Therapeutic control of HPV associated cervical cancerous cell and its possible extinction
Human papillomavirus (HPV) infection is responsible for a large segment of cervical cancers in women. Over $90\%$ of cervical cancers are caused by high risk HPV infections and its long term exposure can lead to develop Cancer. Complete cure to this epidemiological problem is yet to achieve. We formulate a mathematical model to study the causal effects of the disease and how application of therapeutic drugs can slow down the progression of cancer cell. It is shown from analysis of the deterministic model that using drug complete eradication of the cancer cell is not to be achieved. Thus for the complete cure of the disease, stochastic process plays a crucial role for estimating the expected time to extinction of the cancer cell population in analytical sense. In this context the infected cells, Cancer cells, and Cytotoxic T-Lymphocytes are modelled as individuals in the stochastic system. We have studied an approximation of the cellular densities which is derived in favor of quasi-stationary distribution along with the expected time to extinction of the cancer cells that ultimately leads to cure HPV in the long term process. Numerical simulations shows that our model is capable of capturing the observed experimental results.