}^e_1$$ whose stability (both local and global) is shown. In this particular work, we present the analysis of the disease-free equilibrium point and the first endemic equilibrium point ℰ 1 e , $$\mathcal {E}^e_1,$$ which is also known as the CTL free equilibrium. Numerical simulations prove and support the theoretical work presented. We also establish that HPV can be eradicated from the body when ℛ 0 1 , ℛ K 1, \mathcal {R}_{K}