IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 15, Issue 3 Ser. I (May – June 2019), PP 17-29 www.iosrjournals.org DOI: 10.9790/5728-1503011729 www.iosrjournals.org 17 | Page Impact of Chemotherapy treatment on SITR Compartmentalization and Modeling of Human Papilloma Virus (HPV) Eshetu Dadi Gurmu, Purnachandra Rao Koya Department of Mathematics, Wollega University, Nekemte, Ethiopia Corresponding Author: Eshetu Dadi Gurmu Abstract: In this paper, mathematical model of Human Papilloma Virus (HPV) with chemotherapy as treatment is formulated and analyzed. The cancer cells have been divided into four compartments SITR. The well possedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproduction number is derived using next generation matrix method and analyzed the stability of the equilibrium points using Routh Hurwitz criterion. From the analytic and numerical simulation studies it is observed that if the basic reproduction is less than one then the solution converges to the disease free steady state i.e., disease will wipe out and thus the treatment is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the treatment is said to be unsuccessful. Sensitivity analysis of the model is analyzed. Finally, the model formulated in the present study effectively addresses the treatment of Human Papilloma Virus. Keywords: Cervical Cancer, Chemotherapy, Basic Reproduction Number, Stability Analysis, Routh Hurwitz criterion --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 26-04-2019 Date of acceptance: 11-05-2019 --------------------------------------------------------------------------------------------------------------------------------------------------- I. Introduction Cancer is a general name that refers to a group of such diseases in which normal cells divide uncontrollably i.e., grow more rapidly than normal cells and may eventually spread to other parts of the body by a process called metastasis [1]. According to the National Cancer Registry [2] cancer kills more people than HIV/AIDS, malaria and tuberculosis combined. Statistics show that 18.1 million new cases, 9.6 million cancer related deaths, and 43.8 million people living with cancer in 2018. The number of new cases is expected to rise from 18 million to 22 million by 2030 and the number of global cancer deaths is projected to increase by 45% in the period from 2007 to 2030 [3]. The most common types of cancer include: Cervical cancer, Breast cancer, Prostate cancer, Brain cancer, Lung cancer and Skin cancer among others. According to Cervical Cancer Action [4] Report Card 2011, cervical cancer is the most common cancer in women in most developing countries and most common cause of cancer deaths. Human Papilloma Virus (HPV) is the family name of a collection of viruses that include more than 100 different types; more than 30 of these viruses are sexually transmitted. Most of the HPV infections are asymptomatic and can fed away without treatment over the course of only some years. For illustration, about 70% of HPV infections fed away within a year and 90% within two years. However, in some people disease can persist for many years and can cause warts (low risk genotype of HPV), while other types lead to different kinds of cancers (high risk genotype of HPV) including cervical cancer. Although HPV itself cannot be treated, the cellular changes that come from any HPV infection can be treated. For examples, genital warts, cervical, anal, and genital cancers can be treated if the infection is diagnosed during the early stage of development. Pre-cancerous cell changes caused by HPV can be detected by Pap tests and treat individuals who are found already infected. Persistent infection with high-risk types of HPV is the most important risk factor for cervical cancer; the development of cervical cancer is always preceded by infection with one of these viruses [5]. Cervical cancer is a disease of the female reproductive organs, with the burden of it borne disproportionately by women in their perimenopausal (the time when the ovaries stop releasing eggs) years: peak cancer incidence occurs at age 50-54 [6]. Cancer is caused by chemical substances, alcoholic beverages, excessive solar radiation, genetic differences, and so on [7]. Various methods are used to cure or inhibit the growth of cancer. Now-a-days various types of treatments are available such as surgery, radiation therapy, chemotherapy, target therapy, immunotherapy, hormonal therapy, and the latest is a gene therapy. However,